Stopband Prediction with Dispersion Diagram for Electromagnetic Bandgap Structures in Printed Circuit Boards

Transcription

1 Stopband Prediction with Dispersion Diagram for Electromagnetic Bandgap Structures in Printed Circuit Boards Yoshitaka Toota Department of Communication Network Engineering kaama Universit kaama 7 53 Japan toota@cne.okaama-u.ac.jp Arif Ege Engin, Tae Hong Kim, and Madhavan Swaminathan Packaging Research Center School of Electrical and Computer Engineering Georgia Institute of Technolog engin@ece.gatech.edu Kazuhide Uriu EMC Design Group Sstem Engineering Center Matsushita Electric Industrial Co., Ltd. Abstract Electromagnetic bandgap EBG structures that prevent propagation of electromagnetic waves within a given frequenc range are quite effective in suppressing simultaneous switching noise on parallel power planes. However, it is quite time consuming to compute the stopband frequencies of interest using full-wave electromagnetic simulation of the entire structure. In contrast, using dispersion-diagram analsis based on a unitcell network of EBG structures is more efficient and less time consuming. This paper presents an approach for two-dimensional EBG structures b etending a well-known dispersion-diagram analsis of one-dimensional infinite periodic structures. The stopbands predicted with the proposed analsis were compared with good agreement to measured and simulated results. In addition, the concept was applied to test the stopband range of EBG structures formed on an actual printed circuit board with a test coupon of an EBG unit cell placed on the same board. I. INTRDUCTIN Electromagnetic interference EMI has become a critical performance issue in recent mied-signal sstems because of the dense packaging of digital and RF/analog circuits. To isolate sensitive RF/analog signals from simultaneous switching noise SSN, electromagnetic bandgap EBG structures that prevent propagation of electromagnetic waves within a given frequenc range are quite effective in suppressing SSN on parallel power planes. The EBG structure that we have proposed provides an ecellent isolation of more than db within the stopband [1], []. Fig. 1 illustrates two eamples of the proposed EBG pattern, which consists of a lattice with large metal patches and small metal branches connecting adjacent large patches. This pattern is assigned to either the power plane or the ground plane depending on the design. Since this EBG structure requires no additional vias that are essential to the other EBG structures [3], [], a standard printed circuit board PCB fabrication technique is easil applicable for this EBG structure, which is a cost-effective solution. To meet the general demand for more compact wireless devices, furthermore, a size reduction of the EBG structure has been achieved b improving the geometries and materials of the structure [5]. To appl these EBG structures to actual PCBs, it is necessar to quickl and accuratel compute the stopband frequencies of interest in the design stage. Since a full-wave electromagnetic EM simulation for the entire structure is quite time consuming, a more realistic option is to use a wave analsis that focuses on a unit cell in infinite periodic structures. In previous studies, there have mainl been two kinds of approaches used. ne of the approaches is the eigenmode analsis with a full-wave EM solver []. In this case, a high-frequenc structure simulator HFSS is commonl used because it originall included an eigenmode calculation tool for a unit cell with periodic boundaries. However, a HFSS is also time consuming. n the other hand, the other wave analsis, which uses a transmission-line circuit model [] [], is epected to reduce the computational time, but this model needs to be modified whenever the geometrical features of a unit cell change. Port 1 1, 7 Port 1 1,,, a b a b Port 5, 7 Port 5, Fig. 1. Eamples of EBG lattice combining large square patches with small square branches unit in mm. a 1-D lattice 1 unit cells. b -D lattice unit cells X//$. c IEEE 7

2 To compensate for the disadvantages in the above approaches, this paper presents a dispersion-diagram analsis based on a network that epresses a unit cell in infinite periodic structures. With respect to infinite periodic structures, in previous studies [] [1], a well-known one-dimensional 1-D analsis [11] has been commonl used as a substitute for a - D analsis and lost its accurac for -D structures. In contrast, this paper provides an approach for two-dimensional -D structures b etending the 1-D approach and then derives the eigenvalue equation of arbitrar -D EBG structures using the network parameters. The eigenvalue equation is solved in terms of phase or phase constant to displa a dispersion diagram that indicates the passband-stopband characteristics. Predictions for the stopband frequencies are compared with good agreement to the simulated and measured S parameters transmission coefficient for the eamples shown in Fig. 1. In addition, the concept described above is applied to test the stopband range of EBG structures formed on actual PCBs with a test coupon of an EBG unit cell placed on the same board. +a b a +a b c I in V in 11 1 b V I d 1 I out V out I 1 I 3 V V 3 I V II. EIGENVALUE EQUATINS FR PERIDIC STRUCTURES A. Eigenvalue Equation for 1-D Periodic Structure Before discussing the -D case, we will briefl summarize the eigenvalue equation for 1-D infinite periodic structures. As was referred to in [11], the eigenvalue equation based on a twoport network for a unit cell in 1-D infinite periodic structures is derived b focusing on the ABCD transmission matri of the unit cell and assuming hase dela of the unit cell equal to the propagation factor e γλ, where γ = α +jβ is the propagation constant for the periodic structure, and α and β are the attenuation constant and phase constant, respectivel. In this paper, the periodic interval Λ of a 1-D EBG structure is defined as Λ= + a b Fig. a. B using the relations between the ABCD parameters and the parameters shown in Fig. b, the eigenvalue equation for 1-D infinite periodic structures can finall be epressed with the parameters as cosh γλ = B. Eigenvalue Equation for -D Periodic Structure Net, the eigenvalue equation for -D EBG structures is derived. This paper deals with onl the isotropic EBG structure in the and directions. With respect to the periodic interval, we have Λ =Λ Λ= + a b Fig. c. The derivation starts with a four-port network for a unit cell in -D infinite periodic structures. When the unit cell is represented b a fourport -matri network Fig. d, the relations between the input and output variables are written as V I = 11 1 II, V 1 I where ij is a impedance matri and the input and output vectors are written as follows: Fig.. a Unit cell for 1-D EBG structure. b Two-port network epressed b matri. c Unit cells for -D EBG structure. d Four-port network epressed b matri. The dashed lines in a and c indicate the boundaries between adjacent unit cells. V I = I I = V1 V I1 I ; V = ; I = V3 V I3 I ;. Equation can be easil rewritten in the epression form of a transmission matri: V I I I = A C B V D I 3 V I. Now, taking the directions of and into account, we replace 3 with the following input and output vectors: V1 V3 X I = ; X I = ; 1 I 3 5 V V Y I = ; Y I =. I Using 5, we can rewrite to obtain the following epression: XI F = 11 F 1 X, Y I F 1 F Y where Aij B F ij = ij C ij D ij X//$. c IEEE

3 If a -D periodic structure is infinitel long, the voltages and currents at the output terminals of the unit cell should be different from those at the input terminals b onl the propagation factor in the corresponding propagation direction, as the do in the 1-D case. Therefore, assuming the propagation factor e γλ in the + direction and e γλ in the + direction, we have Frequenc GHz 1 Frequenc GHz 1 { F 11 F 1 F 1 F e γλ I e γλ I } X =, Y where I is the unit matri. Equation is an eigenvalue equation for a -D infinite periodic EBG structure. A nontrivial solution for the output vectors eists onl if the determinant of the matri in vanishes. III. DISPERSIN DIAGRAM F PERIDIC STRUCTURES In the previous section, we derived the eigenvalue equations for 1-D and -D EBG structures. nce the network parameters in the equations are given, the eigenvalue equations can provide the relations between phase constant β and frequenc f. The curves of β versus f show the passband-stopband characteristics of the passbands for propagation and the stopbands in which no wave propagates. The diagram is called a dispersion diagram and is equivalent to the Brillouin diagram used to illustrate the energ-band structures in periodic crstalline media. Fig. 3 shows the dispersion diagrams for the 1-D and -D EBG structures obtained from 1 and, respectivel. The calculation of the parameters in the eigenvalue equations is carried out with a commercial simulator, Sonnet, under the condition that both EBG structures have the identical unit cell parameters: = 1 mm; a b = 1 mm; and d=.3 mm. Parameter d is the dielectric thickness. The calculation also assumes that there are no material losses and the dielectric is FR- with ε r =.. Furthermore, α =is set in the -D analsis. As shown in Fig. 3, the horizontal ais of the dispersion diagrams indicates β in the Brillouin zone. The phase constant β in the 1-D case is equal to k, which is the wavenumber in the direction. In the -D case, on the other hand, we have β = k + k, where k is the wavenumber in the direction. The, X, and M in the Brillouin zone represent the high smmetr points in the spectral domain: and X in the 1- D diagram correspond to k =and k = π/λ, respectivel;, X, and M in the -D diagram correspond to k = k =, k = π/λ,k =, and k = k = π/λ, respectivel. Therefore, when calculating a -D dispersion diagram, k =, k = π/λ, and k = k are set in for the regions of -X, X-M, and M-, respectivel. The solid line in Fig. 3a and the circle plots in Fig. 3b are the solutions to their corresponding eigenvalue equations, which means that electromagnetic waves with β propagate through the EBG structure. However, no solutions at given frequencies mean no wave propagation. Therefore, the colored Μ k Fig. 3. Dispersion diagrams: a 1-D EBG. b -D EBG. In b, the triangle plots show the result of a HFSS simulation, which includes solutions that are plotted along the dashed line indicating wave propagation in the air. The colored area in each graph shows the stopband of the corresponding EBG structure predicted with the dispersion diagram. areas in Fig. 3 demonstrate the stopbands. In particular, the colored area shown in Fig. 3b indicates the complete stopband in which no wave propagates in an directions. Note that the stopbands of the 1-D EBG structure do not coincide with those of the -D EBG structure. That is wh the 1-D analsis cannot be substituted for the -D analsis. A proper -D analsis is indispensable in finding the passband-stopband characteristics of -D EBG structure. This dispersion-diagram analsis has the advantage of estimating the stopbands of EBG structures onl with a network matri that epresses the unit cell, without an calculations or measurements for the entire EBG structure. As described in Section V, this concept is applicable to the stopband prediction, without an measurements of the entire EBG board, b measuring the S parameters using a test coupon of an EBG unit cell on the same board. In addition, a further advantage is that less calculation time is necessar when the dielectric thickness d is sufficientl thin compared to the lateral dimensions. This is because not onl the planar field solvers, such as Sonnet, but also SPICE models are applicable to such cases. The SPICE models are computed faster compared to planar field solvers. For eample, calculations made with SPICE models can achieve 7 more improvement compared to Sonnet models in terms of simulation time [1] and are performed much more efficientl b appling the Transmission Matri Method TMM [13]. IV. EVALUATIN F PRPSED ANALYSIS In this section, we show that the proposed analsis for the stopband prediction from a dispersion diagram is valid. First, the comparison with HFSS is described. The triangle plots in Fig. 3b show the results from a HFSS eigenmode simulation. Note that the HFSS results include solutions that are plotted along the dashed line indicating wave propagation in the air. After the solutions are removed, it is seen Μ k X//$. c IEEE 9

4 that the proposed analsis is in a good agreement with the HFSS simulation. The entire analsis, including the networkparameter calculation with Sonnet, is approimatel 9 times faster compared with the HFSS simulation. Net, the transmission coefficient S 1 from Port 1 to Port in the EBG structures as shown in Fig. 1 is used to evaluate the proposed analsis. Fig. 1 shows the 1 geometr for the 1-D EBG and geometr for the -D EBG. In addition to these geometries, 1, 3 1,, and 3 are used for measuring with a vector network analzer VNA and simulated with Sonnet emcluster. For the Sonnet simulation, a dielectric loss of tan δ=., a copper conductivit of σ c = S/m, and a copper thickness of t=3 µm are assumed. Fig. shows the S 1 data from the VNA measurements and the Sonnet simulation, and the solid and dashed lines correspond to the measured and calculated S 1, respectivel. The good agreement between the measurements and calculation of S 1 is seen from this figure. Fig. also shows that the isolation b the EBG structure improves as the number of EBG unit cells between the input and output ports increases. However, the stopband frequencies are independent of the number of unit cells between the two ports. This suggests that the structure of the unit cell determines the stopband frequencies and, therefore, the dispersion-diagram analsis with the infinite periodic EBG structure can be used S 1 db S 1 db Frequenc GHz Frequenc GHz Fig.. Comparison of predicted stopbands with measured and calculated transmission coefficient S 1. a 1-D EBG. b -D EBG. The solid and dashed lines correspond the measured and calculated S 1, respectivel. The colored areas indicate the intrinsic stopbands predicted from the dispersion diagrams in Fig. 3. to predict the passband-stopband characteristics intrinsic to the EBG unit cell. The stopbands predicted from the dispersion diagrams in Fig. 3 are superposed on Fig. as the colored areas. The predicted stopbands agree well with the stopbands estimated from the S 1 characteristics, which demonstrates that the proposed dispersion-diagram analsis is valid for predicting the stopbands of an EBG structure. What should be emphasized again here is that a -D analsis is necessar to obtain the passband-stopband characteristics of a -D EBG structure since the stopbands of the 1-D and -D EBG structure with the same unit cell are in disagreement. V. STPBAND PREDICTIN USING TEST CUPN The dispersion-diagram analsis proposed in this paper is quite useful for stopband prediction in the design stage. In this section, the application of this concept is presented, which is to test the stopband range of EBG structures formed on actual PCBs with a test coupon of an EBG unit cell placed on the same board. To verif the concept, we fabricated a test vehicle in which an EBG unit cell is used as a test coupon. The geometric parameters of the unit cell are as follows: = 15. mm mils; a b =.5 mm 1 mils; and d=.17 mm 5 mils. The dielectric of the board is also FR-. Fig. 5a shows hotograph of the test coupon. The network parameters obtained from a -port VNA measurement using the test coupon provided the dispersion diagram shown in Fig. 5b, after the effect of launch pads was de-embeded. Fig. a shows 1-D EBG structures with 1 and 1 geometries. The are placed on the same board as the test coupon shown in Fig. 5a. The electrical properties of these EBG between Ports 1 and were measured with a -port VNA. The measured results of S 1 for 1 and 1 geometries are shown in Fig. b, on which the stopbands predicted from the dispersion diagram in Fig. 5b are superposed. From Fig. b, we can see that the measured data obtained b testing a unit cell as a test coupon provide stopbands in good agreement with the actual EBG structures. Thus, a test coupon of a unit cell is applicable for estimating the stopband in fabricated PCBs. Fig. 5. a Photograph of test coupon. b 1-D dispersion diagram obtained from -port VNA measurement with test coupon. Frequenc GHz X//$. c IEEE 1

5 S 1 db Frequenc GHz Fig.. a 1-D EBG structures with 1 and 1 geometries unit in mm. b Measured transmission coefficient S 1 for 1 and 1 geometries. The colored area indicates the stopbands predicted from the dispersion diagram in Fig. 5b. VI. CNCLUSINS This paper presents 1-D and -D dispersion-diagram analses with a network matri that epresses a unit cell from EBG structures formed in the power/ground planes. In particular, the -D analsis is etremel significant because the stopbands of the 1-D and -D EBG structures with the same unit cell are in disagreement and, therefore, the 1-D analsis cannot be substituted for the -D analsis. This approach achieves an accurate prediction of the stopbands of both 1-D and -D EBG structures without an measurements or full-wave EM simulations for the entire structure. The stopband prediction based on the proposed analsis is proper for the design stage since the network-matri calculation is efficientl carried out. In addition, this concept can be applied to predict the stopband of an EBG structure formed on an actual PCB with a test coupon of an EBG unit cell placed on the same board. [3] T. Kamgaing and. M. Ramahi, A novel power plane with integrated simultaneous switching noise mitigation capabilit using high impedance surface, IEEE Microw. Wireless Compon. Lett., vol. 13, no. 1, pp. 1-3, Jan. 3. [] S. Shahparnia and. M. Ramahi, Electromagnetic interference EMI reduction from printed circuit boards PCB using electromagnetic bandgap structures, IEEE Trans. Electromagn. Compat., vol., no., pp. 5-57, Nov.. [5] Y. Toota, A. E. Engin, T. H. Kim, M. Swaminathan, and S. Bhattachara, Size Reduction of Electromagnetic Bandgap EBG Structures with New Geometries and Materials in Proc. 5th Electron. Compon. Technol. Conf., San Diego, CA, Jun.. [] A. Sanada, C. Caloz, and T. Itoh, Characteristics of the composite right/left-handed transmission lines,, IEEE Microw. Wireless Compon. Lett., vol. 1, no., pp. -7, Feb.. [7] F. Elek and G. V. Eleftheriades, A two-dimensional uniplanar transmission-line metamaterial with a negative inde of refraction, New J. Phs., Vol. 7, No. 13, 5. [] S. D. Rogers, Electromagnetic-bandgap laers for broad-band suppression of TEM modes in power planes, IEEE Trans. Microw. Theor Tech., vol. 53, no., pp , Aug. 5. [9] T. L. Wu, Y. H. Lin, T. K. Wang, C. C. Wang, and S. T. Chen, Electromagnetic Bandgap Power/Ground Planes for Wideband Suppression of Ground Bounce Noise and Radiated Emission in High-Speed Circuits, IEEE Trans. Microw. Theor Tech., vol. 53, no. 9, pp , Sep. 5. [1] S. Shahparnia and. M. Ramahi, A Simple and Effective Model for Electromagnetic Bandgap Structures Embedded in Printed Circuit Boards, IEEE Microw. Wireless Compon. Lett., vol. 15, no. 1, pp. 1-3, ct. 5. [11] R. E. Collin, Foundations for Microwave Engineering, nd ed. New York: McGraw-Hill, 199, pp [1] A. E. Engin, M. Swaminathan, and Y. Toota, Finite difference modeling of multiple planes in packages, in Proc. 17th Int. urich Smp. Electromagn. Compat., Singapore, Mar., pp [13] J. Kim and M. Swaminathan, Modeling of irregular shaped power distribution planes using transmission matri method, IEEE Trans. Adv. Packag., vol., no. 3, pp. 33-3, Aug. 1. ACKNWLEDGMENT The authors are grateful to Sonnet Software for making emcluster available. REFERENCES [1] J. Choi, V. Govind, and M. Swaminathan, A novel electromagnetic bandgap EBG structure for mied-signal sstem applications, in Proc. IEEE Radio and Wireless Conf., Atlanta, GA, Sep., pp. 3-. [] J. Choi, V. Govind, M. Swaminathan, L. Wan, and R. Doraiswami, Isolation in mied-signal sstems using a novel electromagnetic bandgap EBG Structure, in IEEE 13th Topical Meeting Electr. Performance Electron. Packag., Portland, R, ct., pp X//$. c IEEE 11