Microstrip Coupler with Complementary Split-Ring Resonator (CSRR)

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1 Microstrip Coupler with Complementary Split-Ring Resonator (CSRR) E-242 Course Project Report Submitted by, EMIL MATHEW JOSEPH Guided by, Prof. K J VINOY Department of Electrical and Communication Engineering, Indian Institute of Science, Bangalore 0

2 Microstrip Coupler with Complementary Split-Ring Resonator (CSRR) Emil Mathew Joseph Department of Electrical and Communication Engineering, Indian Institute of Science, Bangalore, India Abstract- A novel microstrip Coupler with Complementary Split- Ring Resonator (CSRR) is simulated and fabricated. The CSRR structure in the grounded plane of a conventional microstrip double-line coupler, increases its even mode characteristic impedance. This results in a higher degree of coupling. The results of simulation and measurement show that the new coupler achieves a high degree of coupling (5 db coupling) over a wide frequency band (26.3% relative bandwidth). Keywords Microstrip double-line coupler, CSRR I. INTRODUCTION In conventional microstrip parallel-coupled couplers to achieve tight backward coupling, excessively small lines-gap is required. Alternative components include directional couplers such as the branch-line or rat-race, however, these couplers are inherently narrowband (less than 15% bandwidth) circuit. The Lange coupler is a solution widely used in the MMIC industry for broadband 3-dB coupling, but it has the disadvantage of requiring bonding wires. Couplers based on CRLH (composite right/left hand) transmission lines, which composed of one or two Left Handed-Transmission Lines constituted of series inter-digital capacitors and shunt shortedstub inductors, can provide arbitrary loose/tight coupling levels. But designing this coupler is too complicated [1]. It has been demonstrated that Complementary Split-Ring Resonator (CSRR) etched in the ground plane or in the conductor strip of planar transmission media (microstrip or CPW) provide a negative effective permittivity to the structure. In this paper, a novel coupled-line backward coupler based on CSRR as discussed by K Y Liu, C Li and F Li in [1], is fabricated and tested. The characteristic even mode impedance can be enhanced by etching CSRR structure in the grounded plane of a conventional microstrip double-line coupler. This results in a higher degree of coupling. II. THEORY A. Backward-wave directional coupler A symmetrical four-port network behaves like a backwardwave directional coupler if the following condition is satisfied [2]: Z 0e Z 0o =Z 0 2 where Z 0e is the even-mode characteristic impedance, Z 0o is the odd-mode characteristic impedance of the microstrip line and Z0 is the characteristic impedance at ports. The maximal amount of coupling between ports 1 and 3 occurs when θ=βl=π/2 rads or l=λ/4 where l is the length of the coupled lines and λ denotes the guide wavelength in the medium of the transmission line. B. Complementary Split-Ring Resonator (CSRR) The CSRR can be considered as the dual of the Split-Ring Resonator model. As is well known, the complementary of a planar metallic structure is obtained by replacing the metal parts of the original structure with apertures, and the apertures with metal plates. Due to symmetry considerations, it can be demonstrated that, if the thickness of the metal plate is zero, and its conductivity is infinity (perfect electric conductor), then the apertures behave as perfect magnetic conductors. In that case the original structure and its complementary are effectively dual, and if the field F = (E,H) is a solution for the original structure, its dual F defined by F = (E,H ) = (- (μ/ε)h, (ε/μ)e), is the solution for the complementary structure [3]. The intrinsic circuit model for the CSRR (dual of the SRR model) is shown in Figure 1. In this circuit, the inductance L s of the SRR model is substituted by the capacitance, C c, of a disk of radius r o -c/2 surrounded by a ground plane at a distance c of its edge. Conversely, the series connection of the two capacitances C o /2 in the SRR model is substituted by the parallel combination of the two inductances connecting the inner disk to the ground. Each inductance is given by L o /2, where L o =2πr o L pul and L pul is the per-unit-length inductance of the CPWs connecting the inner disk to the ground. The capacitance C c is that corresponding to a metallic disk of radius r o -c/2 surrounded by a ground plane at a distance c. Similarly, the inductance L o is that corresponding to a circular CPW structure of length 2πr o, strip width d, and slot width c. An analytical approximate expression for C c and L 0 when a dielectric substrate is present is [3, 5] 1

where a, b, and h are geometrical variables defined in Fig. 2 and function B is defined as B(x) = S 0 (x)j 1 (x)-s 1 (x)j 0 (x), with S n and J n being the nth-order Struve and Bessel functions.

The magnetic (b) and electric field (d) lines of a similar CSRR on the same dielectric substrate are also sketched. III.

The structure of CSRR-based directional coupler is showed in Fig. 4. The substrate employed is the commercially available FR4 (ε r =4.4, thickness h=1.56 mm).

The physical dimensions necessary to achieve this frequency have been calculated by using the design formulas for CSRRs (1,2), resulting in this case c=d=0.3 mm, r 0 =3.2 mm (see Fig. 1).

3 where a, b, and h are geometrical variables defined in Fig. 2 and function B is defined as B(x) = S 0 (x)j 1 (x)-s 1 (x)j 0 (x), with S n and J n being the nth-order Struve and Bessel functions. A Sketch of the electric and magnetic field lines in a SRR and CSRR are shown in Fig. 3. Fig 3: Sketch of the electric (a) and magnetic (c) field lines of an SRR on a dielectric substrate. The magnetic (b) and electric field (d) lines of a similar CSRR on the same dielectric substrate are also sketched. III. DESIGN AND SIMULATION RESULTS To demonstrate the performance of the proposed microstrip coupler based with CSRR in ground plane, prototype device has been designed, simulated and measured. The structure of CSRR-based directional coupler is showed in Fig. 4. The substrate employed is the commercially available FR4 (ε r =4.4, thickness h=1.56 mm). The characteristic impedance at the ports is set to Z0 = 50Ω. The resonant frequency of the CSRR has been set around 1.9 GHz. The physical dimensions necessary to achieve this frequency have been calculated by using the design formulas for CSRRs (1,2), resulting in this case c=d=0.3 mm, r 0 =3.2 mm (see Fig. 1). The width of the slit at each ring has been taken equal to 0.6 mm. Fig 1: Topologies of the SRR (a) and CSRR (b), and their equivalent circuit models. Gray zones represent the metallization. Fig 2: The capacitance and inductance of the CSRR is approximately equal to that corresponding to a metallic disk of radius a = r o -c/2 surrounded by a ground plane at a distance b-a=c, r o being the averaged radius of the CSRR and c the width of the slots in this. The dielectric substrate is characterized by its permittivity ε and thickness h. Fig. 4: Structure of CSRR-based directional coupler (a) Microstrip conductor plane (b) Ground plane with CSRR. 2

$5 db backward coupling, return loss smaller than -12 db and isolation better than 10.5 db over the 1.6 to 2.1 GHz range (26.3% fractional bandwidth wrt. 1.9GHz).$

4 The results obtained by momentum simulation is shown in Fig. 5. The performances of the coupler are the following: 5.25±0.5 db backward coupling, return loss smaller than -12 db and isolation better than 10.5 db over the 1.6 to 2.1 GHz range (26.3% fractional bandwidth wrt. 1.9GHz). Fig 5: Magnitude of the S-parameters for the coupler of Fig. 4 obtained by simulation (ADS) IV. FABRICATION AND MEASUREMENT RESULTS The fabricated structure of CSRR-based directional coupler is shown in Fig. 7 and the measured S-parameters are plotted in Fig. 6. The measured performances of the coupler are the following: 5.25±0.5 db backward coupling, return loss smaller than -11 db and isolation better than 7.5 db over the 1.7 to 2.2 GHz range (26.3% fractional bandwidth wrt. 1.9GHz). Fig. 7: Fabricated CSRR-based directional coupler (a) Microstrip conductor plane (b) Ground plane with CSRR. V. CONCLUSION The results of simulation and measurement show that the new coupler achieves a high degree of coupling(~5db) over a wide frequency band (26.3% relative bandwidth). We would have got better bandwidth (upto 40% relative), smaller return loss (less than -18 db) and better isolation (more than 25 db) if the dimensions of CSRR are calculated more accurately using the design formulas (1,2). REFERENCES Fig 6: Magnitude of the S-parameters for the coupler of Fig. 7 measured by a Network Analyser [1] ] K. Y. Liu, C. Li and F. Li, A New Type of Microstrip Coupler with Complementary Split-Ring Resonator (CSRR), PIERS ONLINE, VOL. 3, NO. 5, [2] Mongia, R., I. Bahl, and P. Bhartia, RF and Microwave Coupler-line Circuits, Artech House, Norwood, MA, [3] R. Marque s, F. Marti n and M. Sorolla, Metamaterials with Negative Parameters Theory, Design, and Microwave Applications, John Wiley & Sons,

5 [4] Falcone, F., T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M. Sorolla, Effective negative-ε stop-band microstrip lines based on complementary split ring resonators", IEEE Microw. Wireless Compon. Lett., Vol. 14, No. 6, , [5] R. Marqués, F. Mesa, J. Martel, and F. Medina, Comparative analysis of edge- and roadside-coupled split ring resonators for metamaterial design. Theory and experiments, IEEE Trans. Antennas Propagat., vol. 51, pp , Oct

Analyzing of Coupling Region for CRLH/RH TL Coupler with Lumped-elements

PIERS ONLINE, VOL. 3, NO. 5, 27 564 Analyzing of Coupling Region for CRLH/RH TL Coupler with Lumped-elements Y. Wang 2, Y. Zhang, 2, and F. Liu 2 Pohl Institute of Solid State Physics, Tongji University,