Study on Transmission Characteristic of Split-ring Resonator Defected Ground Structure

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1 PIERS ONLINE, VOL. 2, NO. 6, Study on Transmission Characteristic of Split-ring Resonator Defected Ground Structure Bian Wu, Bin Li, Tao Su, and Chang-Hong Liang National Key Laboratory of Antennas and Microwave Technology Xidian University, Xi an, 7171, China Abstract A square split-ring resonator (SRR) defected ground structure (DGS) is studied in this paper. This DGS structure has a flat low-pass characteristic and a sharp band-gap property compared to the conventional dumbbell DGS. A detailed analysis of the relationship between the transmission characteristic and the split-ring dimension is made. In order to enhance the out-band suppression, an improved SRR DGS cell with open stubs loaded on the conductor line is then presented and fabricated. DOI: /PIERS INTRODUCTION In 1999, defected ground structure was firstly proposed by Park et al. based on the idea of photonic band-gap (PBG) structure, and had found its application in the design of planar circuits and lowpass filters [1 3]. Defected ground structure is realized by etching a defective pattern in the ground plane, which disturbs the shield current distribution in the ground plane. This disturbance can change the characteristics of a transmission line such as equivalent capacitance and inductance to obtain the slow-wave effect and band-stop property. Split-ring resonators (SRRs) have been successfully applied to the fabrication of left-handed metamaterial (LHM) and the design of planar circuits. Pendry et al. have demonstrated that an array of SRRs exhibits negative permeability near its resonant frequency [4]. Gay-Balmaz et al. study experimentally and numerically the electromagnetic resonances in individual and coupled split-ring resonators [5]. Markos et al. have investigated the dependence of the resonance frequency of the periodic array of SRRs on the ring thickness, inner diameter, radial and azimuthal gap, as well as on the electrical permittivity of the board and the embedding medium [6]. Bonache et al. have found the application of complementary circular split-ring resonators to the design of compact narrow band-pass structures in microstrip technology [7]. In this paper, a square split-ring resonator DGS and its equivalent circuit are investigated. The dependence of the transmission characteristic on the dimension of the split ring is then analyzed. At last, the authors propose an improved SRR DGS cell to improve the out-band suppression. Figure 1: SRR DGS cell model.

2 PIERS ONLINE, VOL. 2, NO. 6, STRUCTURE OF THE SRR DGS CELL The SRR DGS is obtained by etching two concentric split-ring defective pattern which have different size and inverse split direction in the ground plane, as shown in Fig. 1. The permittivity of the microstrip line is ε r = 2.65, the height of the dielectric board is h = 1.5 mm, and width of the conductor line is 4.1 mm. Due to the discontinuity of impedance in defective region, an electromagnetic resonance is obtained and thus a band-gap is formed. Compared with the conventional dumbbell DGS, SRR DGS has a flat low-pass property and a narrow band-gap due to the introducing of a transmission zero of elliptic function, as shown in Fig. 2. As a result, this structure can be used to low-pass filter design and harmonic suppression. However, this structure has the disadvantages such as narrow bandwidth of band-gap and insufficient suppression in high frequency range that need to be improved when implemented to practical engineering. Figure 2: Comparison of band-gap property between SRR DGS and dumbbell DGS. 3. ANALYSIS OF THE TRANSMISSION ZERO FOR THE SRR DGS CELL 5-ohm transmission line is equivalent to right-hand transmission line (RHTL) which is composed of two serial inductors and a shunt capacitor, and the split-ring resonator forms a parallel resonant circuit. Therefore, etching split-ring defective pattern in the ground plane will add a parallel resonant circuit to the equivalent RHTL, but will have a little affection on the value of the elements L2 and C2. The final equivalent circuit is shown in Fig. 3. Figure 3: Equivalent circuit of SRR DGS cell model. The transmission zero location for the SRR DGS cell is determined by the resonant frequency of the shunt circuit, that means it is codetermined by L 1, C 1 and C 2. The impedance of the parallel LC circuit is given by Z 1 = 1 jωc jωl 1 While the impedance of the single capacitor C 2 is ωl 1 = j 1 ω 2 (1) L 1 C 1 Z 2 = 1 jωc 2 = j 1 ωc 2 (2)

3 PIERS ONLINE, VOL. 2, NO. 6, The transmission zero is obtained when Z 1 + Z 2 = (3) Then we have the resonant frequency as f S = 1 2π L 1 (C 1 + C 2 ) (4) 4. TRANSMISSION CHARACTERISTICS OF THE SRR DGS CELL Generally speaking, there is a corresponding relationship between the dimension of the square SRR DGS cell and the element parameters of the equivalent circuit. The authors investigate the dependence of the transmission characteristic on side-length, split-gap and ring-gap of the square SRR DGS by EM simulator Ansoft HFSS software v9. The line-width is chosen to be the characteristic impedance of 5-ohm microstrip line, ring-width is kept constant to 1 mm, and the substrate with 1.5 mm thickness and a dielectric constant of 2.65 is used for all simulations. Three SRR DGS unit circuits without any period are simulated with the different dimension, there is only one parameter varying for each case. In case one, both the split-gap and the ring-gap are 1 mm. As the side-length of SRR DGS is increased, the effective inductance L 1 increases, which gives rise to a lower cutoff frequency. Then in case two, the side-length is kept constant to 8 mm and ring-gap is 1 mm, while the splitgap g varies. The simulation results are shown in Fig. 4. As the split-gap increases, the effective capacitance C 1 decreases so that the transmission zero location moves up to higher frequency. Finally in case three, the ring-gap c is increased while the side-length and split-gap are fixed, as shown in Fig. 4(c). The ring-gap also affects the effective capacitance C 1, which leads to an increasing cut-off frequency. -1 g=1mm c=1mm a=7mm -2 a=8mm a=9mm -25 a=1mm a=11mm Case a=8mm c=1mm -2 g=.5mm g=1.5mm -25 g=2.5mm g=3.mm -3 Case C=.5mm C=1.5mm -25 C=2.mm C=2.5mm Case (c) Figure 4: Variation of transmission curve with side-length a, split-gap g, (c) ring-gap c. -1 a=8mm g=1mm L1=3.3nH -1 C1=.43pF L2=2.818nH C2=.652pF -2 Cp1=pF Cp1=.5pF -3 Cp1=1.pF Cp1=1.5pF Cp1=2.pF Figure 5: Topology of the equivalent circuit with parallel capacitors. Variation of the transmission curves with different parallel capacitances.

4 PIERS ONLINE, VOL. 2, NO. 6, IMPROVED SRR DGS CELL AND MEASUREMENT If two parallel capacitances are symmetrically added at both sides of the equivalent-circuit, the out-band suppression in the high frequency region will be improved when the capacitance increases within an appropriate range, as shown in Fig. 5. The parallel capacitance in a microstrip line can be realized by loading the open stubs on the conductor line. Fig. 6 shows the photographs of the improved SRR DGS cell. The square SRR DGS cell has a side-length of a=1 mm, a split-gap of g=1 mm and a ring-gap of c=1 mm, and the open-stubs placed on the conductor line have a width of w=3 mm and length of L=8 mm. The simulation and measured S-parameters as depicted in Fig. 7 shows good agreement. The cut-off frequency and transmission zero location have been found to be f c =2.5 GHz and f S =2.7 GHz, respectively. Measured pass-band loss is below.5 db, a sharp slop is obtained at band edge. The out-band suppression within a wide frequency range from 2.7 GHz to 7 GHz is obviously enhanced, which can be used as the unit of the lowpass filters. Figure 6: Photographs of the fabricated improved SRR DGS cell. Top view, Bottom view. -1 L1=3.3nH C1=.43pF L2=2.818nH C2=.652pF Cp1=1.546pF -2-3 Circuit simulation result EM simulation result Measured result Figure 7: Simulation and measured results of the improved SRR DGS cell. 6. CONCLUSION A square split-ring resonator DGS and its transmission property are analyzed in this paper. The transmission characteristic mainly depends on the dimension of the split ring. It has been demonstrated that, either an increase in the side-length of the the split-ring or a decrease in the width of split-gap and ring-gap will lead to a decrease in the cut-off frequency of the SRR DGS cell. By loading open stubs on the conductor line which operate as parallel capacitances, the out-band suppression is obviously improved.

5 PIERS ONLINE, VOL. 2, NO. 6, ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China under project no REFERENCES 1. Yablonovitch, E., T. J. Gmitter, and K. M. Leung, Photonic band structure: The face centered cubic case employing nonspherical atoms, Physical Review Letters, Vol. 67, No. 17, , Park, J. I., C. S. Kim, J. Kim, et al., Modeling of a photonic bandgap and its application for the low-pass filter design, Singapore: Asia Pacific Microwave Conference, Kim, C. S., J. I. Park, A. Dal, et al., A novel 1-D periodic defected ground structure for planar circuits, IEEE Microwave Guided Wave Lett., Vol. 1, No. 4, , Pendry, J. B., A. J. Holden, D. J. Robbins, et al., Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwave Theory Tech., Vol. 47, No. 11, , Gay-Balmaz, P. and O. J. F. Martin, Electromagnetic resonances in individual and coupled split-ring resonators, Journal of Applied Physics, Vol. 92, No. 5, , Markos, P. and C. M. Soukoulis, Numerical studies of left-handed materials and arrays of split ring resonators, Physical Review E., Vol. 65, , Bonache, J., F. Martin, F. Falcone, et al., Application of complementary split-ring resonators to the design of compact narrow band-pass structures in microstrip technology, Microwave and Optical Technology Letters, Vol. 46, No. 5, , 25.