COPLANAR STRIPLINE (CPS) COMPONENTS. Previous Page. lower-frequency regions, without affecting the radiation pattern. 3. TRIANGULAR (BOWTIE) ANTENNAS

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1 Previous Page 78 COPLANAR STRIPLINE (CPS) COMPONENTS Directivity gain (dbi) lower-frequency regions, without affecting the radiation pattern. 3. TRIANGULAR (BOWTIE) ANTENNAS A triangular plate antenna above a conducting ground plane and a bowtie antenna are shown in Figs. 1a and 1b. These antennas also possess broadband characteristics, though not as broad as a solid conical antenna. The theoretical characteristics of the bowtie antenna have been obtained numerically [] by using the method of finite-difference time domain (FDTD). Figures 11a and 11b show the calculated input impedance. The input impedance of the triangular plate antenna above the ground plane is half of that of the bowtie antenna. The far-zone electric field patterns in the x y plane and in the x z plane are shown in Figs. 1a and 1b, respectively. Note that the radiation is enhanced in the direction perpendicular to the antenna plate for the antenna length htl, because the radiation from the antenna surface current is added in phase in that direction. The theoretical directivity gain of the bowtie antenna in the direction of the x axis is shown in dbi in Fig. 13 versus the antenna length h/l for various cone angles []. It is noted here that the bowtie antenna can also be simulated by several radial wire rods as the solid biconical antenna. BIBLIOGRAPHY ψ = 15 ψ = 45 ψ = 3 ψ = Length of bowtie antenna h (λ) Figure 13. Directivity gain of a bowtie antenna in x direction (from Ref. ). 1. S. A. Schelkunoff, Principal and complementary waves in antennas, Proc. IRE 34(1):3 3 (1946).. S. A. Schelkunoff, Advanced Antenna Theory, Wiley, New York, P. D. P. Smith, The conical dipole of wide angle, J. Appl. Phys. 19(1):11 3 (1948). 4. C. T. Tai, On the theory of biconical antennas, J. Appl. Phys. 19(1): (1948). 5. C. T. Tai, Application of variational principle to biconical antennas, J. Appl. Phys. (11): (1949). 6. C. H. Papas and R. W. P. King, Radiation from wide-angle conical antennas fed by a coaxial line, Proc. IRE 39(1):49 51 (1951). 7. S. A. Saoudy and M. Hamid, Input admittance of a biconical antenna with wide feed gap, IEEE Trans. Anten. Propag. 38(11): (199). 8. V. Badii, K. Tomiyama, and D. M. Grimes, Biconical transmitting antennas, a numerical analysis, Appl. Comput. Electromagn. Soc. J. 5(1):6 93 (199). 9. J. G. Maloney, G. S. Smith, and W. R. Scott, Jr., Accurate computation of the radiation from simple antennas using the finite-difference time-domain method, IEEE Trans. Anten. Propag. 38(7): (199). 1. G. H. Brown and O. M. Woodward, Jr., Experimentally determined radiation characteristics of conical and triangular antennas, RCA Rev. 13(4):45 45 (195). 11. R. M. Bevensee, Handbook of Conical Antennas and Scatterers, Gordon & Breach, New York, C. Polk, Resonance and supergain effects in small ferromagnetically or dielectrically loaded biconical antennas, IRE Trans. Anten. Propag. 7(special suppl.): (1959). 13. J. R. Wait, Electromagnetic radiation from conical structures, in R. E. Collin and F. J. Zucker, eds., Antenna Theory, McGraw-Hill, New York, S. Adachi, A theoretical analysis of semi-infinite conical antennas, IEEE Trans. Anten. Propag. 8: (l96). 15. C. E. Smith, C. M. Butler, and K. R. Umashanker, Characteristics of a wire biconical antenna, Microwave J. (9):37 4 (1979). 16. O. Givati and A. P. C. Fourie, Analysis of skeletal wire conical antennas, IEEE Trans. Anten. Propag. 44: (1996). 17. S. Adachi, R. G. Kouyoumjian, and R. G. Van Sickle, The finite conical antenna, IEEE Trans. Anten. Propag. 7(special suppl.):s46 S411 (1959). 18. L. L. Bailin and S. Silver, Exterior electromagnetic boundary problem for sphere and cones, IRE Trans. Anten. Propag. 4(1):5 16 (1956); corrections 4(3):313 (1957). 19. A. G. Kandoian, Three new antenna types and their applications, Proc. IRE 7W 75W (1946).. Private communication from Y. He, T. Uno, and S. Adachi, COPLANAR STRIPLINE (CPS) COMPONENTS 1. INTRODUCTION YOUNG-HO SUH Mimix Broadband Inc. Houston, Texas Coplanar stripline (CPS) is an attractive uniplanar transmission line offering flexibility in the design of planar microwave and millimeter-wave circuits, especially in mounting the solid-state device in series or shunt with no via holes. Its balanced structure is useful in applications such as printed dipole antenna feeding, rectennas, uniplanar mixers [1], integrated optic traveling-wave

2 COPLANAR STRIPLINE (CPS) COMPONENTS 781 modulators [], optical control microwave attenuators and modulators [3], and other optoelectric devices [4,5]. CPS characteristics include low loss, small dispersion, small discontinuity parasitics, comparable insensitivity to substrate thickness, and simple implementation of openended or short-ended strips. A few studies regarding CPS components modeling and filter applications have been performed. In 1996, CPS discontinuities such as open and short circuits, series gap, spur slot, and spur strip were investigated [6]. In Ref. 6, each discontinuity was represented as an equivalent lumped element. The CPS open circuit was represented as a shunt capacitor, CPS short circuit was represented as a shunt inductor, and the CPS series gap was represented as a series capacitor. A quarter-wavelength spur slot and spur strip were represented as a series short circuit and a shunt open circuit, respectively. Simons et al. [6] also proposed CPS component measurement method using thru-reflect-line (TRL) calibration with CPS on-water standards for the first time. In 1997, CPS discontinuities and their applications to bandstop [7] and bandpass [8] filters were studied by using the spur-strip and the spurslot resonators. Goverdhanam et al. [7] introduced various CPS components such as a narrow transverse slit, a symmetric step, a right-angle bend, and a tee junction. Fan et al. [9] proposed uniplanar hybrid ring couplers and a branchline hybrid coupler using an asymmetric CPS with 5% and 1% bandwidths, respectively, at a center frequency of 3 GHz in A lumped-element CPS lowpass filter was designed in 1998 [1] using spiral inductors and interdigital capacitors, and a CPS lowpass filter using a transverse slit and a parallel-coupled gap of CPS discontinuities was presented in 1999 [11]. Kim et al. introduced a CPS MEMS phase shifter that could be easily packaged or integrated into the waveguide in 3 [1]. Lumped-element models of CPS circuits and discontinuities were extracted using a full-wave method of moments [13]. A new deembedding technique called a short (circuit)/open(circuit) calibration scheme is applied to calibrate these calculated models for accurate circuit model extraction. Comparably extensive work has been reported in coplanar waveguide (CPW) components such as resonators and filters. Dib et al. investigated CPW discontinuities based on the solution of an appropriate surface integral equation in the space domain in 1991 [14]. In 1998, [15], Hettak et al. reported various types of CPW series resonators and their applications to filters and in 1999 they described CPW shunt stubs printed within the center conductor and implemented miniature filters were with these shunt stubs [16]. However, CPW shunt stub resonator requires additional airbridges or bonding wires, which might increase the fabrication cost and complexity. CPW series resonators require a large conductor area and, the structure of the CPW bandpass filter using CPW series resonators is comparably complex. This article is organized into three major parts: (1) review and investigation of CPS characteristics; () introduction of CPS circuit components such as resonators, filters, and tee junction; and (3) CPS applications to antennas and wireless power transmission. First, a CPS characteristics analysis using a quasi- TEM analytical equation derived by the conformal mapping method is described. The relationship between the characteristic impedance and CPS strip width and gap is analyzed. Transmission-line loss is analyzed as a function of characteristic impedance of CPS. Parameter variations due to change in substrate height are discussed. From the analysis, the design considerations for practical CPS component implementations are discussed. Following a brief analysis of CPS, new types of CPS components and their performances are presented. Six types of CPS resonator are first introduced and their performances are analyzed in terms of Q factor or bandwidth. CPS resonators are realized with open-ended and short-ended strips in various configurations, and lumped-element equivalent circuits for the resonators are presented. The appropriate circuit configuration for high Q factor is analyzed. The relationship between CPS characteristic impedance and CPS attenuation is briefly discussed for high Q factor. Two new classes of CPS bandpass filter are presented using the resonators discussed here for narrow- and wideband applications, and their lumped-element equivalent circuits are presented. A novel, simple CPS lowpass filter is presented using a CPS line loaded with interdigital capacitors. The lowpass filter is easily reproducible using a prototype of the desired filter type with the selected cutoff frequency. A new method of microstrip-fed CPS tee junction is introduced without using bonding wires or via holes. For the tee junction, novel coupled CPS (CCPS) is presented and its performance is discussed. Tee-junction applications are demonstrated in a twin-dipole antenna and a dipole phased array with detailed illustrations and photographs. Microstrip-to-CPS transition for CPS component measurements is briefly discussed. The transition presented in this article enables convenient CPS components measurement with a conventional network analyzer using the common short (circuit)/open (circuit) load-thru (SOLT) calibration method. All the CPS components presented in this article is fabricated on the RT/Duroid 587 substrate with 1 oz copper cladding, mil substrate height, and the dielectric constant of.33.. CPS CHARACTERISTICS ANALYSIS FOR THE DESIGN CONSIDERATION The structure of CPS on a finite substrate is illustrated in Fig. 1. Analytical techniques for calculating the characteristic impedance, the effective dielectric constant, and dielectric and conductor losses of the CPS are described in Refs Closed-form quasi-tem parameters for the symmetric coplanar stripline on finite substrate thickness are necessary for practical purposes, which is extensively discussed in Ref. a. Loss mechanisms considered in this article are conductor (a c ) and dielectric (a d ) losses.

3 78 COPLANAR STRIPLINE (CPS) COMPONENTS Electric field lines Magnetic field lines W s t h ε r Figure 1. Coplanar stripline (CPS) structure (from Ref. b with permission from IEEE). Dielectric loss (a d ) is independent of the geometry of the line and can be expressed as follows: a d ¼ 7:3 e r p e re 1 ffiffiffiffiffi e r 1 e re tan d l ðdb=unit lengthþ ð1þ Effective dielectric constant (e re ) is represented as e re ¼ 1 þ e r 1 K ðk 1 Þ Kðk 1 Þ Kðk Þ K ðk Þ ðf=unit lengthþ where e r is the dielectric constant and K(K), K (K) are the complete elliptic integrals of the first kind and its complement, respectively. k 1 and k are expressed as k 1 ¼ s s þ W ¼ a b k ¼ sinhðpa=hþ sinhðpb=hþ where h represents substrate thickness, s is the gap between the CPS strips, and W is the width of the CPS strip. K(k) can be found with series expansion approximation as for rkr.77 ( KðkÞ¼ p 1 þ k 8 þ 9 k 8 and for.77rkr1 þ 5 k 8 ðþ ð3þ ð4þ 3 4 ) ð5þ þ 36:5 k þ 8 k KðkÞ¼pþðp 1Þ 4 þ 9 p 7 k þ 5 p 37 k 6 þ 3 56 ð6þ where p ¼ ln 4 k p k ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 k K (k) can be obtained from K (k) ¼ K(k ) and applied to series expansions. The conductor loss (a c ) of a CPS expression is given as pffiffiffiffiffi 8:68R s e re a c ¼ 48pKðk 1 ÞK ðk 1 Þð1 k 1 Þ 1 a p þ ln 8pað1 k 1Þ tð1 þ k 1 Þ þ 1 8pb 1 k 1 p þ ln ðdb=unit lengthþ b t 1 þ k 1 a, b, and k 1 are as defined in (3). K(K) and K (K) can be obtained from (5) (8) with the property of K (K) ¼ K(K ). t is the strip thickness and R s is the surface resistance, defined as rffiffiffiffiffiffiffiffi om R s ¼ ðoþ s ð7þ ð8þ ð9þ ð1þ where s is the metallic strip conductivity. These equations assume strip thickness t43d, t5a, and t5(b a), where d is skin depth, expressed as sffiffiffiffiffiffiffiffiffi d ¼ ðunit lengthþ oms ð11þ Total attenuation, including dielectric and conductor losses at 1 GHz, is plotted in Fig. with a fixed strip width (W ¼ 1.5 mm) and separation between the strips (s) increased from.1 to mm. It is observed that the wider is the separation (s), the lower the total attenuation (a c þ a d ) and the higher the characteristic impedance (Z ) are achieved. In other words, the higher the characteristic impedance of CPS, the lower the transmission-line

4 COPLANAR STRIPLINE (CPS) COMPONENTS 783 Attenuation (db/mm) S (mm) Figure. Total attenuation (a c þ a d ) of a CPS as a function of gap separation (s) at 1 GHz. The strip width (W) is fixed at 1.5 mm. A -mil-height,.33 dielectric constant, and 1-oz copper cladding substrate was used (from Ref. b with permission from IEEE). attenuation that can be achieved. In the relationship between the dielectric constant of the substrate and the total attenuation, the higher is the dielectric constant, the higher is the total attenuation. For a practical design, moderate characteristic impedance with a proper dielectric constant substrate is used for low attenuation. Hence, Fig. is useful for selecting CPS component design parameters. 3. CPS RESONATORS Open-Ended T-Strip Resonators Two types (A and B) of open-ended T-strip resonator are presented in this section. The structure of resonator type A and its lumped-element equivalent circuit are illustrated in Fig. 3. Resonator type A consists of open-ended T strips with.5 mm width and around l g / (.4 l g ) or 5.4 mm length, placed outside the strips designed to operate at a center frequency of B4.8 GHz. As shown in.5 mm (gap 1 ) s L 1 C mm C' L' Figure 3. CPS resonator using open-ended T strips and its lumped-element equivalent circuit (type A) (from Ref. b with permission from IEEE). L C Characteristic impedance (Ohm) W Table 1. Simulated Loaded Q (Q L ) and Unloaded Q (Q U )of Resonator Type A (from Ref. b with permission from IEEE) Gap 1 (mm) s (mm) Q L Q U Fig. 3, the CPS transmission line is represented as lumped-element LC circuits. The T strips become inductor, and gap 1 induces coupling capacitance due to the coupling with CPS strips. Hence, T strips can be represented as a shunt series resonator (L C circuit), which exhibits bandstop behavior. The narrower is the gap 1, the higher is the loaded Q (Q L ) value, due to the strong coupling and the low loss at gap 1. As discussed in Section, CPS transmission-line attenuation is reduced when the CPS strip separation (s) widens, as shown in Fig.. Accordingly, the narrower the gap 1, and greater the s will increase the loaded Q(Q L ). Computed loaded (Q L ) and unloaded Q(Q U ) values are displayed in Table 1 with various gap 1 and s values. The computation was performed using a commercial full-wave electromagnetic simulator, which uses the method of moments. Table 1 shows that the narrow gap 1 and the wide s configuration provide a high Q L value, and Q U values are similar in every configuration. Q U calculation of the bandstop resonator [1] is expressed as Q L Q U ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 1 L= Þ Where Q L is the loaded Q, expressed as Q L ¼ f Df 3dB ð1þ ð13þ f, Df 3dB, and L represent the center frequency, the 3 db insertion loss bandwidth, and the insertion loss at the center frequency, respectively. Measured and simulated frequency responses of this type of resonator with.6 mm of s and.5 mm of gap 1 are shown in Fig. 4. A measured Q L of 97.7 is achieved with a resonance frequency of 4.8 GHz with a 3 db insertion loss bandwidth of 44 MHz. Q U of is obtained from (1) with the insertion loss (L) of 7.53 db at the center frequency. Measured Q values agree with simulated result (Q L ¼ 11.9 and Q U ¼ 1.5) displayed in Table 1. Resonator type B consists of open-ended T strips placed inside the CPS transmission line. The structure of resonator type B and lumped-element equivalent circuit are shown in Fig. 5. Gap, gap 3, and the open-ended T-strip width are all.5 mm. To place the open-ended T strips between the narrowly spaced CPS strips, the transmission-line gap s is widened from.6 to.5 mm, which corresponds to the

5 784 COPLANAR STRIPLINE (CPS) COMPONENTS S11 and S1 (db) S11 S Frequency (GHz) Measured Simulated Figure 4. Simulated and measured frequency responses for open-ended T-strip resonator (type A) with gap 1.5 mm and s.6 mm (from Ref. b with permission from IEEE). impedance value increase from 184 to 5 O. Despite this increase in impedance, little insertion loss deterioration occurs and the return loss response is better than 1 db. The open-ended T-strip length is around l g / (.39l g )or 5.4 mm at the center frequency of near 4. GHz. This type of resonator, similar to type A, has also coupling capacitance at gap, and additional capacitance takes place at gap 3. Table describes the simulated Q values of resonator type B with various gap and gap 3 values. The gap 3 value corresponds to s value, which is the CPS separation between two strips. The narrower the gap and the wider the s, the higher the Q L values, due to the stronger coupling capacitance and, accordingly, the lower transmission-line attenuation, as shown in Fig. from CPS analysis in Section. It can be concluded that the higher characteristic impedance corresponds to the higher Q L values for CPS resonators as shown in Tables 1 and and Fig.. Simulated and measured frequency responses of the type B resonator are shown in Fig. 6. Measured Q L and Q U values of resonator type B, with.5 mm of gap and gap 3,.5 mm (gap ).5 mm (gap 3 ) s L 1 C mm C' L' Figure 5. CPS resonator using open-ended T strips and lumpedelement equivalent circuit (type B) (from Ref. b with permission from IEEE). L C W Table. Simulated Loaded Q (Q L ) and Unloaded Q (Q U )of Resonator Type B (from Ref. b with permission from IEEE) Gap (mm) Gap 3 (mm) Q L Q U are 98.4 and 98.9, respectively. The 3 db insertion loss bandwidth is 41 MHz, and the insertion loss (L) is 3. db at the center frequency. The simulated Q L and Q U values are 11.5 and 11.7, respectively, as given in Table. 3.. T-Slot Resonator A T-slot resonator (type C) can be considered as a complementary structure of the type A resonator. Its structure is illustrated in Fig. 7. Similar to the spur-slot resonator in Ref. 7, a T slot can be considered as series short-ended stubs or shunt open-ended stubs where each arm measures a quarter-wavelength. The frequency response of this resonator exhibits bandstop behavior and the lumped-element equivalent circuit is represented as a shunt series resonator (L C circuit). The length of the T slot is about l g / (.47l g ) or 5.4 mm at a center frequency of B4.78 GHz. The width of the T slot (gap 4 ) is.5 mm, and s and W are.6 and 1.5 mm, respectively. It is found that the T-slot resonator has a Q L value much higher than that of open-ended T-strip resonators, mainly because the T-slot resonator s metallic area is much smaller than that of the T-strip resonator due to and thus the radiation loss of the former is much less. Simulated Q L and its corresponding Q U are described in Table 3. Loaded Q (Q L ) of the T-slot resonator is B6.93 with gap 4.5 mm and s.6 mm, while open-ended T-strip resonators such as types A and B have Q L o15. The T-slot resonator is also found to be less sensitive to gap 4 and s than is the open-ended T-strip resonator. Similar to the case of two T-strip resonators, the value of Q L increases when gap 4 is reduced and s is increased. This is due to the higher coupling at gap 4 and lower attenuation when s is increased. Wider s corresponds to higher characteristic impedance with fixed W for CPS as discussed in Section. While the relationship between the characteristic impedance and the value of Q L follows the results of T-strip resonators, values of Q L are not very sensitive to gap 4 and s or the characteristic impedances. This implies that the resonance energy is stored more effectively with the slot configuration than with the strip one. It can be concluded that the higher characteristic impedance corresponds to the higher Q L values for CPS resonators from the results of T-strip and T-slot resonators, and that the T-slot resonator has better performance in

6 COPLANAR STRIPLINE (CPS) COMPONENTS S11 S11 and S1 (db) S1 Measured 3 Simulated Frequency (GHz) Figure 6. Simulated and measured frequency responses for open-ended T-strip resonator (type B) with gap and gap 3.5 mm and s.6 mm (from Ref. b with permission from IEEE). terms of the Q factors but insensitive to the characteristic impedance (see Tables 1 3 and Fig. ). Type C resonator simulated and measured frequency responses are shown in Fig. 8. Measured Q L and its corresponding Q U values of resonator type C, with.6 mm of s and.5 mm of gap 4 are 44. and 45.7, respectively. The 3 db insertion loss bandwidth is 41 MHz, and the insertion loss (L) is 43.7 db at the center frequency. These Q valuesarealsoclosetosimulatedresults(q L ¼6.93 and Q U ¼ 63.37) given in Table 3. s 5.6 mm Gap 4 (.5 mm) W 3.3. Square-Ring-Shape Open-Ended Strip Resonator The square-ring-shape open-ended strip resonator (type D) has two open-ended strips located outside the strips, similar to type A. These open-ended strips are bent to have square forms. The structure of square-ring-shape openended strip resonator is shown in Fig. 9. The length of the open-ended strip is about.3l g (15.5 mm) at a center frequency of B5.8 GHz. This resonator has a shorter coupling arm (4.65 mm) than do types A and B. Therefore, open-ended strips have loose coupling and induce high losses. Two open-ended strips are purposely located asymmetrically to prevent any possible radiation as does the dipole antenna. The asymmetric structure induces a spurious response around 6.1 GHz. Measured and simulated return and insertion losses of this resonator are illustrated in Fig. 1. Measured Q L and Q U of this resonator are 3.51 and 3.87, respectively. The 3 db insertion loss bandwidth is 16 MHz and the insertion loss (L) is 18.3 db at the center frequency. Simulated Q L and Q U are 38.1 and 38.51, respectively. Compared to resonators A and B, which consist of openended T strips, the type D resonator is compact but its Q L is low. Hence, this resonator would be useful for applications requiring spatial efficiency with moderate bandstop purpose Short-Ended Strip Resonators One merit of the uniplanar transmission line is the convenient implementation of the short-ended strips with no via holes. Two types of short-ended strip resonator (types E and F) are introduced and investigated. Resonator type E utilizes a short-ended strip, in contrast to resonator types A, B, and D as illustrated in Fig. 11. The total length of the short-ended strip is about.44l g (13.7 mm), which is around l g /, with.5 mm width at a center frequency of B8 GHz. The transmission line is widened, similar to that of resonator type B, when the shortended strip is placed between the CPS strips but little insertion loss deterioration occurs and return loss is 41 db. The short-ended strip becomes an inductor and gap 4 induces coupling capacitance due to coupling with CPS strips. This short-ended strip and gap 4 consist of a L 1 L Table 3. Simulated Loaded Q (Q L ) and Unloaded Q (Q U )of Resonator Type C C 1 C' L' Figure 7. CPS resonator using T slots and its lumped-element equivalent circuit (type C). C Gap 4 (mm) s (mm) Q L Q U

7 786 COPLANAR STRIPLINE (CPS) COMPONENTS S11 and S1 (db) S1 S11 s 4.65 mm.5 mm W 5 Measured Simulated Frequency (GHz) L 1 L Figure 8. Simulated and measured frequency responses for a T-slot resonator (type C). C 1 L' C C' Figure 9. Square-ring-shape open-ended strip CPS resonator and its lumped-element equivalent circuit (type D) (from Ref. b with permission from IEEE). shunt parallel resonator (L C circuit), which acts as bandpass behavior. Measured and simulated frequency responses of this resonator are illustrated in detail in Fig. 1. A measured insertion loss of.1 db is achieved at a center frequency of 8.1 GHz. This type of resonator can be utilized for bandpass filter applications. The measured bandwidth of o3 db insertion loss and 41 db return loss is around 3 GHz (36.94%) with resonator type E. For resonator type F, two short-ended strips are attached together in a closed polygon configuration as shown in Fig. 13. Similar to the type E resonator, coupling capacitance at gap 5 and the short-ended strip inductance consist in a shunt parallel resonator (L C circuit), which exhibits bandstop behavior. The total length of the shortended strip is about 1.1l g (48.1 mm) at a center frequency of B5.4 GHz. The transmission-line gap s is widened similar to that of resonator types B and E. Frequency responses of this resonator are illustrated in Fig. 14. The measured bandwidth of o3 db insertion loss and 41 db return loss is B.84 GHz (15.67%). A measured insertion loss of.5 db was achieved at a center frequency of 5.36 GHz. The bandwidth of resonator type F is almost half that of resonator type E, which is due to the cascading of two identical resonators. Six different types of resonator are presented, and their performances are analyzed. As discussed, the T-slot resonator (type C) has the highest Q L among four different bandstop resonators and resonator type E has the widest passband bandwidth between the two different short-ended strip resonators. As shown in Tables 1 3 and Fig., CPS resonators can have high Q L when high characteristic impedance and strong coupling capacitance are employed. Many variations and combinations of these six resonators are possible. Therefore, these resonators would be very useful for designing CPS filters. 5 S11 S11 and S1 (db) 1 15 Figure 1. Simulated and measured frequency responses for square-ring-shape resonator (type D) (from Ref. b with permission from IEEE). S1 Measured Simulated Frequency (GHz)

8 COPLANAR STRIPLINE (CPS) COMPONENTS 787 s.5 mm (gap 4 ) 6.1 mm.5 mm W.5 mm (gap 5 ) s 3.3 mm.5 mm W L 1 L L 1 L C 1 L" C" C C 1 L" C" C Figure 11. Short-ended strip CPS resonator and its lumped-element equivalent circuit (type E) (from Ref. b with permission from IEEE). 4. CPS FILTERS This section describes two new classes of CPS bandpass filter that utilize combinations of the resonators presented in Section 3. Design methods for CPS bandpass filters are presented and discussed. These bandpass filters have good passband insertion loss and wide stopband suppressions. The simple CPS lowpass filter design method is also discussed with practical circuit implementation Bandpass Filter Realization Using Multiple Short-Ended Strips This type of bandpass filter uses type E resonators presented in Section 3. The structure and the lumped-element equivalent circuit of this filter are shown in Fig. 15. A transmission line with periodically loaded reactive cells has the characteristic of filters. One reactive cell can be formed with resonator type E, which exhibits bandstop behavior. The total length of the unit cell is around l g / (.41l g ) or 1.5 mm at a center frequency of 8 GHz. The spacing between neighboring cells is one of the most important factors for bandpass filter design in periodic structures. Figure 13. Closed polygon short-ended strip CPS resonator and its lumped-element equivalent circuit (type F) (from Ref. b with permission from IEEE). Because of the structural dimension of the unit cell, uniform spacing between unit cells is impossible. Hence, two neighboring cells are grouped as a subcell. This bandpass filter, correspondingly, has two subcells. The interunit-cell spacing within the subcell is optimal at mm; spacing under mm manifests loose band rejection at stopbands, while spacing exceeding mm between exhibits sharper out-of-band rejection but shows unsatisfactory return loss at passband. A distance between subcells is about l g / (.46l g ) or 14 mm to ensure a good rejection at stopbands similar to conventional periodic structure. As shown in Fig. 15, CPS transmission-line sections are represented as the lumped-element LC circuits. The short-ended strip consists a shunt parallel resonator (L C circuits), discussed in Section 3 for resonator type E. The transmission-line gap s is widened in the same way as in resonator types B, E, and F. For designing CPS components, transmission-line inductance and capacitance values play important roles and should be considered for CPS components modeling. Values of the capacitance and the inductance of CPS strips can be accurately extracted by the method of moments using commercial full-wave electromagnetic software. Simulated and measured frequency responses of this filter are illustrated in Fig. 16. Measured insertion loss of.48 db is achieved at a center frequency of 8.4 GHz. A S11 and S1 (db) S 11 S 1 Measured Simulated Frequency (GHz) Figure 1. Simulated and measured frequency responses for short-ended strip resonator (type E) (from Ref. b with permission from IEEE).

9 788 COPLANAR STRIPLINE (CPS) COMPONENTS 5 S1 Figure 14. Simulated and measured frequency responses for closed polygon short-ended strip (type F) (from Ref. b with permission from IEEE). S11 and S1 (db) S11 Measured 3 Simulated Frequency (GHz) wide bandwidth of 4.16 GHz (5%) is achieved with less than 3 db insertion loss and better than 1 db return loss, and the 1 db insertion loss bandwidth ranges from 6.9 to 9.8 GHz. Stopbands range from to 5.38 GHz in a lower stopband area and from 11.1 to GHz in a higher stopband area. 4.. Bandpass Filter Using Short-Ended Strips with T Strips Figure 17 illustrates the bandpass filter structure using short-ended strips with T strips and shows its lumped-element equivalent circuit. This type of filter consists of types A and F resonators and interdigital capacitors. Closed polygon short-ended strips (type F resonators) are represented as shunt parallel resonators (L C circuits) and T-strips (type A resonators) are represented as a shunt series resonator (L C circuit). An interdigital capacitor (C) is placed inside each type E resonator to provide higher capacitance. The interdigital capacitor is widely used as the microwave circuit s lumped-element component possessing tight coupling. The capacitance of the interdigital capacitor is expressed as e r þ 1 KðkÞ C ¼ e Kðk Þ NlðFÞ ð14þ where K(K) is the complete elliptic integral of the first kind, which is expressed in (5) (8). k is defined as k ¼ sin pw ð15þ d where W is the width of the interdigital capacitor s finger and d is the distance between fingers; k is as defined in (8). A B C D E F G H I J 5.5 mm 1.5 mm mm.5 mm L 1 L L 3 L 4 L 5 C 1 L" C 1 L" C 3 L" C 4 3 L" 4 C" 1 C" C" 3 C" 4 C 5 A B C D E Figure 15. Bandpass filter structure using multiple short-ended strips and its lumped-element equivalent circuit (from Ref. b with permission from IEEE). F G H I J

10 COPLANAR STRIPLINE (CPS) COMPONENTS S11 (db) Simulated Measured Frequency (GHz) (a) 1 S1 (db) Simulated Measured Frequency (GHz) (b) Figure 16. Simulated and measured frequency responses of a bandpass filter using multiple short-ended strips: (a) return loss; (b) insertion loss (from Ref. b with permission from IEEE). The number and length of the interdigital capacitor fingers are N ¼ 3 and l ¼ mm, respectively. All the interdigital capacitor gap distances are uniformly.5 mm, with a capacitance C of B.31 pf from full-wave electromagnetic simulation using the method of moments. Most of the capacitance takes place at the edges of the fingers. Hence, the gap distance between the fingers together with the number of fingers is important factor in determining the capacitance value. The width of the short-ended strip is.5 mm and the length is.79 l g or 41.5 mm. The capacitance (C ) and inductance (L ) values of the short-ended strip are about.563 pf/mm and.763 nh/mm at 5 GHz, which can be found by simulation. The inductance (L ) and total capacitance, including interdigital capacitance (C T ¼ C þ C ), can be found by the following equations L ¼ :463 lðnhþ C T ¼ :31 þ :563 lðpfþ ð16þ ð17þ where l is the total length of the short-ended strip in millimeters. With (16) and (17), the approximate dimensions of the short-ended strip can be found at the desired frequency. Two unit cells are cascaded with a distance of Bl g /4 (.8l g ) or 13.6 mm. A type A resonator (L C circuit) is combined with this filter to enhance the suppression at the lower stopband with a length of 9.1 mm (.48l g ) at a center frequency of B4 GHz. This is a good example an advantage of the uniplanar transmission line, namely, open-ended and short-ended strips together without any via holes. Measured and simulated frequency responses are given in Fig. 18, showing good agreement between measured and simulated data. The measured bandwidth of o1 db insertion loss and 41 db return loss ranges from 4.8 to 5 GHz (3.64%). Stopbands with the suppression of less than db range from 3.56 to 3.98 GHz (.4 GHz) at the lower band and from 5.48 to 6.8 GHz (.6 GHz) at higher band. The low insertion loss of.61 db was measured at a center frequency of 4.94 GHz. Two types of bandpass filters are designed for wideband and narrowband applications using proposed resonators. Bandpass filters show low passband insertion loss and

11 79 COPLANAR STRIPLINE (CPS) COMPONENTS A B C DE F G H 9.1 mm.5 mm L 1 L L 3 L 4 L' C 1 L" 1 C C" 1 C C 3 L" C C" C 4 C' A B C D E F G H Figure 17. Structure of a bandpass filter using short-ended strips with T strips and its lumpedelement equivalent circuit (from Ref. b with permission from IEEE). good stopband suppression. These filters would be useful for uniplanar circuit implementations CPS Lowpass Filter Few CPS lowpass filters have been reported. CPS lowpass filters are very useful in rectenna circuits [15 a]. CPS lowpass filter design examples have been reported [5,6] with complex structures, the design methods are not clear. In this section, a novel lowpass filter with the lumpedelement equivalent circuit is presented. The design method for the desired filter type is described. A simple. db equal-ripple Chebyshev CPS lowpass filter is designed with a cutoff frequency of 7.4 GHz. The structure of the lowpass filter is illustrated in Fig. 19. For designing the lowpass filter with the chosen specification, a ladder circuit and its element definitions should be first performed. Tabulated element values of the ladder circuit can be easily found in Ref. 8. With those element values, a prototype of the lowpass filter can be designed. After proper scaling in terms of impedance and frequency, lumped-element values of the lowpass filter can be found. As shown in Fig. 19, capacitance is realized with the interdigital capacitor, and inductance is realized with the CPS transmission line itself. Capacitance of the interdigital capacitors can be found by simulation or in (14). As mentioned earlier, the CPS transmission line has its own inductance and capacitance, and those values should be considered for designing CPS components. This design demonstrates how the CPS line inherent inductance can be utilized in the design of the CPS components. At the design frequency, the capacitance and inductance of CPS per unit length can be found using a commercial simulator. For inserting interdigital capacitors inside the narrowly spaced CPS strips, the CPS strip gap s is widened in the same way as in CPS resonator types B, E, and F, but little insertion loss deterioration occurs and return loss is better than 1 db. Simulated and measured frequency responses of the CPS lowpass filter are shown in Fig.. Measured data show sharp suppression after the cutoff frequency of 7.4 GHz and suppression better than db up to 13.8 GHz. A low passband insertion loss of.7 db is achieved at passband. Measured and simulated data show good agreement. With this configuration, any kinds of CPS filters can be easily synthesized with desired specifications.

12 COPLANAR STRIPLINE (CPS) COMPONENTS S11 (db) Simulated Measured Frequency (GHz) (a) 6. 1 S1 (db) Simulated Measured Frequency (GHz) (b) Figure 18. Simulated and measured frequency responses of a bandpass filter using shortended strips with T strips: (a) return loss; (b) insertion loss. 5. MICROSTRIP-FED CPS TEE JUNCTION Little work has been reported for CPS tee junctions. A CPS tee junction was introduced in 1997 [7], and a coplanar waveguide (CPW)-fed CPS tee junction was developed for the twin-dipole antenna feeding [9a]. Both methods require bonding wires. In this section, a new microstrip fed CPS tee junction using a coupled CPS (CCPS) is introduced. Because of the inherent CPS structure as shown in Fig. 1a, it is almost impossible to build a CPS tee junction without having a discontinuity in the CPS structure. With the aid of the CCPS structure, which uses the coupling method, a physical discontinuity is introduced to the CPS structure while fields are continuous over the entire transmission line. Bonding wire is not required for constructing the CPS tee junction. The structure of the coupled CPS is illustrated in Fig. 1b. One of the CPS strips is discontinued and is terminated with radial stubs with a rotation angle of 31 and a radius of 1.5 mm for coupling to the bottom-layer metallization. The bottom-layer metallization, which is coupled from the top layer s radial stubs, functions as a CPS strip as shown in Fig.. The radial stub is used to accomplish a smooth field transition. Figure compares metallization at different layers of the CPS with those of the conventional CPS shown in Fig. 1. A little insertion and return loss deterioration takes place because electric fields of the CCPS are not exactly normal to the strips. Measured CCPS frequency responses are shown in Fig. 3, and its performance is compared with that of conventional CPS. Figure 3 also shows that the insertion loss of CCPS is around.5 db deterioration compared with that of conventional CPS at GHz and that the return loss is 41 db. Insertion loss deterioration of o1 db covers a wider frequency range, from 1.7 to 13.3 GHz. The tee-junction configuration is illustrated in Fig. 4. Characteristic impedance of the CCPS is 184 O, and the microstrip feedline has an input impedance of 5 O. A quarter-wavelength transformer was used to transform the microstrip s impedance from 5 O to 9 O. Part of the microstrip feedline s ground plane forms the coupled CPS (CCPS). The measured and simulated frequency responses of the tee junction are shown in Fig. 5. An ideal lossless tee junction equally splits the power between each output port with S 1 ¼ S 31 ¼ 3 db. The measurements in Fig. 5 show an insertion loss of.7 db and a return loss of

13 79 COPLANAR STRIPLINE (CPS) COMPONENTS A B C D E F G H s W L 1 L L 3 L 4 C 1 C C 3 C 4 C 5 Figure 19. CPS lowpass filter and its lumpedelement equivalent circuit. A B C D E F G H 41 db at 4.15 GHz. It is expected that wider bandwidth can be achieved if a binomial or Chebyshev transformer is used instead of a quarter-wavelength transformer at the microstrip feeding. Measured phases are almost identical at each output port as shown in Fig CPS TRANSITION For CPS component measurements, transition to other transmission lines, which enables convenient measurement with the conventional network analyzer, is required. CPS-to-CPW, CPS-to-slotline, and CPS to-microstrip transitions have been reported. In 1993 Ho et al. [3] developed a CPS-to-CPW transition. This transition included CPW-to-slotline transition as an intermediate transition. The measured frequency responses of the CPW-to-CPS-to-CPW back-to-back transition showed less than 1 db insertion loss from 1.6 to 7 GHz (1 4.3), and the return loss was better than 13 db. Simons [31] developed a CPS-to-slotline transition with a bandwidth of 3% at 9.5 GHz in The measured insertion loss was 1.5 db for the frequency range from 8 to 11. GHz (1 1.4) and a return loss of 41 db. 1 S 1 S 11 S11 and S1 (db) 3 4 S 11 S 1 5 Simulated Measured Figure. Simulated and measured frequency responses of CPS lowpass filter Frequency (GHz)

14 COPLANAR STRIPLINE (CPS) COMPONENTS 793 Electric field lines (a) A Top layer metallization Bottom layer metallization h t ε r W s Magnetic field lines A' (b) 3 Figure. Cross-sectional view at A A with field distributions of CCPS for different layers of metallization (from Ref. 9b with permission from IEEE). Radial stub CPS strip Figure 1. Coupled CPS (CCPS) structure: (a) conventional CPS; (b) CCPS (from Ref. 9b with permission from IEEE). In 1994, Tilley et al. [3] presented a wideband CPWto-CPS-to-CPW transition with 1 db back-to-back insertion loss from.45 to 5 GHz (1 11). In 1995, Li et al. [33] proposed a CPW-to-CPS-to-CPW back-to-back transition with the bandwidth ranging from.4 to 3.6 GHz (1 9) using Chebyshev multisection impedance transformers in the CPW transmission line. In, Mao et al. [34] demonstrated a CPS-to-CPW transition operating up to GHz with an insertion loss of o.5 db and a return loss of 41 db. Various methods of designing CPS-to-microstrip transitions have been reported. In 1995, Dib et al. [35] reported a type of uniplanar transitions based on the concept of mode conversion with a 3 db back-to-back insertion loss bandwidth from 7 to 11.5 GHz (1 1.6) for the CPS-to-microstrip transition. In 1997, Qian and Itoh [36] improved the performance with a 3 db back-to-back insertion loss bandwidth from 6 to 13 GHz (1.1) by employing symmetric tee junction for the structure reported by Dib et al. [35]. Simons et al. [37] also proposed a CPS-to-microstrip transition using a coupling method with a.4 db back-toback insertion loss bandwidth from 5.1 to 6.1 GHz (1 1.). However, this design used a CPS-to-microstrip-to-CPS back-to-back structure and required special CPS TRL (thru-reflect-line) on-wafer calibration standards with a National Institute of Standards and Technology (NIST) deembedding software program for a network analyzer calibration [37 39a]. Most of these CPS-to-microstrip transitions used high-dielectric-constant substrate (e r 41) to reduce the CPS characteristic impedance [8 3]. This section introduces two types of broadband CPS-tomicrostrip transitions. One operates from 1.3 to 13.3 GHz (1 1.) with an insertion loss of o3 db and a return loss of 41 db for a back-to-back transition, and the other operates from to GHz (1 1) with an insertion loss of o3.5 db and a return loss of 41 db. Both have simple structures and can be easily fabricated using a low-dielectric-constant substrate (e r ¼.33). Microstrip-to-CPS-tomicrostrip back-to-back structures have been fabricated, which is convenient for CPS component measurement with a conventional network analyzer Transition with a Radial Stub Radius of 5.5 mm and its Performance The structure of a back-to-back microstrip-to-cps-tomicrostrip transition is illustrated in Fig. 7. RT/Duroid 587 is used as the substrate with a dielectric constant of.33 and a thickness of mil. The gap s and strip width W of the CPS are.6 and 1.5 mm, respectively. The CPS characteristic impedance is 184 O, as was simulated with a commercial full-wave electromagnetic simulator, which uses the method of moments. As shown in Fig. 1, electric field lines of CPS are directed from one strip conductor to the other on a layer. Electric field lines for microstrip are directed from top layer conductor to bottom layer ground-plane metallization. The radial stub is used to accomplish the rotation of the electric field lines and is rotated with an angle of f to change electric field orientation from parallel to vertical 1 S 1 S 11 S11 and S1 (db) Conventional CPS Coupled CPS Frequency (GHz) Figure 3. Frequency responses comparison between CPS and CCPS (from Ref. 9b with permission from IEEE).

15 794 COPLANAR STRIPLINE (CPS) COMPONENTS Port s W Port 3 Top layer metallization Bottom layer metallization Port 1 Figure 4. Structure of microstrip-fed CPS tee junction (from Ref. 9b with permission from IEEE). against the substrate. The rotation angle f is optimized at 31 for good coupling. A broadband coupling can be accomplished by terminating one of the CPS strips with the radial stub as shown in Fig. 7. The radius and the rotation angle (f) were optimized at 5.5 mm and 31, respectively. The width of microstrip line was optimized at 1.3 mm for 5 O matching. Length of the microstrip line is chosen as 4 mm. For the impedance transformation from the high characteristic impedance of CPS (184 O) to the microstrip line s impedance (5 O), smooth insertion of the ground plane toward the microstrip line is important with the proper microstrip line width. Since this method does not employ any quarterwavelength transformer, which would limit the bandwidth as seen in other methods [8,9a], broadband performance is achieved. The radial stub length determines the highest operating frequency of the transition. This is because the radial stub creates a virtual short circuit to the bottom metallization with a quarter-wavelength, which is a ground plane of the transition. The shorter is the radial stub, the higher is the operating frequency. Therefore, factors such as radial stub length, rotation angle (f), and length of microstrip determine performance of the transition. The measured return and insertion loss of back-to-back transition, excluding the SMA (end launch assembly) connector loss, are illustrated in Fig. 8. The measured o3 db insertion loss bandwidth of backto-back transition is from 1.3 to 13.3 GHz (1 1.) with a return loss of better than 1 db. The o1 db insertion loss bandwidth for the back-to-back transition is from 1.4 to 7.3 GHz (1 5.). For an insertion loss of less than.5 db for the back-to-back transition, the bandwidth ranges from 1.5 to 6 GHz (1 4) with a return loss of 41 db. The transition can be modified to operate at higher frequencies with shorter-radius radial stubs. Shorter-radius radial stubs enable higher frequency coupling between top Figure 5. Frequency responses of tee junction: (a) simulated; (b) measured (from Ref. 9b with permission from IEEE). Magnitude (db) Magnitude (db) S11 4 S1 45 S Frequency (GHz) (a) Frequency (GHz) (b) S11 S1 S31

16 COPLANAR STRIPLINE (CPS) COMPONENTS Phase (degrees) Phase(S1) Phase(S31) Frequency (GHz) (a) Phase (degrees) Phase(S1) Phase(S31) Frequency (GHz) (b) Figure 6. Phase responses of tee junction: (a) simulated; (b) measured (from Ref. 9b with permission from IEEE). and bottom metallization, but because of the smaller coupling area of the stub, insertion loss is increased. The transition with the radial stub radius of.5 mm has been designed and tested. The geometry of transition with a radial stub radius of.5 mm is illustrated Fig. 9. Frequency responses of the transition are shown in Fig. 3. Measured back-to-back return loss is better than 1 db from to GHz (1 1) with an insertion loss of o3.5 db. Although the insertion loss is higher in the smaller radial stub structure than in the larger radial stub transition, the transition would be useful in feeding high-frequency dipole type antennas. These transitions are convenient in measuring CPS components with the conventional network analyzer without any special on-wafer calibration standards for CPS TRL calibrations and should find many useful 6 mm 4 mm 5.5 mm 1.3 mm Top layer metallization Bottom layer metallization Figure 7. Microstrip-to-CPS-to-microstrip back-to-back transition structure with a radial stub radius of 5.5 mm (from Ref. 39b with permission from IEEE).

17 796 COPLANAR STRIPLINE (CPS) COMPONENTS 1 S 11 S 1 S11 or S1 (db) 3 4 Figure 8. Measured return and insertion losses of the microstrip-to-cps-to-microstrip back-to-back transition with a radial stub radius of 5.5 mm (from Ref. 39b with permission from IEEE) Frequency (GHz) applications for CPS components and circuits measurement as well as dipole type antenna feeding. 7. ANTENNA APPLICATION A MILLIMETER-WAVE PRINTED DIPOLE PHASED-ARRAY ANTENNA FED BY A MICROSTRIP-TO-CPS TEE JUNCTION A printed dipole antenna has the benefits of low profile, light weight, low cost, and compact size. To construct a printed dipole array, several configurations have been proposed. Nesic et al. [4] reported a one-dimensional printed dipole antenna array fed by microstrip at 5. GHz. Scott [41] introduced a microstrip-fed printed dipole array using a microstrip-to-cps balun. In Refs. 4 and 41, the balun designs did not permit easy impedance matching, and the structures were too big and complicated. In 1998, a wideband microstrip-fed twin-dipole antenna was introduced with a double-sided structure operating at the frequency range from.61 to.96 GHz [4]. Zhu and Wu [9a] developed a 3.5-GHz twin-dipole antenna fed by a hybrid finite ground coplanar waveguide (FGCPW)/CPS tee junction. An X-band monolithic integrated twin-dipole antenna mixer was reported [43] with devices directly integrated into the antenna, so no feeding network was necessary. In this section, a new planar printed dipole phased-array antenna using a multi-transmission-line tunable phase shifter controlled by a piezoelectric transducer (PET) [44,45a] is presented at 3 GHz. The phased array antenna uses a new twin-dipole antenna excited by a microstrip-fed CPS tee junction introduced in Section 5. The PET-controlled phase shifter does not require any solid-state devices or their driving circuits. The 1 8 twindipole phased-array antenna has compact size, low loss, low cost, light weight, and reduced complexity as well as good beam scanning with low sidelobe levels Microstrip-Fed CPS Tee Junction at Ka Band The twin-dipole antenna is fed by a CPS. Since the conventional planar transmission line is a microstrip line, a microstip-to-cps transition is needed to feed the dipole. A microstrip-fed CPS tee junction without using bonding wires or airbridges was introduced in Section 5, where an operating frequency centered near 3.5 GHz with.7 db insertion loss ranging from to 4.15 GHz was described. 6 mm 4 mm.5 mm 1.3 mm Top layer metallization Bottom layer metallization Figure 9. Microstrip-to-CPS-to-microstrip back-to-back transition with a radial stub radius of.5 mm.

18 COPLANAR STRIPLINE (CPS) COMPONENTS S1 S11 or S1 (db) S Frequency (GHz) Figure 3. Measured return and insertion losses of the microstrip-to-cps-to-microstrip back-to-back transition with a radial stub radius of.5 mm. The tee junction utilized novel coupled CPS (CCPS). Using the CCPS, the transmission line can exhibit physical discontinuity while the fields are continuous over entire transmission line. The structures of a conventional CPS and a CCPS at 3 GHz are identical to those in Fig. 1, but with different strip width W and gap s between strips. A 31-mil RT/ Duroid 587 substrate with a dielectric constant of.33 is used for the antenna and feeding network simulation and fabrication. The width W of a CPS strip is.65 mm and the gap s between the strips is.5 mm, with a characteristic impedance of O. The wideband coupling performance of radial stubs is described in detail in the microstrip-to- CPS-to-microstrip back-to-back transition in Section 6, where the smaller radius of the radial stub is described as providing higher operating frequency with minimal insertion loss and return loss deterioration compared to the conventional CPS configuration. Performances of CCPS are simulated and compared with those of conventional CPS as shown in Fig. 31. This figure shows that the insertion loss of CCPS deteriorates by B1 db compared with that of conventional CPS for the frequency range from 9. to 35 GHz and that the return loss is better than 1 db. Insertion loss deterioration of less than db covers a wider frequency range, from 6.4 to 35 GHz. From the above mentioned results, CCPS shows that fields are continuous all over the transmission line with the aid of radial stub; however, a physical discontinuity is introduced at one of the CPS strips. The structure of a microstrip-fed CPS tee junction at 3 GHz is shown in Fig. 3. The tee junction has the characteristic impedance of O at each output port (ports 1 and ). The input impedance to the microstrip feed at port 3 is about 11 O, which is half of O. Radial stubs effectively rotate the electric fields from parallel to the normal to the substrate to ensure effective coupling to the bottom metallization, which provides the microstrip-line ground. The tee junction is simulated to verify the performance at 3 GHz. Simulated performance of the tee junction, shown in Fig. 33, reveals that the tee junction splits the power equally to each CPS port with 1. db insertion loss at 3 GHz. Simulated db insertion loss bandwidth of the tee junction is GHz, and the return loss is 4 db. 7.. Phased-Array Antenna with Multi-Transmission-Line PET-Controlled Phase Shifter The structure of the twin-dipole antenna is illustrated in Fig. 34. The antenna array is placed in front of a reflector 5 S 1 Magnitude (db) 1 15 S 11 Conventional CPS 5 Coupled CPS Frequency (GHz) Figure 31. Simulated performance comparison at Ka band between conventional and coupled CPS (from Ref. 45b with permission from IEEE)

19 798 COPLANAR STRIPLINE (CPS) COMPONENTS.65 mm Port 1.65 mm Port.5 mm 3.6 mm Ω.5 mm 5.36 mm Radial stub Port 3 11 Ω 31 mil Substrate air 6 mil Top layer metallization Bottom layer metallization Reflector Figure 3. Structure of Ka-band microstrip-fed CPS tee junction for twin-dipole antenna feeding (from Ref. 45b with permission from IEEE). Top layer metallization Bottom layer metallization for unidirectional radiation. The reflector is spaced from the antenna at the distance of 1.5 mm (6 mil), which is B.15l. The length of the dipole is 5.3 mm or.53l and the distance between dipoles is optimized to 3.6 mm or.36l, which is less than a half-wavelength in order to provide low sidelobe and grating lobe levels as well as low insertion loss incurred from the CPS tee junction. The input impedance of a single-dipole antenna is around O. The strip width W and gap s between strips of CCPS at the CPS tee junction are determined to have a CCPS characteristic impedance identical to the dipole antenna input impedance for good impedance matching. The structure of the 1 8 printed twin-dipole phased array is shown in Fig. 35. The spacing d between the twindipole antennas is about 7.4 mm or.8l. A conventional microstrip power divider with binominal impedance transformers is used to cover the wide bandwidth. The bottom metallization provides good ground plane for the microstrip. To obtain the required phase shift, the 11-O microstrip feeding lines to the antenna, which have the same input impedance as the twin dipole antenna, are perturbed with Figure 34. Structure of printed twin-dipole antenna fed by a microstrip-to-cps tee junction (from Ref. 45b with permission from IEEE). a dielectric perturber actuated by a piezoelectric transducer (PET). The length of dielectric perturber varies linearly from 5 to 35 mm on top of line and on line 8. The first line is not perturbed. The PET is configured to have no deflection (no perturbation) when a DC voltage of V is applied, and full deflection (full perturbation) when a DC voltage of 5 V is applied. A 5-mil RT/Duroid 61 with a dielectric constant of 1. is used as the dielectric perturber. The amount of differential phase shift (DF n ) is linearly proportional to the length of perturber [45a], which is expressed as DF n ¼ L perturber;n Db n ð18þ where L perturber,n is the perturber length along the nth transmission line. Db n represents the differential Figure 33. Simulated performance of tee junction near 3 GHz (from Ref. 45b with permission from IEEE). Magnitude (db) S33 3 S3 35 S Frequency (GHz)

20 COPLANAR STRIPLINE (CPS) COMPONENTS Top layer metallic strip Dielectric perturber PET DC line Y Z X Bottom layer metallization Top layer metallic strip Substrate (31 mil) Spacer (6 mil) Z Y X Reflector (a) Dielectric perturber Up ( V) Down (5 V) (b) PET Bottom layer metallization DC line Figure 35. Structure of printed dipole phased-array antenna controlled by PET: (a) top view; (b) side view (from Ref. 45b with permission from IEEE). propagation constant, expressed as Db n ¼ b unperturbed b perturbed;n ð19þ where b perturbed,n represents the propagation constant of the nth perturbed transmission line, which is microstrip in this case. Since the first perturbed microstrip line (i.e., the second line) has the minimum perturbed length, the following relationship is obtained: DF ¼ F ðþ With a dielectric perturber of 5 mm, the differential phase shift (DF n ) of takes place with a db insertion loss as shown in Fig. 36. The narrower microstrip line generates larger phase shift, but the insertion loss is increased. Hence, a proper microstrip line width should be chosen for having a good phase shift as well as low insertion loss. Table 4 summarizes the design and measured parameters for the twin-dipole phased array. The parameters in Table 4 are useful in analytical calculations of the scan angle (y ), maximally achievable gain, and optimum element spacing d of the phased array. According to (18) and (19), the perturber s length can be determined for a desired phase shift. A length of 5 mm dielectric perturber produces about differential phase shift. Accordingly, the length of each neighboring Differential phase shift (degree) Applied voltage (V) Figure 36. Measured differential phase shift for 5-mm dielectric perturber controlled by PET (from Ref. 45b with permission from IEEE).

21 8 COPLANAR STRIPLINE (CPS) COMPONENTS Table 4. Parameter Values of Twin Dipole Phased Array (from Ref. 45b with permission from IEEE) Frequency (GHz) Single-Element Gain (dbi) Progressive Phase Shift (F) Element Spacing (d) Number of Elements (N) mm 8 Measured unperturbed gain is about.3 db lower than that found in analytical or simulated data. This is due to the insertion loss of the power divider and the mutual coupling effects among elements, which normally degrade antenna gain. The measured gains of steered beams are about. db less than those of the unperturbed beam, due to the insertion loss incurred by dielectric perturbation. perturbed line is increased by 5 mm. The length of perturber for the final microstrip (L perturber,8th )isb35 mm, which gives a differential phase shift of Measured return loss of the 1 8 twin dipole array is plotted in Fig. 37. The measured return loss is B41.9 db at 3.3 GHz for the unperturbed twin-dipole phased-array antenna. With perturbation by the dielectric perturber, the return loss is B31.8 db at 3.7 GHz, which shows a.4 GHz frequency shift compared with the unperturbed result. For a bandwidth from 3 to 31.5 GHz, a measured return loss is better than 15 db Phased-Array Measurements The phased array is measured in an anechoic chamber. As shown in Fig. 35, the antenna is arrayed for H-plane beam scanning. To accomplish bidirectional scanning, two triangular perturbers are used side by side [45a]. PET actuation for the dielectric perturber is configured as V for no perturbation (no PET deflection) and 5 V for full perturbation (full PET deflection). The measured twin-dipole phase-array antenna gain without perturbation ( V for PET) is about 14.4 db, with a 3 db beamwidth of 61 as shown in Fig. 38. The fully perturbed antenna with a dielectric perturber controlled by PET shows about 41 ( 1 B þ 1) beam scanning with a gain of 1. dbi. Sidelobe levels of the steered beam are 411 db less than those of the mainbeam. The beam can be dynamically steered depending on the voltages applied to PET because the amount of phase shift changes according to the applied voltages on PET as shown in Fig. 36. The comparison among analytical, simulation, and measured results of the phased array are exhibited in Table 5. The beam scanning angle follows closely among analytical, full-wave simulation, and measured results. 8. CIRCUIT APPLICATION A HIGH-EFFICIENCY DUAL- FREQUENCY RECTENNA FOR.45 AND 5.8 GHZ WIRELESS POWER TRANSMISSION USING CPS TRANSMISSION LINE As a circuit application of CPS, the dual-frequency rectenna is presented operating at both.45 and 5.8 GHz (ISM bands) simultaneously. The rectenna is an important element for wireless power transmission. Applications of the rectenna are mainly for receiving power where the physical connections are not possible. Various kinds of rectennas have been developed since Brown demonstrated the dipole rectenna using aluminum bars to construct the dipole and the transmission line []. He also presented a thin-film printed-circuit dipole rectenna [3] with an 85% conversion efficiency at.45 GHz. Linearly polarized printed dipole rectennas were developed at 35 GHz [5,46] with conversion efficiencies of 6% and 7%, respectively. A 5.8- GHz printed dipole rectenna was developed in 1998 [6] with a high conversion efficiency of 8%. Microstrip patch dual polarized rectennas were also developed at.45 GHz [7] and 8.51 GHz [47]. More recently, a circularly polarized rectenna, which does not require strict alignment between transmitting and receiving antennas, was developed at 5.8 GHz [48a] with a conversion efficiency of 6%. Strassner and Chang also developed a circularly polarized rectenna using dual-rhombic-loop antennas at 5.8 GHz in 3 [49]. The 4 1 rectenna array showed a conversion efficiency of 8% operating at low power density. Several rectenna operating frequencies have been considered and investigated. Components of microwave power transmission have traditionally focused at.45 GHz and have more recently moved up to 5.8 GHz, where the antenna aperture area is smaller than at.45 GHz. Both Figure 37. Measured return loss of printed twin-dipole phased-array antenna (from Ref. 45b with permission from IEEE). Return loss (db) S11 Unperturbed S11 Perturbed Frequency (GHz)

22 COPLANAR STRIPLINE (CPS) COMPONENTS Unperturbed Perturbed Gain (dbi) Angle (degree) db Figure 38. Measured H-plane radiation pattern for twin-dipole phased-array antenna at 3 GHz. Measured beam scanning is from 1 to þ 1 with full perturbation (from Ref. 45b with permission from IEEE). (This figure is available in full color at interscience.wiley.com/erfme.) frequencies have comparably low atmospheric loss, cheap components availability, and reported high conversion efficiency. If the rectenna operates at dual band, it can be used for wireless power transmission at either frequency depending on power availability. A rectifying diode is analyzed to obtain design parameters for high efficiencies at both frequencies. A diode parameter, that provides high conversion efficiency and insensitivity to operating frequency is discussed. To prevent the higher-order harmonics reradiation generated by the diode, a CPS lowpass filter integrated with two additional open-ended T-strip CPS bandstop filters is presented in this section Dual-Frequency Antenna Design The structure of a rectenna is illustrated in Fig. 39. A schematic of the circuit is shown in Fig. 4. The rectenna consists of a receiving dual-frequency dipole antenna, a CPS input lowpass filter, two CPS bandstop filters, a rectifying diode, and a microwave block capacitor. The antenna receives the transmitted microwave power, and the input lowpass and the bandstop filters pass.45 and 5.8 GHz but block the higher-order harmonics from reradiation. All microwave signals produced by the nonlinear rectifying diode, including fundamental and harmonics, are confined between the input filters and microwave block capacitor. Consequently, the conversion efficiency is improved. As discussed in Section, a low-dielectric-constant substrate produces a low dielectric and conductor losses. Hence, a mil RT/Duroid 587 substrate with a low Table 5. Comparison among Analytical, Simulation, and Measured Results of 1 8 Phased Array (from Ref. 45b with permission from IEEE) Method Beam Scanning y (deg) Unperturbed Gain (dbi) Element Spacing d (mm) Analytical calculation Full-wave simulation Measured B þ dielectric constant of.33 is used for the dual-frequency rectenna design to maximize conversion efficiency. The CPS dipole dual-frequency antenna with a reflector plate is designed for.45 and 5.8 GHz (ISM bands). This type of dual-frequency antenna, introduced in [5], radiates bidirectionally and has a double-sided structure with a microstrip feed operating at.4 and 5. GHz. Double-sided dual-frequency printed dipole antennas were also reported [51,5] operating at.9 and 1.5 GHz. The dual-frequency antenna presented in this section has a uniplanar structure, which has the advantage of convenient device mounting. A reflector plate is required for the unidirectional radiation/reception, and it also increases antenna gain. As shown in Fig. 4, a long dipole is designed for operation at.45 GHz and a short dipole, at 5.8 GHz. The long dipole has a length of 16.7 mm or 1.7l at.45 GHz, and the short dipole has a length of 45.4 mm or.81l at 5.8 GHz. The feeding point has been moved about.8 mm from the edge of the short dipole for impedance matching. The coupling length and gap between the long and short dipole are around 6.3 and 4. mm, respectively. The reflector plate is normally placed at a distance about a quarter-wavelength apart from the circuit at the design frequency for low sidelobes created from image sources. However, for dual-band operation, the reflector plate distance must be optimized in order to produce good radiation patterns and similar gains for both frequencies. The reflector plate distance is optimized at 17 mm, which is about.14l of.45 GHz and.3l of 5.8 GHz. Measured frequency response of the antenna is shown in Fig. 41. This measurement was performed using the wideband CPS-to-microstrip transition presented in Section 6. Measured return losses for the antenna only are better than 3 and 5 db at.45 and 5.8 GHz, respectively. Return losses at second-order harmonics of the antenna-only case are found to be around 8.6 and 3dB at 4.9 and 11.6 GHz, respectively. 8.. CPS Lowpass Filter Integrated with T-Strip Bandstop Filters Filters are required for a rectenna to prevent all the harmonics from reradiating through the antenna. New simple

23 8 COPLANAR STRIPLINE (CPS) COMPONENTS Figure 39. Circuit picture of dual-frequency rectenna. The circuit is separated from a reflector plate at a distance of 17 mm. CPS lowpass filter integrated with bandstop filters are designed and shown in Fig. 4. As shown earlier at Fig. 19, the lowpass filter has a. db ripple Chebyshev response with a cutoff frequency of 7 GHz to pass.45 and 5.8 GHz and to reject 11.6 GHz, which is the second-order harmonic of 5.8 GHz. However, the lowpass filter will pass the second-order harmonic of.45 GHz at 4.9 GHz, and the third-order harmonic level at 7.35 GHz will not be deeply suppressed. Open-ended T-strip CPS bandstop filters, presented at Fig. 3, are placed outside the CPS strips for rejecting second- and third-order harmonics of.45 GHz at 4.9 and 7.35 GHz, respectively. The lengths of bandstop filters are.1 (.45l g ) and 1.5 (.35l g ) mm at 4.9 and 7.35 GHz, respectively. The lowpass filter integrated with two additional openended T-strip bandstop filters needs to transform the antenna s input impedance of 95 O to the CPS characteristic 1.7λ for.45 GHz.81λ for 5.8 GHz Impedance transformation section from 95Ω to 5Ω Bandstop filter for 7.35 GHz Lowpass filter Bandstop filter for 4.9 GHz Substrate (h = mil, ε r =.33) 17 mm Air Schottky barrier detector diode Microwave block capacitor Reflector Load resistor Figure 4. Dual-frequency rectenna circuit schematic (from Ref. 48b with permission from IEEE).

24 COPLANAR STRIPLINE (CPS) COMPONENTS 83 Measured return loss (db) GHz 7.35 GHz GHz 15 5 Antenna only Antenna with filters Frequency (GHz) Figure 41. Measured frequency responses of the antenna and the antenna with filters. Good return loss is achieved at both.45 and 5.8 GHz (from Ref. 48b with permission from IEEE). impedance of 5 O as well as blocking higher-order harmonics. An impedance transformation section consisting of two CPS step discontinuities as shown in Fig. 4 is designed and optimized by a full-wave electromagnetic simulator. The strip width W and the separation gap s of CPS, where the rectifying diode is placed, are designed as 1.5 and.6 mm, respectively, which corresponds to the 184 O of CPS characteristic impedance, (Z ). The CPS characteristic impedance of 184 O is selective to ensure a high.4 mm 8.77 mm Impedance transformer from 95Ω to 5Ω 3.83 mm 1.5 mm T-strip bandstop filter for 7.35 GHz 4.77 mm Lowpass filter.1 mm T-strip bandstop filter for 4.9 GHz.5 mm.5 mm.6 mm.5 mm 1.5 mm Figure 4. Structure of CPS lowpass filter with bandstop filters (from Ref. 48b with permission from IEEE).

25 84 COPLANAR STRIPLINE (CPS) COMPONENTS GHz Figure 43. Measured frequency responses of CPS lowpass filter with bandstop filters. Low insertion losses of.15 and.75 db are achieved at.45 and 5.8 GHz, respectively. Good band rejection performances are achieved at the second harmonics (4.9 and 11.6 GHz) of.45 and 5.8 GHz, and at the third harmonic (7.35 GHz) of.45 GHz (from Ref. 48b with permission from IEEE). S11 and S1 (db) 15 S11 (db) S1 (db) 4.9 GHz GHz Frequency (GHz) conversion efficiency according to the diode analysis, which will be discussed later. Measured frequency responses of the lowpass filter integrated with bandstop filters are shown in Fig. 43. Low insertion losses of.15 and.75 db are achieved at.45 and 5.8 GHz, respectively. Band rejections at the second (4.9 GHz) and the third (7.35 GHz) harmonics of.45 GHz are around 15 and 1 db, respectively, and the band rejection at the second harmonic of 5.8 or 11.6 GHz is about 3 db, which shows good bandstop performance for these harmonics Dual-Frequency Antenna Integrated with Filters For comparison, the frequency response of the antenna integrated with filters is also shown in Fig. 41. Measured return losses of 15.1 and 18. db are achieved at.45 and 5.8 GHz, respectively. Measured return losses at the second-harmonic levels of.45 and 5.8 GHz are found to be 1.58 and. db at 4.9 and 11.6 GHz, respectively. This shows that the lowpass filter integrated with two additional bandstop filters effectively block the second-order harmonics at both frequencies. The third-order harmonic level for.45 GHz is about 1.6 db at 7.35 GHz. Higher-order harmonic levels are expected to be lower than second-order harmonics at both frequencies. Radiation patterns of the antenna with filters are measured in the anechoic chamber. Measured radiation patterns at.45 and 5.8 GHz are shown in Figs. 44 and 45. Measured E-plane gains are 5 and 5.4 dbi with a 3 db beamwidth of and 361 at.45 and 5.8 GHz, respectively. Because the reflector s height has a longer wavelength at 5.8 GHz compared to that at.45 GHz, the radiation pattern for 5.8 GHz has a wider 3 db beamwidth. It is possible to have an identical 3 db beamwidth with similar radiation patterns for both frequencies by adjusting the reflector height, but the input impedances of the antenna for each frequency would be different. Hence, a tradeoff was made between the input impedance and the radiation pattern. 1 5 H-plane Co-polarizations E-plane Figure 44. Radiation patterns of dual-frequency antenna at.45 GHz (from Ref. 48b with permission from IEEE). (This figure is available in full color at interscience.wiley.com/erfme.) Gain (dbi) 5 E-plane 1 H-plane 15 Cross-polarizations Azimuth (degree)

26 COPLANAR STRIPLINE (CPS) COMPONENTS H-plane Co-polarization Gain (dbi) E-plane H-plane E-plane 5 3 Cross-polarization Azimuth (degree) Figure 45. Radiation patterns of dual-frequency antenna at 5.8 GHz (from Ref. 48b with permission from IEEE). (This figure is available in full color at interscience.wiley.com/erfme.) At broadside, the cross polarization at.45 GHz is about 19.4 and 18. db below the copolarizations in E and H planes, respectively. At 5.8 GHz, the cross-polarization is about 3.1 and 5 db below the copolarizations in E and H planes, respectively. These low cross-polarization levels show good alignment between transmitting and receiving antennas. Relatively similar E-plane gains are achieved at both.45 and 5.8 GHz. Second-order harmonic radiation patterns are measured and shown in Fig. 46. At broadside, the second-order harmonic radiation gains at 4.9 and 11.6 GHz are 1 and 15 dbi, respectively. Since the gains for the fundamental frequencies at.45 and 5.8 GHz are 5 and 5.4 dbi, the corresponding suppressions are about 15 and.4 db, respectively. where A ¼ R L pr s Z d ¼ 1 1 þ A þ B þ C 1 þ V bi y on 1 þ V B ¼ R sr L ðoc j Þ p C ¼ R L pr s 1 þ V bi p yon V 1 þ V bi Vbi V V ð1þ 1 cos 3 y on tan y on ðþ cos y on þ tan y on ð3þ ðtan y on y on Þ ð4þ Diode input resistance is expressed as 8.4. Diode Analysis A diode analysis is used to achieve high RF-to-DC conversion efficiencies at both frequencies. RF-to-DC conversion efficiency Z d and input impedance Z d of the diode can be calculated from the closed-form equations in Ref. 6, which are expressed as pr s R d ¼ ð5þ cos y y on on sin y cos y on on where R L and R s represent the load resistance and the series resistance of the diode, respectively. V is an output Measured gain (dbi) GHz GHz Angle (degree) Figure 46. Second-harmonic radiation patterns. These patterns prove that the lowpass filter integrated with two open-ended T-strip bandstop filters effectively blocks higher-order harmonics. The second harmonics of.45 and 5.8 GHz are 4.9 and 11.6 GHz, respectively. (From Ref. 48b with permission from IEEE).

27 86 COPLANAR STRIPLINE (CPS) COMPONENTS voltage produced at the load resistance, and V bi is a diode s built-in voltage. y on is the diode conduction time in radians and C j is the junction capacitance. The closed-form expression for y on and C j is tan y on y on ¼ R L The junction capacitance C j is defined as C j ¼ C j pr s ð6þ 1 þ V bi V sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V bi V bi þ jv j ð7þ Because of the diode dimension, the CPS strip width (s) is fixed at.6 mm and the corresponding characteristic impedance is 184 O. The diode input impedance is matched to this impedance of 184 O, which corresponds to a load resistance of 31 O as determined in Fig. 47. This gives B8% target efficiency. To prevent the diode breakdown due to overload, determining the limit of output DC power is necessary. Typically, the DC power level limit is determined by P DC oðv br =4R LÞ [6], where V br is the breakdown voltage of the diode and R L is the load resistance. Therefore, adequate load resistance R L is required as well as adequate input resistance of the diode (R d ) to ensure a high efficiency and a high output DC power. RF-to-DC conversion efficiency is frequency-dependent, as shown in parameter B in (3). To minimize the conversion efficiency dependence on the frequency, it is necessary to minimize the effect of parameter B. Since parameter B is proportional to the square of oc j, a small value of C j will reduce the effect of parameter B on the conversion efficiency. For a small value of C j, packaged diode is not suitable. From the preceding analysis, a flip-chip-type GaAs Schottky barrier diode (MA4E1317) is selected as the rectifying device. The diode has a built-in voltage (V bi ) and a measured breakdown voltage (V br ) of.7 and 1 V, respectively. The maximum DC output voltage (V ) is about 6 V. The zero-bias-junction capacitance (C j ) is. pf with a series resistance (R s )ofa4o. Using (1) (7), RF-to-DC conversion efficiency Z d and input resistance of the diode R d can be calculated in terms of load resistance R L at.45 and 5.8 GHz, as shown in Fig. 47, where very little difference in conversion efficiency is observed between.45 and 5.8 GHz. This is due to the low zero-bias-junction capacitance (C j ) of the diode. Since C j is low, the corresponding C j is also low [6], and the value of parameter B is very small compared to those of parameters A and C. Consequently, parameter B, which is frequency-dependent, does not contribute much effect to the diode s conversion efficiency. From Fig. 47, the diode input resistance R d and the load resistance R L can be determined as design parameters for a desired target RF-to-DC conversion efficiency Z d Rectenna Measurements The rectenna is measured in free space. The measurement set up is shown in Fig. 48. Transmitting power is generated by a frequency synthesizer (HP 8341B) and amplified by power amplifiers. Two types of power amplifiers, L3-4 and L55-38 (Microwave Power Inc.), are used, which can produce up to þ 4 and þ 38 dbm at.45 and 5.8 GHz, respectively. For the transmitting power monitoring purpose, a directional coupler is used with db coupling along with a -db attenuator for power meter (HP 437B) protection. Standard-gain horn antennas are used for transmitting power at.45 and 5.8 GHz, respectively. From the diode analysis described in Section 8.4, the load resistance R L is taken as 31 O, for 8% target efficiency. The microwave block capacitor not only bypasses the microwave signal to the diode but also cancels the capacitive reactance of the diode by selecting an appropriate distance from the diode at a specific frequency, which maximizes the RF-to-DC conversion efficiency [6]. For dual-band operation of the rectenna, the diode location is optimized at 7.5 mm to have high efficiencies at both frequencies. Conversion efficiency of the rectenna is represented as Z ¼ P DC P received 1ð%Þ ð8þ Figure 47. Diode (MA4E1317) RF-to-DC conversion efficiency analyses in terms of the load resistance (R L ) and the diode input resistance (R d ) at.45 and 5.8 GHz. Diode parameter values of V bi, V, V br are.7, 6, and 1 V, respectively. The zero bias junction capacitance (C j ) of. pf, and a series resistance (R s )of4o are used for the analyses (from Ref. 48b with permission from IEEE). Calculated efficiency (%) Efficiency at.45 GHz Efficiency at 5.8 GHz Load resistance (Ohm) Diode input resistance (Ohm)

28 COPLANAR STRIPLINE (CPS) COMPONENTS 87 Power meter (HP437B) db Attenuator R G Rectenna Frequency synthesizer (HP8341B) Power amplifier (L3-4 and L55-38) Directional coupler ( db coupling) Standard gain horn antennas Load resistor 31Ω Volt meter Figure 48. Rectenna measurement setup. Two different types of power amplifiers (L3-4 and L55-38) and transmitting standard-gain horn antennas are used for dual-frequency power transmissions (from Ref. 48b with permission from IEEE). where P DC is DC power produced at the load resistance (R L ) of the rectenna and P received is power received at antenna of the rectenna. P received is calculated from the Friis transmission equation expressed as l G t P received ¼ P t G r G t ¼ P t A e 4pR 4pR where the effective area A e is represented as A e ¼ l G r 4p ð9þ ð3þ and where P t represents transmitted power, G t and G r represent gains of transmitter and receiver antenna, respectively, and R is the distance between the transmitter and the receiver antennas. For the rectenna measurements, R is taken to the edge of the far field. Parameters for calculating P received of the dual-frequency rectenna are displayed in Table 6. The efficiency is normally expressed as a function of power density. The power density is calculated by Measured rectenna efficiencies are shown in Fig. 49. High efficiencies of 84.4% and 8.7% are measured at.45 and 5.8 GHz, respectively. Experimental efficiencies follow closely with the theoretical efficiency calculations. Received power at each highest efficiency points are and 49.9 mw corresponding to power densities of.38 and 8.77 mw/cm at.45 and 5.8 GHz, respectively, as shown in Fig. 49b. At 8% efficiency points for both.45 and 5.8 GHz, the ideal received power levels at both frequencies are almost identical. Measurements show that received power levels at 8% efficiency points are 35.6 and 39.6 mw at.45 and 5.8 GHz, respectively. Considering the antenna s effective areas (A e ) listed in Table 6, the required power density of 5.8 GHz is around 5.1 times larger than that of.45 GHz to achieve 8% efficiency. As shown in Fig. 46, the second-order harmonic radiations at 4.9 and 11.6 GHz are around 15 and db less than the fundamental frequency radiations at broadside. Therefore, second-order harmonic reradiations are quite small. Observing the return loss plot of the antenna integrated with filters in Fig. 41, higher-order harmonic reradiations are expected to be small. P D ¼ P r A e ¼ P tg t 4pR ð31þ 9. CONCLUSION Table 6. Received Power Calculation parameters for Dual Frequency Rectenna (from Ref. 48b with permission from IEEE) Frequency (GHz) l (cm) Far Field (cm) G r (dbi) G t (dbi) A e (cm ) In this article, the CPS transmission line was analyzed for practical components development. With this analysis, practical CPS components were developed, investigated, and their applications were implemented. It was found that a lower-dielectric-constant (e r ) substrate and a higher CPS characteristic impedance (Z ) are desired for lower CPS attenuation. Different CPS configurations such as varying s and W, can exhibit identical characteristic

29 88 COPLANAR STRIPLINE (CPS) COMPONENTS Measured efficiency (%) GHz efficiency 5.8 GHz efficiency.45 GHz DC output 5.8 GHz DC output DC output voltage (V) Received power (mw) (a) Figure 49. RF-to-DC conversion efficiency for dual-frequency rectenna: (a) efficiency and DC output voltage versus received power; (b) efficiency versus power density (from Ref. 48b with permission from IEEE). Efficiency (%) GHz 5.8 GHz.45 GHz measured.45 GHz calculated 5.8 GHz measured 5.8 GHz calculated Power density (mw/cm) (b) impedance (Z ). Although characteristic impedance values (Z ) are identical with different CPS configurations, their attenuation values might be different. Therefore, attenuation should be verified by plotting in terms of s and W. As for CPS components, six new types of CPS resonators were presented with open-ended T strip, short-ended strip, and T slots, and their performances were analyzed in terms of quality factor (Q factor) or bandwidth. We found that, while T-strip (types A, B, and D) and T-slot (type C) resonators exhibit bandstop behavior, short-ended strip resonators (types E and F) have bandpass frequency responses. The T-slot resonator (type C) has the highest Q factor among the resonators, which means that resonance energy is stored better in the slots than in the strips. As discussed earlier, CPS attenuation is reduced when the characteristic impedance (Z ) is high, meaning that the higher is Z, the higher is the Q factor. Lumped-element equivalent circuits of each resonator were presented. Two types of CPS bandpass filters were designed using the proposed resonators. Multiple short-ended strip bandpass filter exhibited a wide passband bandwidth, but the bandpass filter using short-ended strips with T strips showed narrow passband bandwidth. A simple CPS lowpass filter was developed with a cutoff frequency of 7 GHz using interdigital capacitors and a CPS transmission line. The measured performance showed low insertion loss at passband and deep suppression at stopband. A new CPS tee junction was introduced using a coupled CPS (CCPS). The CCPS developed does not require any bond wires or via holes to connect physically disconnected CPS lines. The performance of CCPS was compared with conventional CPS configuration, and its usefulness was discussed. Using the CCPS, a novel microstrip-fed CPS tee junction has been invented. As an antenna application of CPS, a novel printed twindipole phase-array antenna was developed at 3 GHz using a multi-transmission-line tunable phase shifter controlled by a piezoelectric transducer (PET). The new twindipole antenna was designed using a microstrip-fed CPS tee junction. To construct the tee junction, CCPS was used for a physical discontinuity at CPS while fields were continuous over the entire transmission line. The tee junction effectively split power to each CPS output port with low insertion loss. The PET-actuated phase shifter required only one (unidirectional beam scanning) or two (bidirectional beam scanning) applied voltage sources to produce

30 COPLANAR STRIPLINE (CPS) COMPONENTS 89 the progressive phase shift (F). The twin dipole phasedarray antenna demonstrated a 41 ( 1B þ 1) beam scanning with more than 11 db sidelobe suppression across the scan. As a circuit application of CPS, a dual-frequency rectenna was presented operating at both.45 and 5.8 GHz (ISM bands) simultaneously. The rectenna has a dual-frequency dipole antenna integrated with CPS lowpass and bandpass filter. For high conversion efficiency, a diode analysis and transmission-line analysis were performed for low attenuation. Second-order harmonic reradiations were well suppressed with CPS filters without losing conversion efficiency. Since little research has been done on CPS and its components, this article should provide some useful guidelines for designing and implementing CPS circuits and the practical aspects of printed dipole antennas. BIBLIOGRAPHY 1. H. K. Chiou, C. Y. Chang, and H. H. Lin, Balun design for uniplanar broad band double balanced mixer, Electron. Lett. 31(4): (Nov. 1995).. H. Haga, M. Izutsu, and T. Sueta, Travelling wave modulator switch with an etched grave, IEEE J. Quantum Electron. QE-:9 96 (1986). 3. I. Hong and H. Park, Quasi-static analysis of travellingwave electrodes with asymmetrical finite thickness for electro-optic modulators, Optoelectron. IEE Proc. 147():1 1 (April ). 4. J. H. Son, H. H. Wang, J. F. Whitaker, and G. A. Mourou, Picosecond pulse propagation on coplanar striplines fabricated on lossy semiconductor substrates: Modeling and experiments, IEEE Trans. Microwave Theory Tech. 41(9): (Sept. 1993). 5. S. S. Gevorgian and I. G. Mironenko, Asymmetric coplanarstrip transmission lines for MMIC and integrated optic applications, Electron. Lett. 6(): (Oct. 199). 6. R. N. Simons, N. I. Dib, and L. P. B. Katehi, Modeling of coplanar stripline discontinuities, IEEE Trans. Microwave Theory Tech. 44(5): (May 1996). 7. K. Goverdhanam, R. N. Simons, and L. P. B. Katehi, Coplanar stripline components for high-frequency applications, IEEE Trans. Microwave Theory Tech. 45(1): (Oct. 1997). 8. K. Goverdhanam, R. N. Simons, and L. P. B. Katehi, Coplanar stripline propagation characteristics and bandpass filter, IEEE Microwave Guided Wave Lett. 7(8):14 16 (Aug. 1997). 9. L. Fan, B. Heimer, and K. Chang, Uniplanar hybrid couplers using asymmetrical coplanar striplines, IEEE Trans. Microwave Theory Tech. 45(1):34 4 (Dec. 1997). 1. S. G. Mao, H. K. Chiou, and C. H. Chen, Modeling of lumpedelement coplanar-stripline low-pass filter, IEEE Microwave Guided Wave Lett. 8(3): (March 1998). 11. S. Uysal and J. W. P. Ng, A compact coplanar stripline lowpass filter, Proc. Asia Pacific Microwave Conf., Singapore, 1999, Vol., pp H. T. Kim, S. Lee, J. Kim, J. H. Park, Y. K. Kim, and Y. Kwon, A V-band cps distributed analog mems phase shifter, 3 IEEE MTT-S Digest, Philadelphia June 3, pp L. Zhu and K. Wu, Field-extracted lumped-element models of coplanar stripline circuits and discontinuities for accurate radio-frequency design and optimization, IEEE Trans. Microwave Theory Tech. 5(4): (April ). 14. N. Dib, L. Katehi, G. Ponchak, and R. Simons, Theoretical and experimental characterization of coplanar waveguide discontinuities for filter applications, IEEE Trans. Microwave Theory Tech. 39(5): (May 1991). 15. K. Hettak, N. Dib, A. Sheta, and S. Toutain, A class of novel uniplanar series resonators and their implementation in original applications, IEEE Trans. Microwave Theory Tech. 46(9): (Sept. 1998). 16. K. Hettak, N. Dib, A. Omar, G. Delisle, M. Stubbs, and S. Toutain, A useful new class of miniature CPW shunt stubs and its impact on millimeter wave integrated circuits, IEEE Trans. Microwave Theory Tech. 47(1): (Dec. 1999). 17. G. Ghione, A CAD-oriented analyical model for the losses of general asymmetric coplanar lines in hybrid and monolithic MICs, IEEE Trans. Microwave Theory Tech. 41(9): (Sept. 1993). 18. E. Chen and S. Y. Chou, Characteristics of coplanar transmission lines on multilayer substrates: Modeling and experiments, IEEE Trans. Microwave Theory Tech. 45(6): (June 1997). 19. Z. Du, K. Gong, J. S. Fu, Z. Feng, and B. Gao, CAD model for asymmetrical, elliptical, cylindrical, and elliptical cone coplanar striplines, IEEE Trans. Microwave Theory Tech. 48(): (Feb. ). a. K. C. Gupta, R. Grag, I. Bhal, and P. Bhartia, Microstrip Lines and Slotlines, nd ed. Artech House, Norwood, MA, b. Y. H. Suh and K. Chang, Coplanar stripline resonators modeling and applications to filters, IEEE Trans. Microwave Theory Tech., 5(5): (May ). 1. J. Caroll, M. Li, and K. Chang, New technique to measure transmission line attenuation, IEEE Trans. Microwave Theory Tech. 43(1):19 (Jan. 1995).. W. C. Brown, The history of power transmission by radio waves, IEEE Trans. Microwave Theory Tech. 3(9):13 14 (Sept. 1984). 3. W. C. Brown and J. F. Triner, Experimental thin-film, etchedcircuit rectenna, IEEE MTT-S Digest, 198, pp J. O. McSpadden, T. Yoo, and K. Chang, Theoretical and experimental investigation of a rectenna element for microwave power transmission, IEEE Trans. Microwave Theory Tech. 4(1): (Dec. 199). 5. T. Yoo and K. Chang, Theoretical and experimental development of 1 and 35 GHz rectennas, IEEE Trans. Microwave Theory Tech. 4(6): (June 199). 6. J. O. McSpadden, L. Fan, and K. Chang, Design and experiments of a high-conversion-efficiency 5.8-GHz rectenna, IEEE Trans. Microwave Theory Tech. 46(1):53 6 (Dec. 1998). 7. J. O. McSpadden and K. Chang, A dual polarized circular patch rectifying antenna at.45 GHz for microwave power conversion and detection, IEEE Int. Microwave Symposium Digest, San Diego, CA, 1994, pp G. L. Matthaei, L. Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, Artech House, Boston, a. J. Zhu and K. Wu, Model-based characterization of CPS-fed printed dipole for innovative design of uniplanar integrated antenna, IEEE Microwave Guided Wave Lett. 9(9): (Sept. 1999).

31 81 COPLANAR STRIPLINE TRANSITIONS 9b. Y. H. Suh and K. Chang, Microstrip fed coplanar stripline Tee junction using coupled coplanar stripline, IEEE Int. Microwave Synposium Digest, Phoenix, AZ, 1 pp C. H. Ho, L. Fan, and K. Chang, Broad-band uniplanar hybrid-ring and branch-line couplers, IEEE Trans. Microwave Theory Tech. 41(1): (Dec. 1993). 31. R. N. Simons, Novel coplanar stripline to slotline transition on high resistivity silicon, Electron. Lett. 3(8): (April 1994). 3. K. Tilley, X. D. Wu, and K. Chang, Coplanar waveguide fed coplanar strip dipole antenna, Electron. Lett. 3(3): (Feb. 1994). 33. M.-Y. Li, K. Tilley, J. McCleary, and K. Chang, Broadband coplanar waveguide-coplanar strip-fed spiral antenna, Electron. Lett. 31(1):4 5 (Jan. 1995). 34. S. Mao, C. Hwang, R. Wu, and C. Chen, Analysis of coplanar waveguide-to-coplanar stripline transitions, IEEE Trans. Microwave Theory Tech. 48(1):3 9 (Jan. ). 35. N. I. Dib, R. N. Simons, and L. P. B. Katehi, New uniplanar tansitions for circuit and antenna applications, IEEE Trans. Microwave Theory Tech. 43(1): (Dec. 1995). 36. Y. Qian and T. Itoh, A broadband uniplanar microstrip-to- CPS transition, Microwave Conf. Proc. AMPC, 199, Vol., pp R. N. Simons, N. I. Dib, and L. P. B. Katehi, Coplanar stripline to microstrip transition, Electron. Lett. 31(): (Sept. 1995). 38. G. F. Engen and C. A. Hoer, Thru-reflect-line: An improved technique for calibrating the dual six-port automatic network analyzer, IEEE Trans. Microwave Theory Tech. MTT-7(1): (Dec. 1979). 39a. R. B. Marks, A multiline method of network analyzer calibration, IEEE Trans. Microwave Theory Tech. 39(7): (July 1991). 39b. Y. H. Suh and K. Chang, A wideband coplanar stripline to microstrip transition, IEEE Microwave and Wireless Communication Letters, 11(1):8 9 (Jan. 1). 4. A. Nesic S. Jovanovic, and V. Brankovic, Design of printed dipoles near the third resonance, IEEE Int. Antennas and Propagation Symp. Digest, Atlanta, GA, Vol., 1998, pp M. Scott, A printed dipole for wide-scanning array application, IEEE 11th Int. Conf. Antennas and Propagation, Manchester, UK, 1, Vol. 1, pp G. A. Evtioushkine, J. W. Kim, and K. S. Han, Very wideband printed dipole antenna array, Electron. Lett. 34(4):9 93 (Nov. 1998). 43. K. L. Deng, C. C. Meng, S. S. Lu, H. D. Lee, and H. Wang, A fully monolithic twin dipole antenna mixer on a GaAs substrate, Asia Pacific Microwave Conf. Digest, Sydney, NSW, Australia,, pp T. Y. Yun and K. Chang, A phased-array antenna using a multi-line phase shifter controlled by a piezoelectric transducer, IEEE Int. Microwave Symp. Digest, Boston, Vol.,, pp a. T. Y. Yun and K. Chang, A low-cost 8 to 6.5 GHz phased array antenna using a piezoelectric transducer controlled phase shifter, IEEE Trans. Antenna Propag. 49(9): (Sept. 1). 45b. Y. H. Suh and K. Chang, A new millimeter-wave printed dipole phased array antenna using microstrip-fed coplanar stripline Tee junctions, IEEE Trans. Anten. Propag., 5(8): 19 6 (Aug. 4). 46. P. Koert and J. T. Cha, Millimeter wave technology for space power beaming, IEEE Trans. Microwave Theory Tech. 4(6): (June 199). 47. L. W. Epp, A. R. Khan, H. K. Smith, and R. P. Smith, A compact dual-polarized 8.51-GHz rectenna for high-voltage (5 V) actuator applications, IEEE Trans. Microwave Theory Tech. 48(1):111 1 (Jan. ). 48a. Y. H. Suh and K. Chang, A circularly polarised truncatedcorner square patch microstrip rectenna for wireless power transmission, Electron. Lett. 36(7):6 6 (March ). 48b. Y. H. Suh and K. Chang, A High-efficiency dual frequency rectenna for.45- and 5.8-GHz wireless power transmission, IEEE Trans. Microwave Theory Tech., 5(7): (July ). 49. B. Strassner and K. Chang, 5.8-GHz circularly polarized dualrhombic-loop traveling-wave rectifying antenna for low power-density wireless power transmission application, IEEE Trans. Microwave Theory Tech. 51(5): (May 3). 5. Y. H. Suh and K. Chang, Low cost microstrip-fed dual frequency printed dipole antenna for wireless communications, Electron. Lett. 36(14): (July ). 51. F. Tefiku and E. Yamashita Double-sided printed strip antenna for dual frequency operation, IEEE Int. Antenna and Propagation Symp. Digest, Baltimore, MD, 1996, Vol. 1, pp F. Tefiku and C. A. Grimes, Design of broad-band and dualband antennas comprised of series fed printed-strip dipole pairs, IEEE Trans. Anten. Propag. 48(6):895 9 (June ). COPLANAR STRIPLINE TRANSITIONS 1. INTRODUCTION RAINEE N. SIMONS NASA Glenn Research Center Cleveland, Ohio A balun is a circuit that is used to transform an unbalanced line to a balanced transmission line. In this article, the design of baluns, which transform an unbalanced line, such as a coplanar waveguide (CPW) and a microstrip line, to a balanced line, such as a coplanar stripline (CPS), is presented. The applications of these baluns include double-balanced mixers, balanced amplifiers, and feed network for dipole antennas. These baluns are also commonly referred to as transitions between transmission lines. The baluns are divided into two categories for the purpose of analysis: the Marchand baluns and the double- Y baluns. Almost all the baluns discussed in this article fall into the category of Marchand baluns.. COPLANAR STRIPLINE-TO-COPLANAR WAVEGUIDE TRANSITION.1. Coplanar Stripline-to-Coplanar Waveguide Balun Figure 1 shows a CPS to a CPW balun [1]. In this balun at the balanced end currents of equal magnitude but opposite

32 COPLANAR STRIPLINE TRANSITIONS 811 Unbalanced λg 4 Balanced Coplanar stripline 1 3 Coplanar waveguide Bond wire Dielectric substrate Figure 1. Coplanar stripline-to-coplanar waveguide transition with three strip transmission lines. in direction flow along the two strip conductors. At the unbalanced end currents of equal magnitude but opposite in direction flow along the center strip conductor and the ground planes on either side. A short circuit placed between conductors 1 and at the balanced end results in an open-circuit quarter-wavelength away at the unbalanced end, forcing all the currents to flow between conductors and 3. Further, conductors 1 and 3 are short-circuited at the unbalanced end by a bond wire. This short circuit appears as an open-circuit quarter-wavelength away at the balanced end, and therefore conductor 1 is isolated from the balanced end. This transition, in addition to serving as a balun, also provides impedance transformation. Since RF energy propagates between conductors and 3, the characteristic impedance between these conductors determines the impedance transformation over the quarter-wavelength section. In Ref. the application of this transition to a CPW feed network for a dipole antenna array is demonstrated. A reduced-size lumped-element version of this transition is demonstrated in Ref Coplanar Stripline-To-Coplanar Waveguide Balun With Slotline Radial Stub Figure shows a coplanar stripline (CPS)-to-coplanar waveguide (CPW) balun. In this balun one of the slots of the CPW is terminated in a broadband slotline radial open stub, while the other slot extends further to meet the CPS. In Ref. 4 the characteristics of an experimental balun are reported. The measured insertion loss and return loss of the balun are typically 1. db and less than 13. db, respectively, over the frequency range of GHz. The balun has a bandwidth greater than octaves. In Refs. 5 and 6 a variant of this balun is used for exciting a strip dipole and a spiral antenna, respectively..3. Coplanar Stripline-to-Coplanar Waveguide Double-Y Balun The double-y junction in this balun [7] is formed by placing alternatively three coplanar striplines (CPSs) and three coplanar waveguides with finite-width ground planes (FW-CPWs) as shown in Fig. 3. The advantage Slotline radial stub Bond wire Coplanar stripline Coplanar waveguide Dielectric substrate Figure. Coplanar stripline-to-coplanar waveguide transition with radial slotline stub.

33 81 COPLANAR STRIPLINE TRANSITIONS Coplanar stripline short circuit Input finite width coplanar waveguide Bond wires 1 Coplanar stripline open circuit 6 Finite width coplanar waveguide open circuit Output coplanar stripline Finite width coplanar waveguide short circuit of FW-CPW over CPW in this design is the greatly reduced parasitics. Because of small parasitics the FW-CPW terminations behave almost like ideal open and short circuits, resulting in wider bandwidth. This balun is modeled as a six-port network as explained in Ref. 8. In Ref. 9 the characteristics of an experimental balun are reported. The geometry as well as typical measured characteristics are summarized in Table 1. These characteristics show that the balun has a bandwidth of several decades. 3. COPLANAR STRIPLINE-TO-MICROSTRIP TRANSITION 3 Figure 3. Coplanar stripline-to-coplanar waveguide double-y balun or transition Coplanar Stripline-to-Microstrip Transition with an Electromagnetically Coupled Radial Stub Coplanar stripline (CPS)-to-microstrip transitions [1] in a back-to-back arrangement are shown in Fig. 4. In each transition one of the CPS strip conductors is terminated in a microstrip radial stub of radius R and angle f while the other strip conductor is extended forward to form the microstrip line. The CPS strip conductor width and separation are W and S, respectively. The width of the microstrip line is W m. The resonance frequency of the radial stub depends on the radius R and angle f. At resonance, the microstrip radial stub provides a virtual RF short circuit between the CPS strip conductor and the microstrip ground plane on the opposite side of the substrate. In the CPS, the electric field lines are across the strip conductors and parallel to the substrate. In the microstrip line, the electric field lines are normal to the substrate. Hence, to gradually rotate the electric field lines by 91, the microstrip ground-plane edge is tapered at an angle y. The electric field lines at various cross sections along the transition are illustrated in Fig. 5. In Ref. 1, the characteristics of an experimental transition fabricated on a RT/Duroid 61 substrate are reported. The measured insertion loss and return loss for 4 5 Table 1. Coplanar Waveguide with Finite-Width Ground Planes-to-Coplanar Stripline Double-Y Balun Or Transition Dimensions and Characteristics Substrate Material e r and Thickness (mm) Alumina 9.8,.635 Coplanar Waveguide S (mm).1 W (mm).4 g (mm).1 Z (CPW) (O) 5. Stub length (mm).996 Coplanar Stripline W (mm). S (mm). Z (CPS) (O) 5. Stub length (mm) 1. Measured Characteristics Frequency range (GHz) DC 1. S 11 (db) r 13. S 1 (db). a a For two back-to-back transition. Source: Ref.9. two back-to-back transitions over the frequency range of GHz is.4 db (max) and less than 1. db, respectively. The 1. db return loss bandwidth of both transitions is about 18% centered at 5.55 GHz. The numerical simulation of the transition carried out using the FDTD technique shows good agreement between measured and modeled results [1]. An optimized version of W Ground plane S A W B Coplanar stripline C A R θ B D C L CPS L D Microstrip L m W m Figure 4. Two back-to-back coplanar stripline-tomicrostrip transition: topside circuit pattern W ¼.69 mm, S ¼.19 mm, R ¼ 5.8 mm, f ¼ 61, W m ¼.19 mm, L CPS ¼ 6.9 mm; bottomside circuit pattern L ¼ 7.1 mm, L m ¼ 1.7 mm, ye71. Substrate parameters: h ¼.54 mm, e r ¼ 1.5. Segments A A, B B, C C, and D D refer to the various cross sections along the transition.

34 COPLANAR STRIPLINE TRANSITIONS 813 E ε ε r E h.638 λ gm 5 ohms microstrip (a) (b) h W S 1 S S W Coplanar stripline Quarter wave transformer h 1 W 1 E (c) Figure 5. Electric field lines at various cross sections along the transition: (a) electric field between coplanar striplines at cross section A A; (b) electric field between coplanar stripline and microstrip ground at cross section B B; (c) electric field in cross section of asymmetric microstrip at C C; (d) electric field in the cross section of the symmetric microstrip at D D. this transition has been demonstrated to have a decade bandwidth [11]. In addition, the radial stubs can be replaced by overlapping conductors as demonstrated in Ref. 1 to provide a virtual short circuit. In [13] and in [14] a transition from an asymmetric CPS (ACPS)-to-microstrip with radial stubs and with metal vias respectively, are demonstrated. 3.. Uniplanar Coplanar Stripline-to-Microstrip Transition A uniplanar coplanar stripline (CPS)-to-microstrip backto-back transition [15] in a balanced arrangement is shown in Fig. 6. In this transition, a microstrip line of characteristic impedance 5 O is coupled to two orthogonal microstrip lines of characteristic impedance 7 O through a quarter-wave stepped impedance-matching transformer. The characteristic impedance of 7 O is chosen for ease of fabrication. In an ideal transition, the mean pathlength of the folded loop a through b is equal to.5 l g(microstrip), where l g(microstrip) is the guide wavelength in the microstrip of characteristic impedance 7 O at the center frequency f. In a practical transition for wideband operation, the right-angle bend parasitic elements have to be compensated. A simple solution to this problem is to increase the mean pathlength of the microstrip. Hence, the mean pathlength is chosen as.638 l g(microstrip). This design ensures that the phase of the signals at the input locations a and b to the coupled microstrip line are 181 out of phase. The coupled microstrip lines are excited in the odd mode with the electric field lines predominantly across the gap S. The dimensions of the gap S is chosen such that the odd-mode characteristic impedance is 5 O. The horizontal orientation of the electric field lines in the coupled microstrip makes the transition to a CPS simple. The width W and separation S of the CPS in the experimental transition is the same as the coupled microstrip width and separation. In Ref. 15 the measured characteristics of the transition shown in Fig. 6 is reported. The transition is designed (d) E Wm a l 1 l b W Coupled microstrip (odd-mode) Microstrip ground plane Dielectric substrate ε ε r Figure 6. Two back-to-back balanced uniplanar coplanar stripline-to-microstrip transition. W m ¼.3 mm, W 1 ¼.33 mm, W ¼ W ¼ S ¼ S ¼.1 mm, l 1 ¼ 4.9 mm, l ¼.8 mm, S 1 ¼.1 mm, h 1 ¼.54 mm, h ¼ 1.34 mm. Substrate thickness h ¼.54 mm, e r ¼ 1.5. for operation at a center frequency f ¼ 1. GHz; however, the measurements show that f has shifted to 9.6 GHz. The measured insertion loss and return loss are about. db and less than 1. db, respectively, over 4% bandwidth centered at 9.6 GHz. The numerical simulation of the transition carried out using the FDTD technique shows that the measured and modeled results are in good agreement [15] Stacked Coplanar Stripline-to-Microstrip Transition Figure 7 shows a coplanar stripline (CPS)-to-microstrip transition [16] in a stacked configuration. In this transition the microstrip ground plane is attached using Gold ribbon Microstrip line Coplanar stripline substrate Conducting silver epoxy S Coplanar stripline S W m W Tapered microstrip substrate Coaxial connector Figure 7. Coplanar stripline-to-microstrip transition using ribbon bond.

35 814 COPLANAR STRIPLINE TRANSITIONS electrically conducting epoxy to one of the strip conductors of the CPS. The connection between the remaining strip conductors is by a gold ribbon. Lee and Itoh [16] describe the characteristics of an experimental transition. The geometry as well as the measured characteristics of the transition are summarized in Table. The transition has a wide bandwidth Microcoplanar Stripline-to-Microstrip Transition Figure 8 shows a microcoplanar stripline (MCPS)-to-microstrip transition [17] in a back-to-back arrangement. In this transition, the width of the microstrip ground plane is abruptly reduced to form a symmetric parallel-plate line. The parallel-plate conductors are next flared out to form the MCPS. The cross section at three locations along the transition are shown in the inset in Fig. 8. Sections A A, B B, and C C show the microstrip, the parallel plate, and the MCPS regions, respectively. The relevant parameters of the transition are as follows: h 1 ¼ 54 mm, e r1 ¼1.5, e r E1., W ¼ 889 mm, W m ¼ 54 mm, and the characteristic impedance Z (microstrip) ¼ 5 O. In Ref. 17 the characteristics of an experimental transition are reported. The measured insertion loss and return loss are 1. db and less than 16. db, respectively, for two back-to-back transitions over the frequency range of GHz. These losses also include the loss of the test fixture. The measurements show that the transition has a broad bandwidth. Table. Coplanar Stripline-to-Microstrip Transition Dimensions and Characteristics Coplanar Stripline Substrate thickness (mm) e r 3 1. W (mm) 49 S (mm) 58 Z (CPS) (O) 5 Microstrip Line Substrate thickness (mm) 17 e r. W m (mm) 385 Z (m) (O) 5 Gold Ribbon Width (mm) 35 Length (mm) 5 Measured Characteristics Frequency range (GHz) DC 18. S 11 (db) r 13. a a For two back-to-back transitions. Source: Ref COPLANAR STRIPLINE-TO-SLOTLINE TRANSITION An electromagnetically coupled coplanar stripline (CPS)- to-slotline transition [18] in a back-to-back arrangement is shown in Fig. 9. The CPS and the slotline are on opposite sides of a dielectric substrate. To demonstrate the design C A B C A B Expanded polystyrene ε ε r 1 ε ε r 1 ε ε r 1 W m W m W W h 1. Figure 8. Two back-to-back micro-coplanar stripline-to-microstrip transition. ε ε r ε ε r Section A-A Section B-B Section C-C

36 COPLANAR STRIPLINE TRANSITIONS 815 Coplanar stripline R L s L 1 D L D L 3 C B C B A Ground plane Slotline (on bottom side) Figure 9. Two back-to-back electromagnetically coupled coplanar stripline-to-slotline transition. A A, B B, C C, and D D refer to the various cross-sections along the transition. A Return loss (db) Insertion loss (db) GHz 11. GHz Frequency (GHz) Frequency (GHz) Figure 11. Measured characteristics: (a) return loss; (b) insertion loss. (a) (b) of the transition, the cross sections at four locations along the length are shown in Fig. 1. The input port at section A A is a CPS with strip conductor width W 1 and separation S 1. At section B B the CPS overlaps the ground plane of the slotline and transforms to coupled microstrip lines of width W with odd-mode excitation. The separation S between the coupled microstrip lines gradually diverges beyond B B to C C, but the strip width remains fixed at W. At section C C, the coupled microstrip lines are totally decoupled and behave as two independent lines. Beyond this plane, the CPS is terminated in a short circuit arc of radius R. Coupling between the CPS and the slotline takes place at the location where the short circuit arc crosses S 1 t S W 1 W 1 W W the slotline at right angles. The slotline has a slot of width W s. Further, the slotline is terminated in a short circuit at a distance L 3, which is approximately l g(slotline) /4, where l g(slotline) is the guide wavelength in the slotline at the design frequency f. The measured return loss and insertion loss characteristics of the transition are presented in Figs. 11a and 11b, respectively. Table 3 summarizes the transition performance. Table 3. Coplanar Stripline-to-Slotline Transition Dimensions and Characteristics Substrate High-resistivity silicon (re5 3 O cm) Thickness D (mm).95 e r 11.7 t (mm) E.5 Coplanar Stripline ε ε r (a) D ε ε r. Ground plane (b) W 1 (mm).8 S 1 (mm).54 W (mm).4 S (mm).54 L 1 (mm) 6.35 L (mm) 3.94 R (mm) 1.7 W W Slotline ε ε r (c) W s Figure 1. Cross-sectional view depicting transition between coplanar stripline to slotline: (a) at cross section A A; coplanar stripline; (b) at cross section B B; coupled microstrip lines; (c) at cross section C C; decoupled microstrip lines; (d) at cross section D D; slotline. ε ε r (d) W s. W S (mm).1143 L S (mm) 7.13 L 3 (mm) 3.8 Measured Characteristics per Transition f (GHz) 1. S 11 (db) r 1. S 1 (db) 1.45 Bandwidth (%) at f 3. Source: Ref.18.

37 816 COPLANAR WAVEGUIDE COMPONENTS BIBLIOGRAPHY 1. R. E. DeBrecht, Coplanar balun circuits for GaAs FET high-power push-pull amplifiers, 1973 IEEE G-MTT Int. Microwave Symp. Digest, Boulder, CO, 1973, pp R. N. Simons, G. E. Ponchak, R. Q. Lee, and N. S. Fernandez, Coplanar waveguide fed phased array antenna, 199 IEEE Antennas and Propagation Symposium Digest, Dallas, TX, May 199, Vol. IV, pp Y.-S. Lin and C. H. Chen, Novel lumped-element uniplanar transitions, IEEE Trans. Microwave Theory Tech. 49(1):3 33 (Dec. 1). 4. C.-H. Ho, L. Fan, and K. Chang, Broad-band uniplanar hybrid-ring and branch-line couplers, IEEE Trans. Microwave Theory Tech. 41(1): (Dec. 1993). 5. K. Tilley, X.-D. Wu, and K. Chang, Coplanar waveguide fed coplanar strip dipole antenna, Electron Lett. 3(3): (Feb. 1994). 6. M.-Y. Li, K. Tilley, J. McCleary, and K. Chang, Broadband coplanar waveguide-coplanar strip-fed spiral antenna, Electron Lett. 31(1):4 5 (Jan. 1995). 7. V. Trifunovic and B. Jokanovic, Four decade bandwidth uniplanar balun, Electron. Lett. 8(6): (March 199). 8. R. N. Simons, Coplanar Waveguide Circuits, Components, and Systems, Wiley, New York, 1, Sec B. Jokanovic and V. Trifunovic, Double-Y baluns for MMICs and wireless applications, Microwave J. 41(1):7 9 (Jan. 1998). 1. R. N. Simons, N. I. Dib, and L. P. B. Katehi, Coplanar stripline to microstrip transition, Electron. Lett. 31(): (Sept. 1995). 11. Y.-H. Suh and K. Chang, A wideband coplanar stripline to microstrip transition, IEEE Microwave Wireless Compon. Lett. 11(1):8 9 (Jan. 1). 1. T. Chiu and Y.-S. Shen, A broadband transition between microstrip and coplanar stripline, IEEE Microwave Wireless Compon. Lett. 13():66 68 (Feb. 3). 13. D. Jaisson, A single-balanced mixer with a coplanar balun, Microwave J. 35(7):87 96 (July 199) (corrections on p. 1, Sept. 199). 14. D. Jaisson, Transition from a microstrip line to an asymmetrical coplanar waveguide, Microwave J. 37(6): (June 1994). 15. R. N. Simons, N. I. Dib, R. Q. Lee, and L. P. B. Katehi, Integrated uniplanar transition for linearly tapered slot antenna, IEEE Trans. Anten. Propag. 43(9):998 1 (Sept. 1995). 16. H. Y. Lee and T. Itoh, Wideband and low return loss coplanar strip feed using intermediate microstrip, Electron. Lett. 4(9):17 18 (Sept. 1988). 17. K. Goverdhanam, R. N. Simons, and L. P. B. Katehi, Microcoplanar stripline new transmission media for microwave applications, 1998 IEEE MTT-S Int. Microwave Symp. Digest, Baltimore, MD, 1998, Vol., pp R. N. Simons, Novel coplanar stripline to slotline transition on high resistivity silicon, Electron. Lett. 3(8): (April 1994). COPLANAR WAVEGUIDE COMPONENTS 1. INTRODUCTION RAINEE N. SIMONS NASA Glenn Research Center Cleveland, Ohio Coplanar waveguide (CPW) is a type of planar transmission line suited for microwave integrated circuits (MICs) as well as for monolithic microwave integrated circuits (MMICs). The unique feature of this transmission line is that it is uniplanar in construction, which implies that all the conductors are on the same side of the substrate. This attribute simplifies realization of short- or open-circuited terminations and mounting of series and shunt lumped or active elements. In addition, it also circumvents the need for via holes. Furthermore, simplifies manufacturing and allows fast and inexpensive characterization using on-wafer techniques. In this article, the design considerations for a CPW 3-dB hybrid coupler, 181 hybrid coupler, 3-dB magic-t, and aperture coupled patch antenna are presented. The hybrid couplers and the magic Ts are widely used in MICs as 91 and 181 power dividers and combiners that form the basic building blocks for subsystems such as balanced mixers, balanced upconverters, balanced modulators, balanced amplifiers, and balanced frequency multipliers. In addition, they are also used in the construction of image rejection mixers and upconverters. Furthermore, when hybrid couplers are integrated into the feed system of printed patch antennas and arrays, they can excite the radiator in the desired amplitude and phase to generate a linear or circular polarization. When magic Ts are integrated with antennas, they can form a comparator to produce the monopulse sum and difference signals needed in tracking radars. In contrast with a Lange coupler, the above mentioned couplers do not require narrow strip conductors and slots, which impact tolerance and yield. To keep the chip size small and thus lower the cost, the designs presented here are for reduced-size hybrid couplers and magic Ts.. REDUCED-SIZE 3-dB BRANCHLINE HYBRID Equivalent circuits of standard and reduced-size branchline hybrid are shown in Figs. 1a and 1b, respectively. In a standard hybrid the characteristic impedance of the branchline and the throughline are Z and Z /O, respectively. If in the reduced-size hybrid the characteristic impedance of the both the branchline and the throughline are Z, where Z is greater than Z, then the electrical length of the branchline y 1, the electrical length of the throughline y, and the lumped capacitance C are given

38 COPLANAR WAVEGUIDE COMPONENTS 817 Port 1 Port 4 λ g1 4 5Ω λ g 4 35Ω 35Ω λ g 4 (a) Z = 7.7Ω 5Ω Z = 7.7Ω Port Port 3 by Ref. 1: y 1 ¼ arcsin Z ð1þ Z Z y ¼ arcsin pffiffiffi ðþ Z sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ocz ¼ 1 Z sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ Z : ð3þ Z Z λ g1 4 C λ g C 1 Port 1 Port Z = 7.7 λ g 8 Z = 7.7Ω Port 4 Port 3 C (b) Figure 1. (a) Standard branchline hybrid; (b) reduced-size branchline hybrid. The guide wavelength on the line is denoted as l g. C As an example, when Z ¼ 5 O and Z ¼ 7.7 O, these three equations give y 1 ¼ 451, y ¼ 31. This implies that the branchline and the throughline lengths y 1 and y are l g /8 and l g /1, respectively, where l g is the guide wavelength. The phase difference between the power to the direct port and the power to the coupled port, that is, the phase of (S 1 /S 31 ), is computed in Ref. 1 for the reduced-size hybrid and the standard quarter-wavelength hybrid. The results show that the bandwidth over which the phase difference is 91 is narrower in the case of the reducedsize hybrid. In a coplanar waveguide (CPW) if the center strip conductor width is held fixed and the slot width increased, the characteristic impedance increases and the conductor loss reduces. Hence, the insertion loss of the reduced-size hybrid that has an impedance higher than that of the standard hybrid is not degraded by size reduction. An experimental reduced-size hybrid fabricated on a semiinsulating GaAs is reported in Ref. 1. The constantimpedance transmission line is a CPW with a center strip width of 1 mm and characteristic impedance of 7. O. The lengths of the branchline and the throughline are l g(cpw) / 8 and l g(cpw) /1, respectively, at 5 GHz. Air bridges are used at the CPW junctions to tie the ground planes at equal potential and suppress the coupled slotline even mode. Metal insulator metal (MIM) shunt capacitors are located at the corners of the inner ground metal. The insulator film is Si 3 N 4. The size of the fabricated hybrid is 5 5 mm. This is more than 8% smaller than a standard branchline hybrid. The measured performance of the hybrid in Ref. 1 over the frequency band of GHz shows that the power coupled from port 1 to ports and 3 is within db, return loss at port 1 is better than 1. db, and the isolation between ports 1 and 4 is better than 1. db. As a concluding remark, it may be mentioned that in Ref. a small 91 hybrid coupler based on the Wheatstone bridge principle is demonstrated at a center frequency of 4. GHz. 3. REDUCED-SIZE 181 RING HYBRID The equivalent-circuit representation of a standard 181 ring hybrid is shown in Fig. a. To reduce the size of the hybrid, first the quarter-wavelength lines of 7 O characteristic impedance are replaced by one-eighth wavelength lines of 1 O characteristic impedance with lumped capacitances at the ends. Then, the three-quarter wavelength line of 7 O characteristic impedance is replaced by a p-network consisting of lumped series capacitance and shunt inductances. The lumped shunt inductances and capacitances almost cancel each other, resulting in the equivalent circuit [1] shown in Fig. b. Besides size reduction, the reduced-size ring hybrid has the advantage of being able to interchange ports at the location of the series metal insulator metal (MIM) capacitor [1] as illustrated in Fig. 3. In Fig. 3a, the output ports and 3 are located on opposite sides of port 4. By interchanging the location of ports and 4, the output ports and 3 are located side by side as shown in Fig. 3b. Further, if port 4 is used as the input port, then the outputs at ports and 3 are 181 out of phase as discussed in Ref. 3. This feature greatly simplifies balanced mixer construction using a ring hybrid [4]. An experimental reduced-size ring hybrid fabricated on a semiinsulating GaAs substrate with elevated CPW as the transmission line has been reported in Ref. 5. The

39 818 COPLANAR WAVEGUIDE COMPONENTS 3λ g 4 MIM capacitor 7Ω Port Port 4 Port Port 4 Port 1 C λg, 1 Ω lines 8 λ g 4 7Ω 7Ω λ g 4 C Port 3 (a) Port 1 7Ω λ g 4 (a) Port 3 Port 4 MIM capacitor Port jy Port Port 4 λ g 8 1Ω 1Ω λ g 8 Port 1 C λg, 1 Ω lines 8 Port 1 C 1Ω λ g 8 C Port 3 C Port 3 (b) Figure. Representation of (a) standard 181 ring hybrid or rat race with transmission lines; (b) equivalent reduced-size 181 ring hybrid or ratrace with transmission lines and lumped elements. The wavelength on the line is denoted as l g. elevated CPW has the advantage of reducing both the insertion loss as well as the chip area as discussed in Ref. 3. The hybrid consists of three 1 8th-wavelength 1-O elevated CPWs, a series capacitor and two shunt capacitors in place of the three l g /4, and a 3l g /4 7-O transmission line as in a standard ring hybrid. In the experimental hybrid, the elevated CPW is meandered to further reduce the overall size. The ring hybrid is schematically shown in Fig. 4. The measurements show that the coupling loss (7S 1 7, 7S 4 7) of the hybrid is on the order of db, return loss (7S 7) better than 17. db, and isolation (7S 3 7) better (b) Figure 3. (a) Normal port layout; (b) port layout convenient for balanced mixer applications. than 18. db over the frequency range GHz. The chip size is on the order of.5.55 mm. 4. REDUCED-SIZE 3-dB MAGIC T The circumference of a magic-t circuit is typically about one guide wavelength. To reduce the circumference and thereby the overall size, consider the hybrid ring topology [6] shown in Fig. 5. In this circuit it is assumed that the transmission lines in opposite ring arms are identical and that the hybrid ring is matched at all ports. The phase shifter may be located anywhere in any of the four arms. In this hybrid a signal fed to port 1 (H arm) will be split equally and be in phase between the two output ports

40 COPLANAR WAVEGUIDE COMPONENTS 819 MIM capacitor Port Port 4 λ g 1 Ω,, elevated CPW 8 characteristic impedances of the lines in the ring arms. The impedance Z is the terminating impedance. To obtain real values for characteristic impedances, the following condition must be satisfied [6]: p cos y 1 þ cos y o ffiffiffi ð6þ Port 3 C In a symmetric design all four ring arms are identical. In such a case Eqs. (4) and (5) reduces to [7]: pffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z c ¼ Z 1 cot y ð7þ Port 1 Figure 4. Reduced-size 181 ring hybrid with meandered elevated CPW. and 3 (balanced arms). Similarly, a signal feed to port 4 (E arm) will be split equally and be out of phase between the two output ports and 3. The following design equations hold good [6]: C An experimental reduced-size magic T [6,7] realized with symmetric coplanar striplines is shown in Fig. 6a. Coplanar striplines are chosen because they allow easy crossover of the two strips to realize the 181 phase shifter needed at the E arm. The crossover may be placed at any position along the arm or at the T junction as shown in Fig. 6b. In Ref. 7 y is equal to 61 and for Z equal to 5 O, Z c from (7) is equal to 57.6 O. This design results in a ring circumference of.67 guide wavelength. The magic T is fabricated on a 54-mm-thick alumina substrate (e r ¼ 9.9), W 1 S1 W 1 W S W Z c1 ¼ sin y 1 þ sin y cos y 1 cos y Z sin y 1 ð4þ Balanced-arm Port #3 Crossover g Z c ¼ sin y 1 þ sin y cos y 1 cos y Z sin y where y i (i ¼ 1,) is the electrical length of arm i at the center frequency f. The impedances Z c1 and Z c are the ð5þ H-arm Port #1 Four coplanar stripline arms Z c, θ E-arm Port #4 Output balanced Port #3 Z c1, θ 1, l 1 Zc, θ, l Z Balanced-arm, Port # (a) CPW feedline, Z H-arm Port #1 Z E-arm Port #4 To Port #3 Slotline feed Z 18 phase shift Crossover E-arm Z c, θ, l Z c1, θ 1, l 1 Output balanced Port # Z Figure 5. Generalized ring magic T. To Port # (b) Coplanar stripline (CPS) Figure 6. (a) Reduced-size ring magic T (from Ref. 7, copyright r IEE) (b) alternate implementation with slotline feed for E-arm (from Ref. 6, copyright r IEE).

41 8 COPLANAR WAVEGUIDE COMPONENTS Table 1. Reduced-Size 3-dB Ring Magic T Circuit Parameters and Measured Characteristics Substrate (alumina) e r 9.9 Thickness (mm) 54 Metallization thickness (mm) 4. Coplanar Waveguide Strip width S 1 (mm) 5 Slot width W 1 (mm) 3 Z (O) 5 Coplanar Stripline Strip width S 1 (mm) 3 Slot width S (mm) 6 Z c (O) 57.6 y (deg) 6 Circumference l g.67 Ring radius (mm) 3478 Crossover gap g (mm) 1 Measured Performance Center frequency f (GHz) 6 Frequency range (GHz) Transmission when fed at H-arm mag (S 1 ), mag (S 31 ) (db) Transmission when fed at E-arm mag (S 4 ), mag (S 34 ) (db) Output magnitude balance when fed at H-arm.37.5 mag (S 1 /S 31 ) (db) Output phase balance when fed at H-arm 74 phase (S 1 /S 31 ) (deg) Output magnitude balance when fed at E-arm.47.5 mag (S 4 /S 34 ) (db) Output phase balance when fed at E-arm 1874 phase (S 4 /S 34 ) (deg) Return loss mag (S ) and mag (S 33 ) (db) o 1. Isolation mag (S EH ), mag (S 3 ) (db) o 3. h h 1 Dumbbell shaped aperture a W b S 1 L L L t L 1 Microstrip patch Antenna substrate ε ε r CPW input port Feed substrate ε ε r1 antenna [1], the patch and the GCPW feed structure, with a series gap L 1 in the center conductor, are fabricated on separate substrates, and the aperture is etched in the common ground plane. The aperture is located directly R W Common ground plane S W Bond wires CPW feed line Figure 7. Grounded coplanar waveguide aperture-coupled patch antenna: S ¼.76 cm, W ¼.5 cm, L ¼.711 cm, L 1 ¼.5 cm, L ¼.5 cm, W ¼.69 cm, a ¼.76 cm, b ¼ 1.14 cm, h 1 ¼.51 cm, e r1 ¼., h ¼.5 cm, e r ¼., L t ¼.711 cm, S 1 ¼.355 cm, R ¼.843 cm. and the conductor thickness is 4 mm. The geometric parameters and the measured performance of the magic T are summarized in Table 1. The magic T has a bandwidth slightly larger than 1 octave. As a concluding remark, it may be mentioned that other designs for magic Ts can be found in Refs in the literature. Amplitude, db Angle, deg (a) COPLANAR WAVEGUIDE APERTURE-COUPLED PATCH ANTENNA Aperture-coupled feeding is attractive because of certain advantages, such as lack of physical contact between the feed and radiator, wider bandwidth, and better isolation between antennas and the feed network. Furthermore, aperture-coupled feeding allows independent optimization of antennas and feed networks by using substrates of different thickness or permittivity. A grounded coplanar waveguide (GCPW) aperture-coupled patch antenna is schematically illustrated in Fig. 7. In the experimental Amplitude, db Angle, deg (b) Figure 8. Measured radiation patterns for the grounded coplanar waveguide aperture-coupled patch antenna: (a) E plane; (b) H plane

42 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 81 above the series gap. Thus, microwave power is coupled from the GCPW feedline to the patch through the aperture. In the experimental antenna, the patch is displaced by B.3 cm from the center of the aperture and the GCPW stub length L is adjusted to provide the best impedance match to the feedline. The radiation from the antenna is linearly polarized with the plane of polarization parallel to the patch side of dimension a. The measured return loss is about 16.9 db at the design frequency of 1.65 GHz as reported in Ref. 1. Typical measured E- and H-plane radiation patterns [1] for the GCPW aperture-coupled patch antenna are shown in Figs.8aand8b,respectively.Thepatternslookfairlysymmetric and exhibit a 3 db beamwidth of about 61 and 51 in the E and H planes, respectively. The measured front-toback ratio is B14. db, which is typical for an aperture-coupledpatchantenna.finally,inref.13anaperture-coupled patch antenna with series slotline stubs in the CPW ground planes, instead of a series gap in the CPW center strip conductor,is demonstrated.the characteristics of this antenna are similar to those presented above. BIBLIOGRAPHY 1. T. Hirota, A. Minakawa, and M. Muraguchi, Reduced-size branchline and rat-race hybrids for uniplanar MMIC s, IEEE Trans. Microwave Theory Tech. 38(3):7 75 (March 199).. M. -H. Murgulescu, P. Legaud, E. Penard, and I. Zaquine, New small 91 hybrid coupler, Electron. Lett. 3(16): (Aug. 1994). 3. R. N. Simons, Coplanar Waveguide Circuits, Components, and Systems, Wiley, New York, 1, Chap., Sec T. Hirota and M. Muraguchi, K-band frequency up-converters using reduced-size couplers and dividers, 1991 IEEE GaAs IC Symp. Monterey, CA, Oct. 3, 1991, pp H. Kamitsuna, A very small, low-loss MMIC rat-race hybrid using elevated coplanar waveguides, IEEE Microwave Guided Wave Lett. (8): (Aug. 199). 6. M. -H. Murgulescu, E. Penard, and I. Zaquine, Design formulas for generalized 181 hybrid ring couplers, Electron. Lett. 3(7): (March 1994). 7. M. -H. Murgulescu, E. Moisan, P. Legaud, E. Penard, and I. Zaquine, New wideband,.67l g circumference 181 hybrid ring coupler, Electron. Lett. 3(4):99 3 (Feb. 1994). 8. L. Fan, C.-H. Ho, S. Kanamaluru, and K. Chang, Wide-band reduced-size uniplanar magic-t, hybrid-ring, and deronde s CPW-slot couplers, IEEE Trans. Microwave Theory Tech. 43(1): (Dec. 1995). 9. M. Aikawa and H. Ogawa, A new MIC magic-t using coupled slot lines, IEEE Trans. Microwave Theory Tech. MTT-8(6): (June 198). 1. T. Hirota, Y. Tarusawa,and H. Ogawa, Uniplanar MMIC hybrids a proposed new MMIC structure, IEEE Trans. Microwave Theory Tech. MTT-35(6): (June 1987). 11. M. Aikawa and H. Ogawa, Double-sided MIC s and their applications, IEEE Trans. Microwave Theory Tech., 37(): (Feb. 1989). 1. R. Q. Lee and R. N. Simons, Coplanar waveguide aperturecoupled microstrip patch antenna, IEEE Microwave Guided Wave Lett. (4): (April 199). 13. R. N. Simons and R. Q. Lee, Coplanar waveguide aperture coupled patch antennas with ground plane/substrate of finite extent, Electron. Lett. 8(1):75 76 (Jan. 199). COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 1. INTRODUCTION LEI ZHU Nanyang Technological University Singapore The coplanar waveguide (CPW) was invented by Wen [1] in 1969 as a novel surface strip transmission line fabricated on a dielectric substrate. As the strip conductor is deposited on the same surface as the two ground planes in close proximity, the CPW transmission line has demonstrated several advantageous features over the conventional microstrip line, for instance, easy surface mounting of external devices, easy fabrication of both shunt and series passive elements, low-frequency dispersion, and easy adjustment of desirable characteristic impedance. Since its proposal, the CPW technology has been progressively gaining a tremendous application in exploration of advanced RF and microwave integrated circuits, modules, and subsystems. For this purpose, much effort has been carried out to construct a new variety of modified CPW transmission lines with varied cross-sectional configurations and accurately characterize their propagation performance in theory and experiment, as summarized in two relevant books [,3]. In particular, various static and fullwave methods have been effectively developed to deal with these inhomogeneous transmission lines and derive the two per unit length transmission parameters, i.e., effective dielectric constant and characteristic impedance. This article focuses on the fundamentals of various CPW transmission lines developed so far, including their geometric schematics, transmission characteristics, modeling techniques, and closed-formed design formulas: 1. The three most popular CPW lines with infinite and finite ground widths as well as the backed conductor are comprehensively described to exhibit their transmission performance versus strip/slot dimension ratios, operating frequency, and strip conductor profile.. Low-transmission-loss shielded CPW, suspended CPW, nonleaky CPW, micromachined CPW, and cavity-assisted CPW are briefly investigated. 3. Various coupled CPW transmission lines and the extent of their weak and tight parallel coupling are discussed.

43 8 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 4. Various periodic slow-wave CPW transmission lines with series inductive and/or shunt capacitive loading in periodical intervals with the objective of miniaturization of CPW circuits are discussed, and their complete propagation characteristics in terms of effective per unit length transmission parameters are demonstrated.. BASIC CPW: GEOMETRY AND ANALYSIS The conventional CPW transmission line [1] consists of the central strip conductor and the two infinite-width ground planes on two sides that are formed in close proximity on the same surface of a dielectric substrate with finite height, as illustrated in Fig. 1a. By equalizing the electric potentials at the two ground planes, only the even symmetric dominant CPW mode can be excited. At high frequencies, this CPW mode becomes non-tem with a longitudinal component of magnetic field. In such a case, the tangential magnetic field, on the surface of the coupled slots between the strip conductor and two ground planes, becomes elliptically polarized. This conventional CPW was developed by Wen [1] for suitable applications in nonreciprocal ferrite devices. However, the CPW has been extensively utilized as a quasi-tem transmission-line candidate for exploration of a variety of MMIC s circuits Ground Substrate (a) Strip Electric field lines Magnetic field lines Ground and modules. In this way, the cross-sectional dimensions, such as slot and strip widths, are readily selected electrically short in the frequency region of operation, so as to minimize the longitudinal magnetic field component. Figure 1b shows the cross-sectional configurations of the electric and magnetic fields of the dominant quasi- TEM mode. The electric field lines start from the central conductor and then are symmetrically expanded with respect to the central plane toward the ground planes at two sides, whereas the magnetic field lines are perpendicular to their electric counterparts at any given location and surround the central conductor in terms of closed loops. Figure 1c illustrates the distribution of electric current densities on the strip conductor and ground planes, respectively, that are longitudinally oriented in an antiparallel pattern. The current density strength inherently tends to increase and then approach the infinity in an exponential function as the observed point moves to the metallic edges, regardless of either strip conductor or ground sides. In Wen s work [1], the relative permittivity is assumed much larger than the unity (e r b1) so that the finite height of a substrate can be reasonably treated as the infinity (h-n) for simplifying the theoretical analysis. But, in practice, e r and h have to be finite as shown in Fig. a. Also, the actual ground width of this CPW is usually finitely wide so as to formulate the call finite-ground CPW or FGCPW as shown in Fig. b. Further, an additional conductor plate is often formed on the opposite surface of a finite-height substrate in order to improve both the mechanical strength and power-handling capability, thus constructing the conductor-backed CPW (CBCPW) as illustrated in Fig. c. Moreover, many other modified CPW structures with dielectric multilayers and/or upper/lower b a ε r (a) t h (b) Electric current density c b a ε r (b) t h (c) Figure 1. Schematic of infinite-ground coplanar waveguide (CPW) transmission line and distribution profiles of electromagnetic field and current density in cross section: (a) 3D schematic; (b) electric and magnetic field lines; (c) electric current density. b a ε r (c) Figure. Cross-sectional view of three typical CPW transmission lines: (a) infinite-ground CPW; (b) finite-ground CPW; (c) conductor-backed CPW. t h

44 Z (Ω) COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 83 shielding conductors [,3,5 7] are built on the basis of these three basic CPW in order to meet various requirements in realizing the preferred electrical performance and employing advanced fabrication techniques. So far, extensive work in theory has been done to characterize a variety of CPW transmission lines in terms of per unit length characteristic impedance and propagation constants by developing the quasistatic and full-wave analysis approaches [,3]. Assumption of quasi-tem mode at low frequencies, the quasistatic conformal mapping technique was initially utilized to model the CPW line with infinite dielectric thickness [1] and then was significantly extended to consider a number of CPW structures with shielded and multilayered configurations [4 7]. In this way, the total per unit length capacitance can be derived as the algebraic sum of all the partial line capacitances [4 7] and separately calculated both above and below the slot interface. Generally speaking, this technique is strictly valid for the hypothesis that the interface of a substrate is considered as the magnetic wall or electric field lies on the dielectric interface. However, an accuracy of 41% for a wide range of physical dimensions and dielectric permittivity is achieved as compared with that of the full-wave spectral-domain method [6]. Of vital importance, this technique gives rise to analytical expressions for effective dielectric constants and characteristic impedance in terms of the ratio of complete elliptic integral of the first kind and its complement, K(k)/K (k), where k is the variable. The detailed mathematics of this procedure can be found in the literature [e.g., 1 7] and are not discussed here. In this section, the three sets of closed-form design formulas are used to characterize three basic CPW structures in Figs. a c with respect to various physical dimensions. For the reader s convenience, the analytical expressions of the ratio K(k)/K (k), are provided below in two different regions of the variable k for infinite- and finite-width-ground CPWs: KðkÞ K ðkþ ¼ p 4p ln½ð1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffi 4p 1 k Þ=ð1 ffiffiffiffiffiffiffiffiffiffiffiffiffi ð k 1 k ÞŠ :77Þ ð1aþ As such, the per unit length effective dielectric constant and characteristic impedance can be deduced: e re ¼ 1 þ e r 1 Kðk Þ K ðk Þ Z ¼ p 3p ffiffiffiffiffi K ðk 1 Þ Kðk 1 Þ e re K ðk 1 Þ Kðk 1 Þ Figures 3a and 3b show simulated results from Eqs. (3) and (4), respectively, with respect to the ratio of slot to strip widths (S/W in Fig. 3) under different h/w (height/ width ratios). The impedance (Z ) definitely increases as the slot is widened for all the four listed h/w because of reduced capacitive coupling between the strip conductor and two ground planes. As h/w increases, the Z o curve converges to that with very thick thickness (h/w ¼ ). Meanwhile, the effective dielectric constant (e re ) falls down ε r =1. W=1.mm h/w= S/W (a) ð3þ ð4þ KðkÞ K ðkþ ¼ ln½ð1 þ pffiffiffi k Þ=ð1 p pffiffiffi k ÞŠ ð:77 k 1Þ ð1bþ ε re = (β/k) Infinite-Ground CPW For conventional CPW with infinite-width ground as in Fig. a, the two variables k 1 and k are defined in terms of the dimensions a, b, and h, respectively, where the strip width W ¼ a and S ¼ b a: k 1 ¼ a b k ¼ sinhðpa=hþ sinhðpb=hþ ðaþ ðbþ 3.5 h/w= S/W Figure 3. Per unit length transmission parameters of the infinite-ground CPW transmission line as a function of slot width (S/W) with varying substrate thickness (h/w): (a) characteristic impedance (Z ); (b) effective dielectric constant (e re ). (b)

45 Z (Ω) 84 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES as the slot width is enlarged under the fixed finite thickness (h/w) and it eventually becomes almost independent of h if h/w is larger than as can be seen in Fig. 3b. It can be further deduced from these results that the effect of finite dielectric substrate is almost ignorable if h exceeds b ¼ W þ S... Finite-Ground CPW Practical CPW has finite-width ground planes as illustrated in Fig. b. In order to factor in the effect of finite ground, the two modified variables, k 3 and k 4, are defined as below; thus Eqs. (3) and (4) are still valid for this finite-ground CPW by using k 3 and k 4 instead of k 1 and k : sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 3 ¼ a 1 b =c b 1 a =c sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 4 ¼ sinhðpa=hþ 1 sinh ðpb=hþ= sinh ðpc=hþ sinhðpb=hþ 1 sinh ðpa=hþ= sinh ðpc=hþ ð5aþ ð5bþ The calculated results are depicted in Figs. 4a and 4b, in which W 1 ¼ a, S ¼ b a, and W ¼ c b indicate the strip, slot, and finite-ground widths, respectively. As the groundto-strip width ratio of W /W 1 is reduced, Z tends to increase and the effective e re also goes up slowly. This may be attributed to the weakened strip-to-ground coupling and partial transfer of field energy from the free space to dielectric substrate. Moreover, we can find that the effect of the two lateral finite grounds becomes much smaller as W is widened beyond W 1, especially for the narrow slot width (S)..3. Conductor-Backed CPW An additional conductor plate is put on the lower interface of a substrate to form the conductor-backed-cpw (CBCPW) as shown in Fig. c. This CBCPW resembles a mixed coplanar-microstrip structure, thus supporting a parasitic microstriplike mode in addition to the dominant CPW mode. The CPW-mode characteristic impedance may be considerably reduced by the shunt connection of the two per unit length capacitances between strip and lateral ground as well as the strip and backed conductor. The performance of this CBCPW can also be characterized using the conformal mapping technique [,3]. For this purpose, an alternative variable k 5 is defined as follows: k 5 ¼ tanhðpa=hþ tanhðpb=hþ As such, the two per unit length parameters can be calculated in terms of the two closed-form equations: Kðk 5 Þ=K ðk 5 Þ e re ¼ 1 þðe r 1Þ Kðk 1 Þ=K ðk 1 ÞþKðk 5 Þ=K ðk 5 Þ Z ¼ 6p 1 pffiffiffiffiffi Kðk 1 Þ=K ðk 1 ÞþKðk 5 Þ=K ðk 5 Þ e re ð6þ ð7þ ð8þ ε re = (β/k ) ε r =1. h=1.7mm 6 W 1 =1.mm S/W 1 = W /W 1 (a) W /W 1 (b) Figure 4. Per unit length transmission parameters of finiteground CPW transmission line as a function of finite-ground width (W /W 1 ) with varying slot width (S/W 1 ): (a) characteristic impedance (Z ); (b) effective dielectric constant (e re ). Figures 5a and 5b show the results of these two parameters versus the thickness-to-strip aspect ratio (h/w) under varied slot-to-strip aspect ratios (S/W). When the substrate is thin (i.e., with small h/w), the capacitive coupling between the strip and backed conductor is significantly tightened, causing this CBCPW to operate like a microstrip line with decreased characteristic impedance (Z ), as can be observed in Fig. 5a. Meanwhile, the electromagnetic field is moved to the substrate region underneath the strip conductor, thereby enlarging the effective dielectric constant (e re ) toward the dielectric permittivity (e r ), as illustrated in Fig. 5b. At a narrow slot width of S/ Wr.5, the backed-conductor effect becomes negligibly small if the thickness (h) exceeds the strip width (W), implying that this CBCPW operates as a conventional CPW as in Fig. a. For the wide slot width (S/W41.), both Z and e re seem to depend on the substrate thickness (h/w) to some extent because of the concurrent existence of the strip-to-ground and strip-to-conductor coupling S/W 1 =

46 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 85 Z (Ω) ε re =(β/k ) ε r =1. W=1.mm S/W= h / W (a) S/W= h / W (b) Figure 5. Per unit length transmission parameters of conductorbacked CPW transmission line as a function of substrate thickness (h/w) with varying slot width (S/W): (a) characteristic impedance (Z ); (b) effective dielectric constant (e re ). Until now, the three basic CPW transmission lines have been characterized under the quasistatic assumption. The formulas presented above are well verified at low frequencies in comparison with the spectral-domain approach as discussed in Ref. 6. However, because of the inhomogeneous layers in these CPW, the two per unit length parameters become frequency-dispersive as the operating frequency increases as demonstrated extensively in the literature [,3,8]. In addition, the higher-order modes may operate above their relevant cutoff frequencies and their parasitic effects cannot be taken into account in the design formulas above. Also, many other factors, such as the strip/ground conductor thickness and cross-sectional profiles, may seriously affect these two parameters. In order to rigorously model these CPW structures, a number of full-wave numerical approaches, such as the mode-matching method, spectral-domain method, method of lines, and the finite-element method, were successfully developed in the 197s 199s. As the detailed procedures of these methods can be found in a contributed book [8], a lengthy and complicated formulation of these approaches in mathematics would be beyond the main objectives of this article and is not included here. We nevertheless include some typical results using these full-wave approaches to demonstrate the electrical performance of CPW transmission lines with varied strip/ conductor configurations [9,1]. Figures 6a and 6b show the calculated frequency-dispersive effective dielectric constants (e re ) of the conductor-backed CPW, CBCPW, with rectangular or trapezoidal conductor configurations. In all these structures, e re seems to be frequency-independent at low frequencies (fo GHz) with a substrate thickness of h ¼ 1 mm. This parameter increases sharply at the beginning and then more gradually as f increases, and eventually reaches to the relative permittivity of this substrate (i.e., e r ¼ 1.9), as f is beyond 1 GHz. In fact, ε re ε re t= 7 5μm 6 1μm 5 ε r =1.9 h=1μm W=7.4μm S=18.1μm f(ghz) (a) ε r =1.9 θ = 45 h=1μm 7 9 W=7.4μm S=18.1μm 6 S W S t ε r h f(ghz) (b) Figure 6. Frequency-dependent effective dielectric constant (e re ) of conductor-backed CPW transmission line with rectangular or trapezoidal edge profile versus (a) conductor thickness (h) and (b) edge angle (y). S W ε r θ S θ t

47 86 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES all the electromagnetic (EM) fields definitely tend to be moved into the substrate region with high permittivity at high frequencies, thus causing the slow-wave propagation behavior with reduced velocity, which is the common frequency-dispersive feature for all CPW transmission lines. As can be observed in Fig. 6a, e re at low frequencies gradually decreases as the strip/ground thickness (t) increases from to 1 mm. Because of tightened coupling between the central strip and two-side grounds for nonzero t, a small portion of EM fields in the substrate is moved to the free-space slot region. Figure 6b shows us that the varied angle (y) of conductor edge wall affects the transmission properties. As y increases, e re at low frequencies appears to drop because of the upward-oriented EM fields between the strip and ground. S d W (a) d S h 1 t h 3. MODIFIED CPW WITH ENHANCED PERFORMANCE In this section, a variety of modified CPW transmission lines that have many promising features for applications in high-performance and millimeter-wave circuits will be overviewed. Figure 7a is the cross-sectional view of an initial CPW with metallic enclosure. This shielded CPW can completely avoid the unexpected radiation loss that occurs in the unbounded CPW discussed above. However, because of the high conductivity loss and serious frequency dispersion, the preferred construction for the CPW is suspension in a metallic enclosure as shown in Fig. 7b. This type of CPW was originally reported by Hatsuda [11], and the dominant-mode performance for this CPW is analyzed approximately using the relaxation method under the quasistatic assumption. To facilitate the mechanical installation, an improved CPW, the nonsymmetrically shielded CPW (NSCPW) [1] is shown in cross section Fig. 7c. This NSCPW is constructed by mounting the CPW in a nonsymmetric enclosure with respect to the upper and lower regions through the grooves. In addition to the low transmission loss and low frequency dispersion, this shielded NSCPW is best suited for mounting solid-state devices, constructing matching elements in series and shunt, and formulating the biasing circuits [1]. The propagation characteristics of the dominant and high-order modes are theoretically studied using full-wave methods [1,13], and the predicted phase constants of these modes are experimentally verified [1] by measuring the multiple transmission peaks of the two-port NSCPW resonator with coaxial launchers at two ends. The theoretical characteristics of multilayered CPW transmission lines have been reported in the literature [5 7]. Three of these CPW structures that exhibit enhanced electrical performance, namely, elevated, insulated, and nonleaky CPW, are discussed here (see crosssectional views in Fig. 8). The elevated CPW in Fig. 8a is proposed [14] for construction of a nonlinear transmission line fabricated with Schottky diodes on GaAs substrate. This CPW has several attractive features such as low loss, high wave velocity, and broad frequency bandwidth. Its propagation performance is characterized with respect to varied elevated heights [15] using the full-wave approach. The CPW is fabricated on silicon substrate for low-cost S S W (b) W d (c) d 1 d Figure 7. Cross-sectional view of enclosed CPW transmission lines: (a) shielded CPW; (b) suspended CPW; (c) suspended CPW with pedestal. application in radiofrequency integrated circuits (RFICs). Due to high attenuation, the CPW is usually constructed by forming an insulated layer, such as low-loss polyimide [16] or SiO [17], above the silicon substrate, as shown in Fig. 8b. The measured results show that attenuation can be reduced if the insulated layer is thick relative to the strip and slot widths [16]. Figure 8c shows the multilayered CBCPW with the upper metallic cover, and this CBCPW is one of two possible nonleaky CPW structures [18]. As demonstrated in the early literature, the presence of the backed conductor in the CBCPW causes unexpected power leakage into transverse directions in the form of a parallel-plate wave. As discussed by Liu et al. [18], this nonleaky CPW is established by forming an additional upper layer or insulated layer with higher permittivity above or below the strip/slot interface. Simulated results S S h 1 t h h h t h h 1

48 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 87 S W S S W S GaAs (a) d t h h S W S t h 1 S W (a) S Silicon h (b) θ h S W S Air h 1 (b) h h 3 S W S (c) Figure 8. Cross-sectional view of unbounded CPW transmission lines: (a) elevated CPW; (b) insulated CPW; (c) nonleaky CPW. (c) h show that the dominant CPW mode is purely bound without leakage over certain frequency ranges as verified by experiment [18]. Microshield line originated with Dib et al. [19] as a new type of monolithic transmission line. Figure 9a shows its cross-sectional geometry, in which the ground plane is deformed to totally or partially surround the inner conductor. By using the membrane technology, the inner conductor can be suspended in air, thus eliminating dielectric loss even at high frequencies. This line may be considered as an enhancement of the CPW or microstripline structure. As compared with the conventional CPW investigated above, this microshield line may have several advantages, such as no requirement for via holes or airbridges for ground equalization, reduced radiation loss, reduced electromagnetic interference, and a wide impedance range [19]. Since then, various types of microshield lines have been developed and analyzed using the efficient static or accurate full-wave methods. The V-shaped microshield line with triangular cavity profile is illustrated in Fig. 9b. Using the conformal mapping technique under the static assumption [], a set of closed-form expressions is derived for characterization of symmetric and asymmetric V-shaped lines. In addition, Figs. 9c and 9d show the microshield lines with upward- and downward-oriented trapezoidal shapes, respectively, which may be the practical shape in fabrication. Their performances are studied in [1] with respect to positive or negative sidewall slope [i.e., angle (f)], implying that the effect of these nonvertical sidewalls can be minimized by keeping these sidewalls away from the slot edges. The silicon micromachining technique has been developed to effectively remove the lossy dielectric material below, above, or around the coupled apertures in CPW in an effort to minimize propagation loss and reduce frequency dispersion. Figure 1a shows the micromachined CPW S W Figure 9. Cross-sectional view of microshielded CPW transmission lines with various cavity profiles: (a) rectangular shape; (b) triangular shape; (c,d) trapezoidal shape. [], where the material underneath the coupled apertures is partially removed for construction of the freespace V-shaped grooves. This resulting line minimizes the total propagation loss since the EM fields are distributed mainly in the lossless V-shaped region and current density flow on the conductor is reduced. Figure 1b shows a practical microshielded membrane CPW that is fabricated by attaching two silicon wafers together [3,]. The upper wafer, with a metallized cavity, supports a membrane with the CPW. Because of an extremely thin electric membrane, the overlapping capacitances between the top ground planes and cavity sidewalls are very large in the microwave region, thus virtually short-circuiting the overlapped region. The lower wafer is metallized on the top surface and provides the bottom wall of the cavity. Figure 1c shows a micromachined overlay CPW [3]. By partially elevating the edges of the central conductor and further overlaying them with the two outer ground planes, this CPW has a lower propagation loss because the current density is redistributed on the conductors and the impedance range widens. In practice, the CPW is usually placed on a ground plane for mechanical support, inadvertently giving rise to (d) S h

49 88 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES S W S c V-groove Silicon h 1 h b a ε r t h (a) (a) the conductor-backed CPW. In this CBCPW, the dominant CPW mode may be coupled to the parallel waveguide mode, which propagates transversally, causing the unwanted power leakage [4,5]. In addition, the substrate and side ground planes are always finitely widened, and this transversal leakage leads to substrate resonance and multiple-mode interference. In order to address this issue, the highly lossy silicon-doped substrate is inserted between the CPW and backed conductor as illustrated in Fig. 1d. This silicon submount layer operates as the absorbing layer to absorb this transversal leakage and eventually suppress the potentially harmful resonance. This suppression method is examined in numerical simulation and also verified by experimental characterization of the fabricated GaAs CBCPW [5]. Tien et al. [4] have shown that by laterally short-circuiting the side grounds with the lower ground, the electromagnetic field of the dominant CPW mode can be confined mostly within the surrounded conductor, thus alternatively suppressing this parasitic resonance. 4. COUPLED CPW S S S W (b) W (c) W (d) S S S E Silicon Silicon Silicon Figure 1. Cross-sectional view of silicon-based low-loss CPW transmission lines: (a) micromachined CPW with V-shaped groove; (b) microshielded membrane CPW; (c) micromachined overlay CPW; (d) Si-layer submounted CPW. h t h 1 h h 1 c b a ε r d (b) b a ε r c b a d (d) (c) Figure 11. Cross-sectional view of various coupled CPW transmission lines: (a) edge-coupled; (b) backed-conductor-coupled; (c) broadside-coupled; (d) parallel-coupled. odd-mode propagation velocities. As shown in Fig. 11a, it is constructed by placing the two parallel strip conductors in close proximity. Due to strong interaction between these two conductors, the EM power is coupled from one line to the other, and the amount of coupling depends mainly on the distance of separation a and longitudinal length of the coupling section. Under the approximate assumption of infinitely thick substrate, the static conformal mapping technique is applied to characterize the two per unit length capacitances in conjunction with the even and odd dominant modes. As a result, the two sets of closedform formulas can be derived to calculate the characteristic impedance values and effective dielectric constants. Because the substrate is always electrically finite, the even- and odd-mode transmission parameters of the coupled CPW in Fig. 11a with finite thickness are obtained using the same static technique as employed by Wen [6]. The relevant analytical formulas can be found in Ref. 7. In the even-mode case, the two transmission parameters, e re,e and Z,e, can be obtained ε r t h t h t h The traditional coupled CPW was originally presented [6] for design of directional couplers with improved isolation due to smaller difference between the even- and e re;e ¼ 1 þ e r 1 Kðk e ÞK ðk e1 Þ K ðk e ÞKðk e1 Þ ð9þ

50 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 89 where Z ;e ¼ p 6p ffiffiffiffiffiffiffiffi e re;e K ðk e1 Þ Kðk e1 Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b k e1 ¼ a c a sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sinh ðpb=hþ sinh ðpa=hþ k e ¼ sinh ðpc=hþ sinh ðpa=hþ ð1þ ð11aþ ð11bþ In the odd-mode case, the two corresponding parameters, e re,o and Z,o, can be given as e re;o ¼ 1 þ e r 1 K ðk o1 Þ Kðk o1 Þ Z ;o ¼ p 6p ffiffiffiffiffiffiffiffi e re;o Kðk o Þ K ðk o Þ þ Kðk o3þ K ðk o3 Þ K ðk o1 Þ Kðk o1 Þ ð1þ ð13þ in which the three variables k o1, k o and k o3 can be analytically expressed as a function of the incomplete elliptical integral of the first kind with respect to all transverse dimensions [7]. These formulas are effectively verified by Cheng [7] in comparison with the results from the fullwave method. In fact, the traditional coupled CPW in Fig. 11a usually has weaker coupling due to edge coupling, thus resulting in a limited operating bandwidth. In order to tighten the coupling to a certain degree, an extra finite-extent backed conductor is formed on the opposite surface of a dielectric substrate underneath the coupled strip conductors [8], as shown in Fig. 11b. This backed conductor is strongly coupled with each upper strip conductor in a surface-to-surface format, thus increasing the degree of coupling between the two strip conductors. Figure 11c shows the cross-sectional view of a broadside-coupled CPW [9], in which the two CPW lines are formed at the upper and lower surfaces of a thin substrate. Under the assumed upper and lower shielding covers, the even- and odd-mode characteristics of this substrate are studied using the quasistatic technique. Numerical results [9] demonstrate a significant increase in the ratio of the two impedances, causing the coupling enhancement. However, as was the case in the CBCPW, the parallel-plate mode may be excited in such a broadside-coupled CPW to transversally propagate in the substrate between the two ground planes. This unexpected mode raises some problematic issues, such as power leakage, EM interference, and increased power loss. Thus, this broadside-coupled CPW should be constructed in a metallic enclosure that maintains electrical contact with all the ground planes. In addition, a triple-line-coupled CPW has been characterized by Cheng [3], and its cross-sectional geometry is drawn in Fig. 11d. By equalizing the electrical potential in the central strip with those in the two side ground planes, this arrangement can effectively suppress spurious coupling between the two CPW lines so as to avoid any signal distortion. Also, this triple line constitutes a basic block for the parallel-coupled bandpass filter. Its coupling performance is investigated using static and full-wave approaches such as conformal mapping [3]. 5. PERIODIC SLOW-WAVE CPW An infinite-extended CPW structure, loaded with identical obstacles at each periodic interval, may be considered as an effective uniform CPW transmission line [31]. This periodic CPW exhibits two fundamental properties: passband stopband selectivity and slow-wave propagation. The passband performance is basically realized by periodically interrupting the uniform CPW with series capacitive or shunt inductive elements, in which the periodicity is comparable to the guided-wavelength operation in the passband. However, because of the unexpected occurrence of multiple ripples within the passband, this periodic CPW has rarely been studied for practical design of CPW circuits. On the contrary, various periodic CPW transmission lines with slow-wave and bandstop behaviors [3 4], have generated increasing interest since the early 198s. Regardless of the various configurations and different terminologies, to my best knowledge, this class of periodic CPW commonly has two distinct features for the dominant mode: slow-wave propagation at low frequencies and stopband attenuation in the midfrequency range. In order to reduce the loss in uniform slow-wave CPW with metal insulator semiconductor (MIS) and Schottky contact configurations, a crosstie conductor grating with a periodic pattern [3] is embedded underneath the uniform CPW surface to make up the initial periodic slow-wave CPW transmission line, as shown in Fig. 1a. Then, a modified crosstie overlay slow-wave CPW [33] is constructed by swapping the crosstie conductor with the CPW layer, as illustrated in Fig. 1b. Observing the cross section of the crosstie conductor in Fig. 1a or 1b, we see that the capacitive coupling between the central strip conductor and the two outer ground planes are significantly increased, thus reducing the characteristic impedance at this section. Actually, this crosstie conductor grating can be equivalently treated as extra shunt capacitive elements that are periodically loaded on the uniform CPW without a crosstie layer [4]. Alternatively, a slow-wave CPW is formed on periodically doped semiconductor substrate. Its schematic is shown in Fig. 1c, and Wang and Itoh [34] have shown that it can reduce the attenuation. In Refs. 3 34, these periodic CPW lines are approximately characterized by the well-known Floquet theorem as well as the approximation that the effects of each junction discontinuity between two constituent sections with and without crossties are neglected [3 34]. After these two sections are analyzed using the two-dimensional (D) numerical technique, two effective per unit length transmission parameters of these periodic CPW lines are derived to explicitly demonstrate the fundamental guided-wave characteristics, namely, slow wave at low frequencies and bandstop or band rejection at certain midfrequencies. To satisfy the requirements in miniaturizing millimeter-wave integrated circuits (MMICs), in a novel class of periodic slow-wave CPW lines [35 38], the strip conductor and/or ground-plane configurations are irregularly

51 83 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES GaAs S W S Dielectric p q Crosstie conductor grating (a) GaAs T S W S Dielectric p q Crosstie conductor grating (b) Substrate Insulator S W S \p\q\ Periodically doped region Figure 1. Schematic of traditional periodic slow-wave CPW transmission lines with (a) embedded crosstie grating; (b) overlaid crosstie grating; and (c) periodically doped substrate. (c) rearranged with periodically varied patterns. Figure 13a shows the periodic CPW with the central conductor in the form of a meanderline [35]. Because of an increased inductance per unit length, the slow-wave factor in the periodic CPW is at least twofold greater than that in the uniform CPW, resulting in a reduction in the longitudinal length. Figure 13b shows the shunt-capacitive-loaded slow-wave CPW [36] with interdigitated capacitors between the inner strip conductor and outer ground planes. Experimental study is performed to extract its complex propagation constant and characteristic impedance, thereby confirming the theoretically predicted slow-wave behaviors. By forming the periodic fingers in the two grounds and inserting them into the transversal slits of a central meander strip, a modified meanderline CPW [37] is constructed as illustrated in Fig. 13c. Its enhanced capacitance per unit lengths results in further lowering the velocity of propagation as exhibited in experiment. The work [38] describes the slow-wave CPW with periodic slots in the ground plane as shown in Fig. 13d. Since the uniform CPW is periodically loaded by these short-end slotline stubs, the extra series inductance per unit length is increased so as to raise the slow-wave factor involved here. The calibration method in experiment has been utilized [38] to extract the velocity and characteristic impedance from the measured S parameters. Figure 13. Top view of uniplanar slow-wave CPW transmission lines with series inductive and/or shunt inductive loading: (a) meanderline; (b) interdigitated capacitor; (c) modified meanderline; (d) periodically slotted ground. The terms, photonic and electromagnetic bandgap CPW, introduced in 1999 [39], have again aroused significant interest in characterizing periodically loaded CPW transmission lines with nonuniform patterns on the backed conductor or CPW central strip/ground surface. In this aspect, the periodicity is selected to be electrically comparable to the CPW guided wavelength at high frequencies, thus inducing wave attenuation within a certain frequency range referred to as the bandstop [31], bandreject [33], or bandgap characteristic [39]. Extensive work has been undertaken in theory and experiment to characterize a large number of finite extended periodic CPW structures with varied unit configurations in terms of S parameters, thus illustrating the bandstop behavior of a two-port device [39]. Following the results in much of the

52 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES 831 T (c) T (a) γ/k =jβ/k +α/k.5 Uniform CPW (b) (a) (b) 1.5 T=mil 1 =1mil β/k (c).5 α/k (b) (a) Frequency (GHz) (a) (c) (b) (a) 175 T Z (Ω) Re(Z ) Re(Z ) 75 (c) Figure 14. Top view of series inductively periodic CPW transmission lines with slow-wave and bandstop transmission behaviors: (a) T-slotted ground; (b) T-slotted strip; (c) T-slotted strip and ground. 5 5 early literature [31 38], one can deduce that the two per unit length transmission parameters are critically important in exposing the complete guided-wave characteristics of various periodic CPW transmission lines with infinite extension. Figure 14 illustrates the three modified periodic CPW transmission lines reported in Ref. 4, extended from the original structure described in Ref. 38. They are constructed by etching a pair of transverse slots on the ground planes and/or strip conductor so as to enhance the shunt inductive loading with low radiation loss. With no hypothesis in theoretical modeling, the two per unit length transmission parameters of these infinite-extended periodic CPW lines [4] are directly extracted using the full-wave self-calibrated method of moments. Figure 15a plots the three relevant sets of extracted complex propagation constants (g) normalized to the freespace wavenumber (k ), specifically, g/k ¼ a þ jb, where a and b are the attenuation and phase constants, respectively. Initially, the nonzero b/k increases slowly and then rises rapidly while a/k remains zero at low frequencies, regardless of the (varied) configurations. As the frequency further increases, b/k begins to fall after peaking and a/k appears, increasing and decreasing until it disappears again. These frequency ranges with nonzero a/k are the so-called bandstop, band rejection, or bandgap for the guided wave propagating in these periodic CPW transmission lines. One of these lines, the periodic CPW (Fig. 15c) has the largest slow-wave factor at low frequencies and achieves the widest stop bandwidth because of inductive loading of paired slots on both inner and outer conductors. Figure 15b shows three sets of complex characteristic impedances, Z ¼ Re(Z ) þ j Im(Z ). In the lowpass frequency region, the real Re(Z ) tends to increase slowly and then exponentially rapidly to infinity, while the imaginary Im(Z ) remains zero. Then, Re(Z ) suddenly disappears and is converted to its infinity imaginary counterpart, Im(Z ), and this Im(Z ) drops off very quickly to zero. These nonzero Im(Z ) and zero Re(Z ) within the whole stopband provide an alternative physical view on the guided-wave bandstop behaviors of all the periodic slow-wave CPW transmission lines discussed here. 6. CONCLUSIONS Uniform CPW Frequency (GHz) (b) Figure 15. Per unit length transmission parameters of the three T-slotted periodic CPW transmission lines in Fig. 16: (a) complex propagation constant; (b) complex characteristic impedance. This article systematically describes the fundamental geometries and propagation characteristics of various

53 83 COPLANAR WAVEGUIDE (CPW) TRANSMISSION LINES uniform CPW and periodic slow-wave CPW transmission lines. First, the three basic CPW lines with infinite or finite ground width and backed conductor are discussed, including detailed design formulas. Then, a variety of modified CPW lines, namely, shielded, suspended, and micromachined CPW, including their performance advantages such as low conductivity and low material and radiation losses, are briefly discussed. Next, four coupled CPW lines are roughly investigated in terms of relative coupling. Finally, several typical infinitely extended periodic CPW lines are characterized as an effective uniform CPW transmission line and their complete guided-wave performance, such as slow-wave propagation and stopband attenuation, are demonstrated in terms of dispersive and complex propagation constants and characteristic impedance per unit length. BIBLIOGRAPHY 1. C. P. Wen, Coplanar waveguide: A surface strip transmission line suitable for nonreciprocal gyromagnetic device applications, IEEE Trans. Microwave Theory Tech. 17(1): (1969).. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, Artech House, Norwood, MA, R. N. Simons, Coplanar Waveguide Circuits, Components, and Systems, Wiley, New York, C. Veyres and V. F. Hanna, Extension of the application of conformal mapping technique to coplanar lines with finite dimension, Int. J. Electron. 48(1):47 56 (198). 5. G. Ghione and C. U. Naldi, Coplanar waveguides for MMIC applications: effect of upper shielding, conductor backing, finite-extent ground planes, and line-to-line coupling, IEEE Trans. Microwave Theory Tech. 35(3):6 67 (1987). 6. S. S. Bedair and I. Wolff, Fast, accurate and simple approximate analytic formulas for calculating the parameters of supported coplanar waveguides for (M)MIC s, IEEE Trans. Microwave Theory Tech. 4(1):41 48 (199). 7. S. Gevorgian, L. J. P. Linner, and E. L. Kollberg, CAD models for shielded multilayered CPW, IEEE Trans. Microwave Theory Tech. 43(4): (1995). 8. T. Itoh, Numerical Techniques for Microwave and Millimeter- Wave Passive Structures, Wiley, New York, L. Zhu and E. Yamashita, Effects of conductor edge profile on transmission properties of conductor-backed coplanar waveguides, IEEE Trans. Microwave Theory Tech. 43(4): (1995). 1. M. Goano, F. Bertazzi, P. Caravelli, G. Ghione, and T. A. Driscoll, A general conformal-mapping approach to the optimum electrode design of coplanar waveguides with arbitrary cross section, IEEE Trans. Microwave Theory Tech. 49(9): (1). 11. T. Hatsuda, Computation of coplanar-type strip-line characteristics by relaxation method and its application to microwave circuits, IEEE Trans. Microwave Theory Tech. 3(5):795 8 (1975). 1. F. Alessandri, U. Goebel, F. Melai, and R. Sorrentino, Theoretical and experimental characterization of nonsymmetrically shielded coplanar waveguides for millimeter-wave circuits, IEEE Trans. Microwave Theory Tech. 37(1): 7 (1989). 13. L. Zhu and E. Yamashita, Full-wave boundary integral equation method for suspended planar transmission lines with pedestals and finite metallization thickness, IEEE Trans. Microwave Theory Tech. 41(3): (1993). 14. U. Bhattacharya, S. Allen, and M. J. W. Rodwell, DC-75 GHz sampling circuits and subpicosecond nonlinear transmission lines using elevated coplanar waveguide, IEEE Microwave Guided Wave Lett. 5():5 5 (1995). 15. S. Hofschen and I. Wolff, Simulation of an elevated coplanar waveguide using -D FDTD, IEEE Microwave Guided Wave Lett. 6(1):8 3 (1996). 16. G. E. Ponchak and L. P. B. Katehi, Measured attenuation of coplanar waveguide on CMOS grade silicon substrates with polyimide interface layer, IEE Electron. Lett. 34(13): (1998). 17. C. M. Nam and Y. S. Kwon, Coplanar waveguide on silicon substrate with thick oxidized porous silicon (OPS) layer, IEEE Microwave Guided Wave Lett. 8(11): (1998). 18. Y. Liu, K. Cha, and T. Itoh, Non-leaky coplanar (NLC) waveguides with conductor backing, IEEE Trans. Microwave Theory Tech. 43(5): (1995). 19. N. I. Dib, W. P. Harokopus, and P. B. Katehi, Study of a novel planar transmission line, IEEE MTT-S Int. Microwave Symp. Digest, 1991, pp K. K. M. Cheng and I. D. Robertson, Simple and explicit formulas for the design and analysis of asymmetrical V-shaped microshield line, IEEE Trans. Microwave Theory Tech. 43(1):51 54 (1995). 1. K. K. M. Cheng and I. D. Robertson, Quasi-TEM study of microshield lines with practical cavity sidewall profiles, IEEE Trans. Microwave Theory Tech. 43(1): (1995).. K. J. Herrick, T. A. Schwarz, and L. P. B. Katehi, Si-micromachined coplanar waveguides for use in high-frequency circuits, IEEE Trans. Microwave Theory Tech. 46(6): (1998). 3. H. T. Kim, S. Jung, J. H. Park, C. W. Baek, Y. K. Kim, and Y. Kwon, A new micromachined overlay CPW structure with low attenuation over wide impedance ranges and its application to low-pass filters, IEEE Trans. Microwave Theory Tech. 49(9): (1). 4. C. C. Tien, C. K. C. Tzuang, S. T. Peng, and C. C. Chang, Transmission characteristics of finite-width conductor-backed coplanar waveguide, IEEE Trans. Microwave Theory Tech. 41(9): (1993). 5. S. J. Kim, H. S. Yoon, and H. Y. Lee, Suppression of leakage resonance in coplanar MMIC packages using a Si sub-mount layer, IEEE Trans. Microwave Theory Tech. 48(1): (). 6. C. P. Wen, Coplanar-waveguide directional couplers, IEEE Trans. Microwave Theory Tech. 18(6):318 3 (197). 7. K. K. M. Cheng, Analysis and synthesis of coplanar coupled lines on substrate of finite thicknesses, IEEE Trans. Microwave Theory Tech. 44(4): (1996). 8. C. L. Liao and C. H. Chen, Full-wave characterization of an edge-coupled coplanar-waveguide structure with backed conductor, IEEE MTT-S Int. Microwave Symp. Digest,, pp S. S. Bedair and I. Wolff, Fast and accurate analytic formulas for calculating the parameters of a general broadside-coupled coplanar waveguide for (M)MIC applications, IEEE Trans. Microwave Theory Tech. 37(5): (1989). 3. K. K. M. Cheng, Analytical formula for calculating the coupling characteristics between parallel coplanar lines, IEE Electron. Lett. 3(13):18 19 (1996).

54 CORRUGATED HORN ANTENNAS R. E. Collin, Periodic structures and filters, in Foundations for Microwave Engineering, McGraw-Hill, New York, 199, Chap S. Seki and H. Hasegawa, Cross-tie-slow-wave coplanar waveguide on semi-insulating GaAs substrate, IEE Electron. Lett. 17(5): (1981). 33. Y. Fukuoka and T. Itoh, Slow-wave coplanar waveguide on periodically doped semiconductor substrate, IEEE Trans. Microwave Theory Tech. 31(1): (1983). 34. T. H. Wang and T. Itoh, Compact grating structure for application to filters and resonators in monolithic microwave integrated circuits, IEEE Trans. Microwave Theory Tech. 35(1): (1987). 35. W. H. Haydl, Properties of meander coplanar transmission lines, IEEE Microwave Guided Wave Lett. (11): (199). 36. E. H. Bottcher, H. Pfitzenmaier, E. Droge, and D. Bimberg, Millimetre-wave coplanar slot transmission lines on InP, IEE Electron. Lett. 3(15): (1996). 37. A. Gorur, C. Karpuz, and M. J. Lancaster, Modified coplanar meander transmission line for MMICs, IEE Electron. Lett. 3(16): (1994). 38. R. Spickermann and N. Dagli, Experimental analysis of millimeter wave coplanar waveguide slow wave structures on GaAs, IEEE Trans. Microwave Theory Tech. 4(1): (1994). 39. F. R. Yang, K. P. Ma, Y. Qian, and T. Itoh, A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuits, IEEE Trans. Microwave Theory Tech. 47(8): (1999). 4. L. Zhu, Guided-wave characteristics of periodic coplanar waveguides with inductive loading unit-length transmission parameters, IEEE Trans. Microwave Theory Tech. 51(1): (3). CORRUGATED HORN ANTENNAS 1. INTRODUCTION L. LUCCI G. PELOSI S. SELLERI University of Florence Florence, Italy R. NESTI National Institute for Astrophysics Florence, Italy Corrugated horns are microwave antennas commonly used as feeds for high-performance reflector antenna systems. Although rectangular corrugated horns have been successfully used, circular corrugated horns are used more frequently, and this type of radiation device is treated in detail in this article. Corrugated horns are attractive as feeds as they possess several unique properties: 1. They have high beam symmetry and low sidelobes.. They show very low cross-polarization. 3. They exhibit high return loss over a quite broad band (3 4%). Corrugated horn properties have been investigated since the 195s, and the book by Clarricoats and Olver [1] gives an accurate analytical description of their electromagnetic features, introducing simple and powerful design tools, and thus so far is the major reference text on the subject of corrugated horn antennas. These antennas are widely used in the field of radio astronomy, remote sensing, and telecommunications on both ground-based and satellite platforms, whenever simple and easy-to-fabricate solutions to efficiently feed reflector antennas are required. More recently, research activity on corrugated horns has been devoted mainly to studying complex profiles for the corrugations. The effects of profiling the horns using an exponential taper are accurately described in Ref., an exhaustive description of different methods for profiling the horn corrugations is given in Ref. 3, a profile specific for the electrical requirements typical of radio astronomy applications with reduced size and weight is shown in Ref. 4, and the effects of tuning the phase center position by shaping the exponential profile, without changing in practice other features such as beam size, sidelobe levels, return loss, and cross-polarization, have also been investigated [5]. This work is intended to give the reader a brief introduction to corrugated circular horns highlighting their electromagnetic features, analysis tools, and design aspects.. ELECTROMAGNETIC PROPERTIES OF CORRUGATED WAVEGUIDES In this section we attempt to explain the theory of electromagnetic propagation in circular corrugated waveguides, with a short but thorough characterization of corrugated waveguides, highlighting their main aspects, as this knowledge is of great importance in understanding the features of corrugated horns. Figure 1 shows a longitudinal section of a circular corrugated waveguide in a cylindrical coordinate system (O,r,j,z). The metallic corrugated boundary extends between an inner radius a and an outer radius b and is described in terms of a slot depth s, a slot width g, and a tooth width t, for a total longitudinal periodicity of period w. On the basis of this periodicity, the Floquet theorem ensures that if one knows the field within the period ½E ðpþ ðr; j; zþ; H ðpþ ðr; j; zþšo; for z ½; wþ ð1þ it is possible to obtain an arbitrary field configuration in the whole domain, (rrob, rjop, NozoN), whose wave nature is characterized by means of a propagation constant b, as follows (propagation is assumed,

55 834 CORRUGATED HORN ANTENNAS o ρ φ z s a g w t b of TE and TM modes. Such a combination can be seen as another couple of modes, which are called hybrid modes, each of which can propagate individually. Thus, searching for the generic eigenmode solution, we proceed in a classical way [7] by considering the longitudinal components of the fields as scalar potentials; they have to satisfy the Helmholtz equation: ðr t þ k t Þ½E zðr; jþ; H z ðr; jþš ¼ ð5þ Figure 1. Corrugated waveguide geometry. without loss of generality, in the þ z-axis direction): ½Eðr; j; zþ; Hðr; j; zþš ¼½E ðpþ ðr; j; zþ; H ðpþ ðr; j; zþše jbz The periodical part of the field can be expanded in a Fourier series: ½E ðpþ ðr; j; zþ; H ðpþ ðr; j; zþš ¼ X1 n ¼ b n ¼ np w ½E n ðr; jþ; H n ðr; jþše jb nz ; From now on a series of assumptions will be performed largely to simplify the treatment. These assumptions are, however, justified as they are relate to physical features of corrugated horns. The first simplification is that the corrugation period is supposed to be very small compared to the wavelength, w5l, so that in the Fourier spatial harmonic expansion (3) the term n ¼ is predominant and can be the only one considered. So the total field in the corrugated waveguide is reduced to the following: ½Eðr; j; zþ; Hðr; j; zþš ¼½E ðr; jþ; H ðr; jþše jbz The transverse function of the field representation in (4) ½E ðr; jþ; H ðr; jþš is assumed to be valid in the cylinder (rroa,rjop); the general form of the field solution is obtained by imposing the boundary condition in r ¼ a. For the sake of simplicity, the subscript will be omitted in the following equations. The solution appears to be similar to the one in the circular waveguide [6], but substantial differences emerge, especially for the eigenmode functions, due to the presence of the corrugations. As in the more general case, such as, for example, optical fibers, in corrugated waveguides the boundary conditions at r ¼ a cannot be reduced to a perfect electric conductor or a perfect magnetic conductor; hence the field cannot be expanded in terms of only TE or only TM modes of a circular waveguide of radius a, but rather by a couple ðþ ð3þ ð4þ In this expression rt is a D operator on the variables (r,j) and the transverse eigenvalue k t is introduced; at this point it is unknown but must satisfy the relation p ¼ k l ¼ k t þ b ð6þ in which l is the wavelength and k is the free-space propagation factor; each eigenvalue will thus produce a different propagation constant b. One should observe that the eigenvalue k t in Eq. (5) is the same for both E z and H z, so that each mode of the associated pair TE and TM exhibits the same phase velocity and group velocity, hence producing a hybrid mode that is able to satisfy boundary conditions. From a mathematical point of view, since the problem shows azimuthal symmetry, the solution to the Helmholtz equation (5) is the same as in a circular waveguide: 8 >< >: E z ðr; jþ¼ P1 m ¼ J m ðk t rþ ½A m cosðmjþþc m sinðmjþš B m Z H z ðr; jþ¼ P1 m ¼ sinðmjþþ D m Z J m ðk t rþ cosðmjþ where J m is the mth-order first-kind Bessel function; A m, B m,c m,d m, are complex constants; pand the characteristic impedance of the medium Z ¼ ffiffiffiffiffiffiffi m=e is introduced, where m is the magnetic permeability and e is the electric permittivity of the medium. We must now point out the following observations: * Equation (7) represents essentially the Fourier expansion of the potential in the azimuth coordinate j for a given transverse eigenvalue k t that has still to be determined by imposing boundary conditions. * If a mode has no azimuth variation (m ¼ ), then it has a single polarization state, but, for each mode having m4, two linear polarizations exist and are associated to the two terms in the bracket on the right side of (7). Thus, given a generic mode with m4 (the eigenvalue k t is also fixed), if A m ¼ B m ¼, then one has one of the two possible field polarizations while if C m ¼ D m ¼, one has the other one; the fields associated with each of these two polarization states are orthogonal, as can be easily seen by ð7þ

56 CORRUGATED HORN ANTENNAS 835 computing the flux of the coupled Poynting vector S ¼ 1 E ða m ¼ B m ¼ Þ H ðc m ¼ D m ¼ Þ over an arbitrary circular section and verifying that it gives zero as result. * Radial-type discontinuities excite modes having the same azimuth variation; thus the harmonic number m is preserved in a field propagating in a corrugated waveguide. We can also state that, in this kind of structure, there is no power transfer between fields characterized by a different harmonic number m. Considering a corrugated waveguide excited by the circular waveguide TE 11 fundamental mode and choosing one of the two polarization states, a generic couple of hybrid mode potentials can be expressed as follows: ½E z ðr; jþ; H z ðr; jþš ¼ J 1 ðk t rþ A cosðjþ; B ð8þ sinðjþ Z Before applying the boundary conditions, it is now useful to write the electromagnetic field generated by the potentials in (8), also expressing the z-variation terms: 8 E z ðr; j; zþ¼aj 1 ðk t rþcosðjþe jbz H z ðr; j; zþ¼ B J 1 ðk t rþsinðjþe jbz Z E j ðr; j; zþ¼j k A b J 1 ðk t rþ þ BJ1 ð k t k k t r k trþ >< k H j ðr; j; zþ¼ j AJ1 ð k t Z k trþþb b J 1 ðk t rþ k k t r E r ðr; j; zþ¼ j k k t A b J1 ð k k tr k H r ðr; j; zþ¼ j A J 1ðk t rþ >: k t Z k t r ÞþB J 1ðk t rþ k t r þ B b J1 ð k k trþ sinðjþe jbz cosðjþe jbz cosðjþe jbz sinðjþe jbz This set of expressions is a generic hybrid mode-field configuration with azimuth harmonic m ¼ 1, in which the TM part ðao; B ¼ Þ and the TE part ða ¼ ; BOÞ can be noted. We now return to the particular problem under consideration here, namely, the corrugated waveguide geometry of Fig. 1. As already mentioned, in corrugated horns a small corrugation period, compared to the wavelength, is assumed; this fact allows us to further assume that inside the grooves of the corrugations (arrob) only a TEM wave propagating in the radial direction exists, with all higherorder modes in cutoff. In such a TEM wave (which is rigorously the exact solution in the asymptotic limit as the frequency and/or the radial co-ordinate approach infinity) all the field components are equal to zero except the z component of the electric field and the j component of the magnetic field. Since the walls are perfect electric conductors, no power loss is present and the Poynting ð9þ vector in r ¼ a must be imaginary; hence H j ða; jþ E z ða; jþ ¼ 1 jx s ð1þ where X s assumes the meaning of a reactance. The reactance of the total field at r ¼ a is given by two main contributions: 1. A contribution that holds for the portion of w of length g associated to the slot can be obtained by considering that the corrugation slot behaves like a transmission line of length s closed with a short circuit, thus having at the section r ¼ a a reactance value given by X ¼ Z tanðk sþ ð11þ. A contribution that holds for the width t associated with the tooth is given by a short circuit at r ¼ a, producing X ¼. As a first approximation, the total reactance of the field at r ¼ a is given by considering both contributions according to their respective lengths of action. We can therefore apply the following boundary condition: X s ¼ Z tanðk sþ 1 t ð1þ w Thus, substituting (1) and (1) in the field representation (9) and also taking into account the following condition E j ða; jþ¼ we obtain the following relations 8 g ¼ A B ¼ k u J 1 ðuþ b J 1 ðuþ >< y Z ¼ k J 1 ðuþ X s k t J 1 ðuþ þ >: u k t a b gk t u ð13þ ð14þ where g is the hybrid factor, y represents the normalized susceptance, a new variable u is introduced, and J 1 ðuþ¼ðd=duþj 1 ðuþ. Substituting these relations in the electric field expansion given in (9), using some algebraic and trigonometric formulas, and neglecting the z dependence, a very interesting representation is found for the transverse component E t of the electric field, which is useful for analyzing the properties of corrugated waveguides: E t ðr; jþ¼ j k B k t g b þ 1 J ðk t rþ ^x þ 1 g b k k J ðk t rþ½cosðjþ ^x þ sinðjþ ^yš ð15þ

57 836 CORRUGATED HORN ANTENNAS Eliminating the hybrid factor g in (14), the characteristic equation is obtained as follows: " y k a ¼ J 1ðuÞ u 3 J u J 1 ðuþ b # ð16þ 1 ðuþ J 1 ðuþ Thus, solving this equation for the variable u, the eigenvalues k t of the hybrid modes can be obtained. A detailed analysis of (16) is beyond the scope of this work; the reader is referred to the text by Clarricoats and Olver [1] for a more in-depth treatment of this topic. Here we are interested only in some cases of practical interest: 1. If we assume that the slot length s is a quarterwavelength, then the normalized susceptance y is zero, and using the asymptotic limit b-k, where the frequency is much greater than the cutoff frequency of the mode (fbf t ), we can approximate (16) by u J 1 ðuþ 1 ¼ ) u J 1 ðuþ J 1 ðuþ J 1 ðuþ ¼1 ð17þ. In the same asymptotic limit b- k, Eq. (17) is also obtained as an approximation of (16) independently from the slot length s, assuming that the radius a is large enough that the first side of (16) tends to zero. These two cases are important in practice because in the region close to the throat (small a), corrugations are designed in order to satisfy condition 1, while condition is satisfied in the region close to the aperture (large a). Equation (17) can be easily solved using the recurrence formulas for Bessel functions thus giving k J n ðuþ¼ J n 1 ðuþþ ðn 1ÞJ n 1ðuÞ u ¼ J n þ 1 ðuþþ ðn þ 1ÞJ n þ 1ðuÞ u ( J ðuþ¼ J ðuþ¼ ð18þ ð19þ As can be noted from the first line of (14), in the asymptotic limit b-k, the first line of (19) is equivalent to g ¼ 1 and the second, to g ¼ 1. The dual condition g ¼1is termed the balanced hybrid condition. If this condition is satisfied, the right side of (16) is always zero, thus producing a more general solution in the case in which the left side of (16) is zero. In this particular case two sets of hybrid modes, HE and EH, corresponding to, respectively, g ¼ 1 and g ¼ 1, are simply given by analytical formulas. The eigenvalues of these modes are 8 >< >: HE 1n ) k t ¼ k HE 1n ¼ u n a EH 1n ) k t ¼ k EH 1n ¼ u n a ðþ where u n and u n are the well-known and tabulated zeros of the first-kind Bessel functions, the zero-order J and the second-order J, respectively. Although these modes are approximated solutions of corrugated waveguides, in the sense explained above, they accurately describe wave propagation with the major advantage of a relatively simple analytical form. Using solutions () in the electric field expression (15), with the asymptotic approximation b-k, we obtain * For the EH 1n modes ðg ¼ 1Þthe transverse electric field is given by E t 1n ðr; jþ ffi j k a BJ r u n u n a ½cosðjÞ ^x þ sinðjþ ^yš ð1þ * For the HE 1n modes ðg ¼ 1Þ, we can use the following approximation for (16) thus leading to y k a ¼ 1 b 1 u k g ð1 g Þ ffi u 1 g b k ) 1 g b ¼ yu k k a E t 1n ðr; jþ ffi j k a B u n u n J a r ^x þ yu n 4k a J u n a r ½cosðjÞ ^x þ sinðjþ ^yš ðþ ð3þ While EH modes show undesired field configuration features, since there is no preferential direction for field polarization, as can be noted in the electric field configuration of the EH 11 mode of Fig. b, this is not the case for the HE modes. In fact, regarding the HE 11 fundamental hybrid mode, one should note that, in the case in which the first term inside the braces predominates over the second one, the field is essentially linearly polarized, as can be seen in Fig. a, and shows high azimuthal symmetry in amplitude. These features are of prime importance because they yield high beam symmetry and very low cross-polarization. The second term inside the braces is highly undesired as it has the same negative polarization features as do EH modes. Its contribution should be as low as possible, and this may be achieved, as mentioned above, by keeping the susceptance y very small using quarter-wavelength slots.

58 CORRUGATED HORN ANTENNAS 837 x x ideal triangle formed by the corrugated wall envelope and the aperture diameter (Fig. 3), which is approximately the horn length. This results in the following analytical expression for the field: y y E t 1n ðr; jþ ffia J r u 1 e jðkr =LÞ ^y R ð4þ (a) Figure. Corrugated waveguide electric field distribution of hybrid modes: (a) HE 11 ; (b) EH RADIATION PROPERTIES OF CORRUGATED CONICAL HORNS A very useful method for accurate analytical description of the radiation properties of corrugated horns is the Gaussian beam approach, using the Gauss Laguerre expansion of the electromagnetic field [8]. Although this approach is valid in the paraxial beam approximation [9] (i.e., for narrow beams), it is a very good tool for fast analysis and design of all the corrugated horns of practical interest. It enables accurate description of the main lobe shape, up to approximately db relative to the maximum, and accurate prediction of the phase center position. As a drawback sidelobes are not characterized and there is only a lower bound limit estimate for the cross-polarization level. These features can be taken into account, together with flange effects and other second-order phenomena, by resorting to numerical methods, as described later. Referring to Fig. 3, let s consider a corrugated horn of conical shape excited by a perfectly azimuth symmetric fundamental HE 11 hybrid mode that is assumed to be polarized in the y-axis direction. Thus the electric field contribution due to J in (3) gives the amplitude distribution at the horn aperture, where it is also possible to accurately estimate the phase distribution. Indeed, using the same approximation usually applied to common conical waveguides, the radius of curvature of the aperture phase distribution is assumed equal to the height L of the L z a z a (b) R z x z Figure 3. Conical corrugated horn geometry. y φ The constant A may be given an explicit value if, on the horn aperture surface S, the following power normalization rule is adopted: leading to ZZ S E t 1n ðr; jþ½et 1n ðr; jþš ds : ¼ 1 1 A ¼ pffiffiffi p RJ1 ðu 1 Þ ð5þ ð6þ The successive step is to expand the field in the space of the Gauss Laguerre complete set ð ro1þ of orthonormalized functions: u 1 J R r 3 4pffiffiffi p RJ1 ðu 1 Þ 5e jðkr =LÞ " rffiffiffi # ¼ X1 1 a n p w L n r w e ðr =w Þ n ¼ e jðkr =LÞ ð7þ where a n are the expansion coefficients and L n is the Laguerre zero-order nth polynomial. Of particular interest is the zero term of the expansion rffiffiffi 1 GðrÞ¼a p w =w Þ e ðr e jðkr =LÞ ð8þ which represents the normalized fundamental Gaussian beam mode. Neglecting a detailed analysis of the Gaussian beam, which can be found in Ref. 1, it is important to highlight that, in the expansion (7), w is an arbitrary parameter that can be chosen according to different objectives, each corresponding to different expansions. The most convenient choice for our purposes is the one maximizing the a coefficient; thus, by taking the fundamental Gaussian beam mode only, the horn aperture field is already nicely approximated. Then, the expression p a ¼ ffiffiffi Z 1 J ðu 1 uþ e ðu =p Þ udu 1 pj 1 ðu 1 Þ ð9þ in which p ¼ w/r and u ¼ r/r, must be maximized with respect to p. Figure 4 shows the a coefficient as a function of p. It has a maximum at p ¼.6435, with a ¼.99, corresponding to a power coupling between the HE 11 mode and the Gaussian beam mode (8) of B98%.

59 838 CORRUGATED HORN ANTENNAS a p Figure 4. Coupling between the HE 11 mode and the Gaussian beam mode. Once the best-coupled Gaussian beam has been completely determined on the aperture (z ¼ ), the electromagnetic field is known, in our case, on the infinite halfspace z4, thanks to the Gaussian beam propagation formula: Gðr; z Þ¼ w wðz Þ e ½r =w ðz ÞŠ e j½kr =Hðz ÞŠ e jkz ð3þ where a new coordinate z ¼ z þ z a is introduced for convenience (Fig. 3), where z a gives the horn aperture position with respect to z. The term w, termed beam waist, is a fundamental parameter governing all features of the Gaussian beam according to what is demonstrated in the following points: 1. The function w(z ) determines the transverse size of the beam; for each z it gives the radial coordinate r at which the field has a e 1 ratio with the on-axis maximum. This size has a minimum value that is exactly w at z ¼, and its general expression is given analytically by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wðz Þ¼w 1 þ z ð31þ z c where z c, the confocal distance, may be interpreted as the limit between near-field and far-field regions and is given by z c ¼ pw l ð3þ where l is the wavelength. From (31) we can see that in (3), the amplitude factor Aðz Þ¼ w wðz Þ ð33þ. The term H(z ) gives the radius of curvature of the wavefronts and is a function of the beam waist, through the confocal distance z c, according to Hðz Þ¼ z þ z c z ð34þ This equation gives very important insights on Gaussian beam behavior. The radius of curvature is infinite in two cases: (1) in the near-field region at z ¼, which means that the field has a planar phase front exactly at the waist, which is on the horn axis, commonly located in the inner corrugated region of the horn; and () while approaching infinity as z tends to infinity, meaning that, since this occurs in the far region, the field has a spherical phase front. It must, however, be noted that the radius of curvature tends to infinity as z, implying that the farfield phase center of the Gaussian beam is the beam waist position z ¼. An even more important fact is that Eq. (34) gives the radius of curvature of the beam at every distance from the waist, so that, to the extent that the Gaussian beam is a good approximation of the field radiated by a corrugated horn, the phase center position of the horn is known simply and accurately everywhere, including the near-field region, with dramatic simplification in the design task of the optics of reflector antenna systems fed by corrugated horns. It is now possible to characterize both phase center position and radiation patterns of corrugated horns. By considering the phase center position, the problem is to determine the horn aperture abscissa z a, where the field expansion is completely known as a consequence of having determined the waist w(z a ) ¼ pr, with p ¼.6435, and the radius of curvature H(z a ) ¼ L. To do this, the following inverse formulas, obtained by manipulating (31) and (34), are useful: pr w ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! ; u t 1 þ pðprþ 1 l L L z a ¼ l 1 þ L pðprþ ð35þ The relations in (35) are very important because they give analytically both the far-field phase center position with respect to the horn aperture (z a from the aperture toward the throat) and the waist w, which governs, as mentioned above, the Gaussian beam propagation. Thus, the field radiated by the horn (z 4z a ) can be analytically evaluated everywhere. As a consequence, we can also characterize the corrugated horn radiation pattern. To do this, we approximate, in the far field, the expression (3) as follows: decreases with a 1/z law for large on-axis distances from the waist. wðz ÞffiwðzÞ ffiw z z c ð36þ

60 CORRUGATED HORN ANTENNAS 839 Remembering the confocal distance expression (3) and passing to a spherical coordinate system z ¼ r cosðwþ; r ¼ r sinðwþ ð37þ it is possible to rewrite the field radiated by the aperture distribution (4) with the Gaussian beam approximation (8) as follows rffiffiffi pw jeðr; WÞj ffi a 1 p l r cosðwþ e tan ðwþðpw =lþ ð38þ which is assumed to be valid for r4 and Wop=. Moreover, it is possible to use the inverse formulas (35) to express the radiated field in terms of the geometric parameters R and L and expand the ^y versor in spherical coordinates, neglecting the radial component. Proceeding in this way, we have a full characterization of the radiated field, including its polarization, and obtain the following expression Eðr; W; jþ¼ a r exp 1 6 tan ðwþ l 4 1 R ðp pþ þ R 7 5 p L sinðjþ^i W þ cosðjþ cosðwþ ^i j : ð39þ where rffiffiffi pw a ¼ a p l 3 ð4þ Figure 5 shows the accuracy that can typically be achieved with the Gaussian beam approximation. The plot gives the j ¼ 451 plane radiation pattern of a corrugated horn obtained by a full-wave analysis, which is assumed to be the reference, and by its best-fit Gaussian beam. The cut E (db) ϑ (deg) Full-wave model Best fit guassian beam Figure 5. Corrugated horn radiation pattern at j ¼ 451: L ¼ 44l; R ¼ 3.4l. chosen is representative of every j cut, at least up to a level of approximately 35 db, because of the high azimuthal symmetry of the horn. Thus we are lead to the conclusion, which is more or less valid in general for standard corrugated horns, that the Gaussian beam approach gives high accuracy with respect to the beam pattern up to about 15 db below the on-axis maximum. 4. DESIGN ASPECTS OF CORRUGATED HORNS Thus far we have presented a quite general theory to help the reader understand the electromagnetic properties of corrugated horns. This knowledge is, however, sufficient only to a first step and rough design; for accurate design, further aspects are needed and are developed in the following paragraphs. In particular, we intend to focus on arguments that constitute requirements for most applications. As seen above in (39), the mainbeam radiation is controlled by the aperture size and the horn length. A very important task is the design of the throat region because it controls primarily the input return loss and the proper excitation of the HE 11 fundamental hybrid mode. Another important feature of corrugated horns is the cross-polarization, which is of importance mainly in modern dual-polarization applications. When the horn is used as a feed for a reflector, the phase center position must be accurately known; this, according to the Gaussian beam approximation, coincides in the far field with the waist position (35), while in near field it is given by the center of curvature of the phase front according to (34). For a very accurate characterization of the properties mentioned above, numerical techniques are needed. A very accurate full-wave analysis method is presented below MainBeam Radiation of Corrugated Horns As stated above, an accurate analytical characterization of the mainbeam pattern is given in (39). In practice, typical specifications related to the mainbeam are given in terms of gain, edge taper, or sometimes the waist, each of which may be used to determine the geometric parameters R and L of the horn. When complex reflector arrangements are to be fed by a corrugated horn, the waist is typically given as a requirement because the design of the optics is efficiently done using the Gaussian beam approach. If a waist w is given, then the mainlobe can be determined. In particular, we can define the 1/e halfbeamwidth as the angle at which the field intensity is 1/e down from the on-axis maximum. Neglecting the cosðwþ term, from (38) we have the following approximation: W 1=e ¼ tan 1 l pw ð41þ To obtain the geometric parameters of the horn, it is possible to proceed by fixing the phase shift on the horn

61 84 CORRUGATED HORN ANTENNAS aperture b ¼ pr ll ð4þ to a maximum allowed value b, where b ¼ p=16 is a practical choice. Proceeding this way, it is possible to use the inverse formulas (35) to simply have R ¼ w p L ¼ pr lb qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ p 4 b ; ð43þ As already mentioned, the Gaussian model is valid in the paraxial beam approximation and, in practice, the wavelength can be regarded as the lower limit for the waist (w 4l) in a design approach of this kind. It is interesting to note that fixing the phase shift b is equivalent to fixing the wavelength-normalized radius R l and the half-flare angle a defined by R l ¼ R l ; a ¼ R tan 1 L ð44þ The edge taper is the level, relative to the on-axis maximum, at which the horn illuminates a certain elevation angle, usually individuated by the edge of the reflector that is fed directly. For example, an edge taper of X db at an angle W t may be necessary. This information may be used to directly obtain the waist by using (38), neglecting the cosðwþ term again, yielding directivity D : power density in W ¼ G ffi D ¼ 4p horn aperture outgoing power UðW ¼ Þ ¼ 4p P rad ð47þ The power out from the aperture can be written as the flux of the real part of the Poynting vector: P rad ¼ 1 Re ZZ S ¼ 1 ZZ ReðY mþ j E H ^z ds S E t j ds ð48þ where E t indicates the tangential component of the electric field, S is the horn aperture surface, and Y m is the field admittance on the aperture. In the case of the hybrid HE 11 fundamental mode, under the balanced hybrid condition (19), introducing the field impedance Z m ¼ 1/Y m, we have Z m ¼ z, the characteristic impedance of the medium. The power density radiated in the free space on-axis direction is given by UðW ¼ Þ¼ r z je radðw ¼ Þj ð49þ The radiated electric field E rad in the far-field approximation > 1Þ may be given as a function of the tangential electric field distribution E t on the horn aperture. This can be simply obtained by using the field expansion as a spectrum of plane waves, and this method is outlined in detail in Ref. 11. Essentially, the far-field approximation can be obtained as the plane-wave spectrum 1 X= ¼ e tan ðw tþðpw =lþ ð45þ E rad ðr; W; jþ¼pj e jkr k cosðwþ r ^Eðx; ZÞ ð5þ leading to w ¼ l pffiffiffiffi :95p X tanðw t Þ ð46þ Once the waist has been calculated, it is possible to proceed in the same way as in the previous case with the waist given directly. In practice, because of the approximation in the Gaussian beam model, this method gives accurate results for edge taper levels X up to 5 db and taper angles W t not greater than 31. If the gain is given as specification, an efficient way to proceed for simple, accurate, and fast design is as follows. First, it is more convenient to refer to the gain G in the on-axis direction of the horn and, due to the high return loss and the low ohmic losses of corrugated horns, to approximate the gain with the asymptotically evaluated at the stationary point x ¼ sinðwþ cosðjþ; Z ¼ sinðwþ sinðjþ, where the spectrum is the D Fourier transform of the tangential electric field E t on the aperture: ^Eðu; vþ¼ 1 ZZ ðpþ E t ðx; yþe jux e jvy dx dy S In the on-axis direction W ¼, we have ^Eð; Þ¼ 1 ZZ ðpþ E t ds S E rad ðr; W ¼ ; jþ¼j 1 l l e jkr r S ZZ UðW ¼ Þ¼ 1 ZZ 1 E t ds z S E t ds ð51þ ð5þ ð53þ ð54þ

62 CORRUGATED HORN ANTENNAS 841 Obviously, the traditional approach based on the auxiliary potential formulation according to the theory developed in Ref. 1 can be used, leading to the same results. It is thus possible to rewrite the on-axis gain expression (47) as a function of the tangential electric field distribution E t on the horn aperture alone ZZ G ¼ 4p ZZS l z Z m E t ds S je t j ds ð55þ where, in our case, Z m ¼ z, as already stated. We can use the effective area concept, in this case given by for ZZ E t ds S A e ¼ ZZ je t j ds S G ¼ 4p R l Z A ð56þ ð57þ where the aperture radius normalized to the wavelength R l is as defined in (44) and Z A ¼ A e =A is the aperture efficiency, where A ¼ pr is the geometric area of the aperture. The aperture efficiency, which is a measure of how much of the aperture is effectively used, can be expressed in a more useful way by using (4) (omitting the amplitude A ¼ 1) ZZ S je t j ds ¼ p S Z R J u 1 ¼ pr J 1 ðu 1Þ ZZ E t ds ¼ 4p R 4 Z 1 r R J ðu 1 xþe jðprl tanðaþþ x xdx rdr ð58þ ð59þ whereweusetherelationtanðaþ¼r=l. Thus we obtain a useful aperture efficiency expression as a function only of the geometric parameters R and L: Z A ¼ Z 1 4 J 1 ðu 1Þ J ðu 1 xþe jðpr l tanðaþþ x xdx ð6þ This function is plotted against the parameter R l tanðaþ in Fig. 6. We observe that it has a maximum Z A ¼ :69 in the origin, corresponding to the case of a corrugated waveguide with a null half-flare angle a. It has to be noticed that, in order to have the same efficiency, if we enlarge the aperture radius R, the horn length also has to be increased so that R l tanðaþ remains constant. η A R λ tan(α) Figure 6. Corrugated feed horn aperture efficiency. Concluding, according to (57) and (6), it is possible to express the on-axis gain as a function only of the geometric parameters R and L, which is the desired form, analogously to the other cases of the waist and edge taper specifications, in order to design corrugated horns. Together with the curve in Fig. 6, another useful design chart is given in Fig. 7, where parametric curves based on the on-axis gain expression (57), with the aperture efficiency given by (6), are plotted against R l, with the flare angle a used as a parameter. Given a particular on-axis gain specification, it is thus possible, both analytically and graphically, to obtain the most convenient solution in terms of R and L. 4.. Design of the Throat Transition Region The initial part of the corrugated horn, the throat region, is of primary importance because it directly determines the input matching and the excitation of the HE 11 fundamental hybrid mode. Because circular waveguides are the most convenient solutions to feed corrugated horns, the design of the throat is not straightforward. As mentioned previously, the ideal condition to support the propagation of the HE 11 mode is that the widths of both the tooth and the slot be much smaller than the wavelength and that the slot depth be a quarter-wavelength. This latter condition would produce very poor input matching if applied directly to the initial corrugations connected to the circular waveguide. This is because a perfect magnetic wall results at a quarterwavelength distance (the slot depth) from the metallic enclosure, constituting, with respect to the wave coming from the circular waveguide, an equivalent open circuit as a boundary condition at r ¼ a. This produces abrupt discontinuities at the boundary, which presents, alternately, short circuits (tooth sections) and open circuits (groove sections) within a small fraction of the wavelength. This is the required boundary condition for the desired HE 11 mode but is incompatible with the fundamental TE 11 mode of the feeding circular guide; hence high reflection coefficients would be present.

63 84 CORRUGATED HORN ANTENNAS G(dB) α=6 α=45 α=3 α= α=1 α= R λ Figure 7. Corrugated horn gain versus aperture radius and halfflare angle. The solution is a transition region where the corrugations begins with approximately half-wavelength slot depths and with the teeth thicker than the slots; the steady-state geometry is gradually reached with a few corrugations. Proceeding this way, two important objectives are obtained: 1. The equivalent boundary conditions for a half-wavelength-depth slot is a short circuit at r ¼ a, and hence there is no abrupt discontinuity, with a gradual variation giving a good input matching.. A half-wavelength slot also ensures the proper propagating condition for the circular waveguide TM 11 mode, thus producing an adequate condition to excite the hybrid HE 11 mode of the corrugated waveguide (formed by the TM 11 and TE 11 modes). This type of solution is given in Fig. 8, where typical values for the transition region geometry are explicitly given. In practice transition regions may be formed by 1 corrugations. Problems associated with the design of the transition region have been encountered in the literature. Only an intuitive explanation of the proposed solution has been.5λ Circular TE 11.1λ.3λ λ.1λ.3λ.5λ Corrugated HE 11 Figure 8. Corrugated horn throat: transition region typical geometry. given here; a very detailed theoretical approach on this can be found, for example, in Ref Cross-Polarization A large part of modern applications is based on dualpolarization channels, where two channels exist at the same frequency in the same medium (free space or waveguide). This means that the transmitter and receiver subsystems, carrying the dual-polarized signal, need to keep the two polarizations separate, introducing negligible coupling between them. Thus, a related figure of merit here is the extent to which the two polarizations may be kept uncoupled. With respect to corrugated horns, this parameter is given by the cross-polarization level and, instead of the ordinary W and j components of the radiated field, in these applications a more useful characterization is given in terms of copolar (CP) and cross-polar (XP) components. According to the Ludwig definition [14], a Huygens source, (one electric and one magnetic elementary dipole, mutually orthogonal, in phase and whose amplitudes are in a ratio equal to the characteristic impedance of the medium) radiates a pure copolar field with null crosspolarization. Thus this source is taken as a reference, and the CP or XP pattern of any antenna is defined by projecting the antenna s radiated field on the fields generated by two mutually orthogonal Huygens sources. The Huygens source reference for the copolar field is oriented so as to produce an electric field that is parallel to the one generated by the antenna in the far field and in the direction of maximum radiation. According to this definition, it is possible to demonstrate that, given the spherical coordinate components E W ðw; jþ, E j ðw; jþ of the radiated field, the copolar (E CP ) and cross-polar (E XP ) components are given by " # " # E CP ðw; jþ E W ðw; jþ ¼ MðjÞ E XP ðw; jþ E j ðw; jþ ð61þ where the conversion matrix MðjÞ depends on the direction of the far-region electric field vector; in the case of an y-directed or x-directed electric field, we have, respectively sinðjþ MðjÞ¼M y ðjþ¼4 cosðjþ cosðjþ MðjÞ¼M x ðjþ¼4 sinðjþ 3 cosðjþ 5; sinðjþ 3 sinðjþ 5 cosðjþ ð6þ As in a more general case of azimuth-symmetric feed, for a corrugated horn producing a field with a first-order harmonic variation in the azimuth coordinate (m ¼ 1), the radiated field may be obtained once the E-plane and H-plane cut patterns, respectively C E ðwþ and C H ðwþ, are given. For example, in the case of an antenna radiating an y-polarized far-region electric field, the following relation

64 CORRUGATED HORN ANTENNAS 843 can be verified: cross-polarization pattern: E W ðw; jþ¼c E ðwþ sinðjþ; E j ðw; jþ¼c H ðwþ cosðjþ ð63þ Combining these relations with (61), using the first row of (6), the following results are obtained 8 E CP ðw; jþ¼c E ðwþ sin ðjþþc H ðwþ cos ðjþ >< E XP ðw; jþ¼½c E ðwþ C H ðwþš sinðjþ cosðjþ >: ¼ 1 ½C EðWÞ C H ðwþš sinðjþ ð64þ and the same expression can be verified analogous [C E ðwþ and C H ðwþ are exchanged in the first expression] in the case of an x-axis polarization. From (64) it should be noted that, in general, the cross-polar component of the field has a maximum in the 451 plane cut. Usually the level of cross-polarization is given as a level with respect to the maximum of the copolar; if we assume the copolar maximum in the direction W ¼, we can give the cross-polarization pattern, in decibels, as XPðWÞ¼1 log jc EðWÞ C H ðwþj jc E ðw ¼ Þj ð65þ and the cross-polarization maximum can be found by searching for the maximum of this expression for all the allowed values of W: XP max ¼ ( 1 4 max 1 log jc ) EðWÞ C H ðwþj 1 Wð;18 Þ jc E ðw ¼ Þj ð66þ To obtain the cross-polarization characterization of corrugated horns, we can use the field expression (39). Proceeding this way, we have the cross-polar features of the perfectly balanced hybrid HE 11 mode that radiates unperturbed, according to the Gaussian beam model, thus neglecting contributions to cross-polarization coming from the nonideality of the fundamental mode itself, higherorder modes and flange effects. From (39), we can readily find that C E ðwþ¼ exp tan 1 6 ðwþ R l ðppþ þ 5 ; p tan ðaþ C H ðwþ¼ C EðWÞ cosðwþ 3 ð67þ where p ¼.6435 and the wavelength-normalized aperture radius R l and the half-flare angle a are as already defined in (44), giving the following expression for the XPðWÞ¼1 log >< cosðwþ exp tan >= : 6 ðwþ R l ðppþ þ 5 >: p tan ðaþ >; ð68þ This expression is plotted in Fig. 9, with R l as a parameter, for a corrugated waveguide (a ¼ ). Curves related to the maximum of cross-polarization are given in Fig. 1 as a function of R l, with a as a parameter. Results shown in Figs. 9 and 1, even if obtained from an approximate theory, provide an important insight into the behavior of the cross-polar field of a corrugated horn, also giving the optimum limit for achievable cross-polarization performances. As we can see from both plots, the cross-polarization is only very slightly affected by R l and a, which, on the contrary, significantly influence the mainbeam pattern. In fact, the geometry of the corrugations is of prime importance in maintaining the cross-polarization down at the levels given in Figs. 9 and 1. The corrugations must give the appropriate boundary conditions for propagation of the HE 11 mode. As already stated regarding the transition region, typical optimum values, coming from a mix between theory and experimental data, are those given in the right side of Fig. 8, which are practically used for the steady-state corrugation geometry from the end of the transition region to the radiating aperture, consisting of a.5l slot depth, a.1l tooth width, and a.l slot width. These values, in practice, guarantee a cross-polarization level better than B35 db down the co-polar maximum, for bandwidth of about 3 4%. XP (db) R λ = ϑ (db) Figure 9. Corrugated waveguide cross-polar pattern for different values of the wavelength normalized aperture radius.

65 844 CORRUGATED HORN ANTENNAS XP max (db) α=6 α=45 α=3 α= α=1 α=5 α= R λ Figure 1. Cross-polarization maximum parametric curves for corrugated horns Phase Center The phase center is theoretically defined as the origin in space of the spherical phase fronts of the radiated field. In general, for practical antennas, the definition holds only approximately, but corrugated horns are radiating structures for which a rather well-defined phase center exists. In the Gaussian beam model, as we have seen, it is possible to predict the phase center position in both the near and far regions, by using (34) and (35). However, it is sometimes important to estimate a more accurate phase center position as a function of the radiating pattern. In particular, in the design of a corrugated horn, it is important to minimize the phase shift of the radiated field on a given spherical surface subregion (e.g., as delimited by the edges of the illuminated reflector). Thus the center of curvature of the phase-shift-minimized wavefront on that surface can be defined as the operative phase center of the antenna. Knowledge of this point is important in optimizing the position of a feed in a system of reflectors, to produce the best optical design. Computation of the phase center, given the radiated phase pattern, can be carried out in different ways leading to different degrees of approximation in the evaluation. The one here shown is based on the minimization of a given phase pattern in the far-field region. To better explain this method, we refer to Fig. 11, showing the geometry of a horn feeding a reflector antenna. The aim is to minimize the phase variation of the radiated far field inside the solid angle delimited by the elevation angle W (for sake of simplicity, a symmetric configuration is assumed), which is generally not necessarily associated with the reflector edges. Let s suppose that O and O are two points separated by a distance d on the axis of the horn (where, by symmetry, the phase center is located); it can be shown that, in the far-field approximation, the phase patterns having the above mentioned points as phase reference are related by f PðW;jÞ O ðdþ¼f PðW;jÞ O k dcosðwþ ð69þ Horn O y d in which f PðW;jÞ C is the phase at the observation point P with respect to the generic point C and k is the wavenumber. The right hand side of (69) can be seen as a function of the variable d; thus the computation of the phase center can be mathematically formulated as the minimization of the function f ðdþ¼ X i X j x O ϑ ϑ W ij jf PðW i;j j Þ O PðW ¼ Þ Reflector Figure 11. Reference geometry for phase center numerical evaluation. ðdþ fo ðdþj n ð7þ in which the absolute value of the phase shift, eventually powered to an arbitrary value n, is suitably weighted by W ij coefficients, with the double summation extended over the samples ðw i ; j j Þ of the angular region of interest Profiled Horns As stated in the introduction (Section 1), corrugated horns possessing profiles of corrugations consisting of complex curves have been studied extensively. The effect of the curved profile is to excite an appropriate higher-order set of modes to add degrees of freedom with respect to standard linear profiled horns. These additional parameters can be used to control electrical requirements (the radiation pattern and the phase center location) or mechanical requirements (space occupation and weight reduction). In fact, using higher-order modes, it is possible to modify the standard corrugated horn aperture field in order to obtain a radiated mainbeam a bit closer to a rectangle, which is the optimum shape when feeding reflector antenna systems because both aperture and spillover efficiency are maximized. The same approach is also valid if low sidelobe levels are required, and in this case an exponential taper ending section is most appropriate to excite the correct set of higher-order modes; the longer is the exponential section, the lower is the sidelobe level. The property of exciting higher-order modes by varying the profile can be also used to satisfy requirements on the horn mainbeam and at the same time to reduce as much as possible the horn dimensions, which is an attractive feature especially in spacecraft applications. A further advantage of adopting curved profiles is z P

66 CORRUGATED HORN ANTENNAS 845 the possibility of controlling the phase center position and its stability versus frequency; for example, if the profile is quite flat in the region near the radiating aperture, resembling an open corrugated waveguide, the phase center is very close to the aperture itself, and is also very stable with respect to frequency. Thus phase center position and stability can be controlled by properly designing the slope and the shape of the end part of the profile. When dealing with optical systems, especially in those applications in which feed clusters are required, this feature gives some degree of freedom to the design of the geometric configuration of the feeds, which can be very critical because of mutual coupling, for example. Typically, the design of profiled horns begins with the design of a standard linear horn, matching as closely as possible the specifications. Then, using numerical techniques performing the electromagnetic analysis and the optimization, the design is refined to fully satisfy all the requirements. Here we discuss in analytical detail the so-called dual profile [5]. As shown in Fig. 1, it is formed by two elementary curves, the sine square r s at the beginning and the exponential r e at the end, according to the following rule r s ðzþ¼r i þðr s R i Þ ð1 A s Þ z þ A s sin p z ð71þ ; z L s L s L s r e ðzþ¼r s þ e aðz LsÞ 1; L s z L e þ L s ; a ¼ 1 L e lnð1 þ R R s Þ ð7þ where A s 1 modulates the first region profile between a straight line and a pure sine square. The principal effect of the sine square profile is the shaping of the mainlobe by properly exciting higher-order modes, while the exponential taper controls mainly the phase center position and the sidelobe levels. A more flexible version for the shaping of the horn corrugation profile can be obtained by using parametric curves. Among these the nonuniform rational B-splines (NURBS) are particularly versatile [15]. NURBS curves are generated by an ordered set of points {P i }, i ¼,y,n, defining the control polygon, through a function expressed as a ratio of vector-valued polynomials PðuÞ¼ P n i ¼ P n i ¼ q i P i N i;p ðuþ q i N i;p ðuþ ð73þ where q i are an assigned set of weights and N i,p (u) are the normalized B-spline basis functions of degree p. Design methods based on NURBS have already been successfully used [16], and a typical corrugated horn NURBS profile is shown in Fig. 13, where the upper part of the horn longitudinal cut is given and the control polygon is highlighted Numerical Techniques for Corrugated Horns Thus far theoretical aspects of corrugated horns have been discussed on the basis of simple models. Formulas and graphs derived in this way are very useful in the design and, in general, are also sufficient if requirements are not too stringent. This is seldom the case in many modern applications, where high levels of accuracy are required in the design phase. Taking advantage of the computational power of modern computers, numerical techniques for the analysis of electromagnetic problems are now used successfully in microwave applications as a refinement of the simple design approach described above. Regarding the analysis of circular corrugated horns, a hybrid numerical technique is the most efficient, using a combination of different methods according to their ability to accurately analyze different regions. This technique is presented in Ref. 17 and is based on the mode-matching method (MM) [18] and the method of moments (MoM) [19]. The internal part of the horn is best analyzed with MM Sine square region Exponential region R s R R i z r n =R P i,q i r i L s L e R i =r z L Figure 1. Dual-profile corrugated horn. Figure 13. NURBS-profile corrugated horn.

67 846 CORRUGATED HORN ANTENNAS making use of the generalized scattering matrix (GSM) concept. The horn can be seen as a cascade of single-step discontinuities in circular waveguide for which the MM method allows computation of the GSM. The overall horn geometry is analyzed by respectively cascading all the GSMs of the steps to find the overall GSM of the corrugated structure. MM is convenient for these structures because of its efficiency and small storage demand. In fact, whenever a new step is solved, it is immediately cascaded with the following step to form a partial GSM that includes all the steps solved thus far. In the corrugated horn analysis only a particular subset of modes may be chosen. In the case of a circular waveguide TE 11 excitation, the subset of TE 1n /TM 1n modes is sufficient to fully represent the field inside the horn if the azimuth symmetry is preserved everywhere. The rule for choosing the number N of modes in a single circular waveguide section for accurate numerical results and computation efficiency depends on the wavelengthnormalized radius of the waveguide; typically, this is about N ¼ R l. The outer part of the horn, including the radiating aperture and the external metallization, is analyzed with the application of MoM to a combined field integral equation (CFIE). Formulating an equivalent problem in which the horn aperture and the external feed shape form a closed metallic surface, the CFIE enforces the boundary conditions for both the electric and magnetic fields. The axial symmetry of the structure is used to apply the body of revolution (BoR) formulation [] to the MoM, so that an efficient expansion for electromagnetic sources and fields is possible. In particular, a subsectional basis function expansion is applied only along the generating curve of the BoR surface, while expansion in entire domain harmonic-type basis functions is used along the azimuth angle. In this way, CFIE may be solved easily for an unknown set of amplitudes of the basis functions used to expand electric surface current density on the external horn surface. Finally, to complete the analysis, the coupling between the inner and the outer parts of the horn must be taken into account. This is done by applying the tangential field continuity over the horn aperture leading to a magnetic field integral equation (MFIE), which is solved by MoM. Combination of MM and MoM allows us to compute the GSM of the horn in the presence of the actual outer feed shape. This also enables us, given the excitation, to estimate the input matching and calculate the external horn surface equivalent sources, allowing an easy computation of the radiated fields by means of the well-known free-space Green function. In conjunction with analysis techniques, numerical optimization procedures have been developed to produce complete tools for corrugated horn design. Optimization techniques search for the optimum geometry satisfying a given set of specifications. Typically a cost is defined as a function of a particular set of electromagnetic performances so that the optimum solution is an extreme point of the cost function (a minimum or a maximum). Then the optimization procedure searches in the space of the allowed geometry parameters of the structure to be optimized to find this extreme point. The existing used methods to search for the optimum geometry may be grouped into two categories: deterministic and stochastic. A commonly used deterministic technique is the quasi- Newton method [1], while genetic algorithms [] are an example of the stochastic type. The quasi-newton method searching for the optimum value is governed mathematically by computing the differentiation, up to the second order, of the cost function. This is an iterative procedure where, at each computation step, the higher-order derivative information is used to directly evaluate the next point, in the space of the geometry to be optimized. Such a point is a potential candidate to be the optimum. This is quite a fast optimization method, performing very well if the iteration starting point is already within the basin of attraction of the optimum point itself; otherwise, as is well known, it remains confined to the nearest local minima. Genetic algorithms are an evolutionary method producing successive populations of individuals according to their capabilities to adapt themselves to the environment. This capability is expressed in terms of a cost function, where individuals represent the codification of the space of the allowed geometric parameters. Individuals with higher capabilities (better cost functions) have a greater probability of reproducing themselves in successive generations (new sets of geometric parameters). In the genetic algorithm scheme, each successive generation is produced with genetic laws of crossover and mutation, yielding individuals that may have better capabilities, that is better cost functions. From a practical point of view, genetic algorithms, like other stochastic methods, have complementary features with respect to direct searching techniques. They are generally more CPU-demanding and slower, but have the advantage of performing global searches for the optimum point without being trapped in local minima. A hybrid method based on genetic algorithms and the Quasi- Newton method has been successfully applied to corrugated horn design [3]. Artificial neural networks [4] (ANNs) are another useful approach for corrugated horn design. ANNs can be considered as universal approximators with the ability to model any given transfer function if properly instructed. On the basis of a given set of data related to horn geometry and performance, the network is able to learn how the horn operates. This learning process matures, generating an evolving model of the horn that may be perceived as a blackbox having geometric parameters such as input and electromagnetic performance such as output. The accuracy of the ANN model is refined by using the information coming from a cost function evaluating the distance, in terms of the performances, between the model and the real horn. The major advantage of this method is that, once the learning phase has produced, an accurate ANN model, the ANN-based horn analysis, is very fast, and thus is of prime interest in the horn design phase, where a very large number of simulations are commonly required. Examples of ANN applications to horn design can be found in Ref. 5.

68 CORRUGATED HORN ANTENNAS 847 Specifications Theoretical tools Geometry Frequency (Wavelength) 1) Gain G Eq.(57) Fig. 6,7 Feeding waveguide dimension Analysis and optimization L ) Taper (XdB@θ t ) Horn length (L) Aperture radius (R) Eq.(46) Eq.(4) Eq. (43) R 3) Waist W Throat region corrugations Return loss Cross polarization Steady-state corrugations 1) Beam shape ) Side lobes 3) Phase center Profile of the corrugations Theoretical and numerical tools Figure 14. Schematic flow chart for corrugated horn design Summary of Corrugated Horn Design To summarize the previous concepts, a practical design procedure is outlined, following the sketch in Fig. 14, showing a flowchart for corrugated horn design. In the flowchart the design should be seen as a process linking a set of specifications (grouped under specifications ) to a set of geometric parameters (geometry) that completely characterize the fundamental aspects of horn mechanics, at least from an electromagnetic perspective. The frequency is the fundamental specification involved (by means of the wavelength) in all the horn geometry; however, from a design perspective, it directly fixes the dimension of the input waveguide feeding the horn once single fundamental mode propagation is imposed in the operative band. Three equivalent specifications can be used to theoretically determine the horn length L and the aperture radius R; if the horn gain G is given, it is possible to use (57) and the graphs of Figs. 6 and 7 for best choice of L and R; if the waist w is given, then (4) and (43) can be 1 E (db) Simulation Measurement Figure 15. High-gain feed horn at 3 GHz (Courtesy of the Institute of Radioastronomy of the Italian National Research Council.) ϑ (deg) Figure 16. E-plane pattern cut of the 3-GHz high-gain corrugated horn.

69 848 CORRUGATED HORN ANTENNAS used; if the taper X db at y t is given, then the equivalent waist specification can be obtained from (46), proceeding as in the previous case. Both theoretical and numerical tools should be used for the other specifications. Return loss is related mainly to the geometry of the throat region corrugations; crosspolarization affects the geometry of the steady-state region corrugations; and mainbeam shape, sidelobe, and phase center specifications should be used to design the curvature of the corrugation profile. The electromagnetic phenomena governing the preceding relations between specifications and horn geometry have been explained in the text above and values have been suggested to quantify these relations since this would be of greater help to the designer. However, those quantitative values should not be taken as an arbitrary rule; rather, they require further verification by analytical simulations according to the particular application, and this is the meaning of the term numerical tools introduced here. Once the horn geometry has been determined, analysis and optimization routines should be used to verify and refine the design. 5. CORRUGATED HORN DESIGN EXAMPLES To give the reader an idea of the performances of corrugated horns, two examples are presented here. Example 1. Assume a high-gain corrugated horn operating in Ka band at 3 GHz with gain of B8 db. Thus, according to the graph of Fig. 7, a 6 l aperture radius with an half-flare angle of B81 has been chosen, leading to the prototype of Fig. 15 with an aperture diameter of B11 cm and an overall length of B38 cm. The gain was verified to be correct by full-wave simulations, showing a B1 db variation in a % band, while the copolar radiation pattern is given in Fig. 16, highlighting results close to measurement data. Particular attention in the design has been devoted to keep both the input reflection coefficient and the Figure 18. Dual-profile corrugated horn at GHz (Courtesy of the Institute of Radioastronomy of the Italian National Research Council.) cross-polarization maximum as low as possible. As is shown in the plots of Fig. 17, the measured reflection coefficient is less than 3 db with very good agreement with simulation data. Example. Given a dual-profile corrugated horn at GHz for use as a feed for a reflector antenna illuminated with an edge taper of 1 db at The horn, whose prototype is given in Fig. 18, has been optimized for compactness, reducing about % space occupation with respect to a standard horn. It is interesting to observe the measured beam pattern of the horn that is compared in the plot of Fig. 19 with the results of the full-wave simulation. Comparing the dual-profile horn pattern with the one of the standard horn in Fig. 16, we note the differences in the shape of the mainbeam and the secondary lobe due to the contribution to the radiation of higher-order modes, excited by the curved profile. 5 3 Simulation Measurement 1 Simulation Measurement S 11 (db) 35 4 E (db) Frequency (GHz) Figure 17. Reflection coefficient for the 3-GHz high-gain corrugated horn ϑ (deg) Figure 19. H-plane pattern cut of the -GHz dual-profile horn.