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A Microstrip Highpass Filter with Complementary Split RingResonators

C. Li, K. Y. Liu, and F. LiInstitute of Electronics, Chinese Academy of Science, China

Abstract— An accurate equivalent circuit model for the microstrip line with a complementarysplit ring resonator (CSRR), and the parameter extraction method, are presented. A highpassfilter with steep rejection is designed based on the model. The measurement results confirm theefficient analysis and design procedure and the validity of the highpass filter configuration.

DOI: 10.2529/PIERS060906062902

1. INTRODUCTION

Recently, split ring resonators (SRRs) and complementary split ring resonators (CSRRs) havegained growing interest for their potential applications. Originally, SRRs combined with metal wiresare proposed to make left-handed materials (LHMs) [1]. LHMs are artificial periodical structureswith both negative permittivity and permeability. The presence of SRRs leads to the negativepermeability in a narrow band above resonance [2]. CSRRs can be made by etching the negativeimage of SRRs in the ground plane [3]. Hence they are the dual counterpart of the SRRs and exhibitnegative permittivity upon their resonance. Since SRRs and CSRRs are both planar configurations,they open a way to develop novel planar microwave circuit and devices [4–7].

In this paper, we proposed an accurate equivalent circuit model for the CSRRs coupling toa microstrip line. The results obtained from the full wave simulation and the equivalent circuitmodels agree well over a wide frequency band. Based on the equivalent circuit model, a novel highpass microstrip filter with steep rejection is designed and verified by experiment.

2. EQUIVALENT CIRCUIT MODEL OF CSRRS:

Figure 1(a) shows a typical layout and its equivalent circuit for a microstrip line with CSRRetched in the ground plane. The substrate for simulation and later experiment has a relativedielectric constant of 2.65 and a thickness of 1.5 mm. The dimensions are as follows: s = 0.8mm,rout = 4.2mm, rin = 2.2mm, gap = 0.6mm, w = 4.1mm. The line width is chosen for thecharacteristic impedance of 50 Ohm for a typical microstrip line. The equivalent circuit of theCSRR-based microstrip line shown in Fig. 1(b) consists of a three-element LC tank circuit withtwo segments of 50 Ohm microstrip line at both sides. The LC tank circuit includes a series LCresonator (L and C1) and a capacitance element (C2) connected in parallel.

Figure 1: Layout and equivalent circuit of microstrip with CSRR.

Firstly, the performance of the CSRR-based microstrip line is obtained by full wave simulation.To determine the element values of the equivalent circuit, three independent equations are required.

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The first is given by the resonance condition of the whole tank circuit, which leads to the zeros ofS11 at f1. The second is given by the resonance condition of the series LC circuits (L and C1),which leads to the zeros S21 at f2. The third arises from the 3 dB insertion loss at f3. Finally, thelength of the microstrip line in the equivalent circuit can be obtained by fitting the phase of theS parameters. After some derivation, the element values in the equivalent circuit (Fig. 1) can beexpressed by these three special frequency points as follows,

C2 =Y0(f2

2 − f23 )

πf3(f21 − f2

3 )(1)

C1 = (f21

f22

− 1)C2 (2)

L =1

4π2f22 C1

(3)

where Y0 is the characteristic immittance of the ports for S parameters. Since f1 < f3 < f2

(Fig. 2), it’s easily determined from Eq. (1) that the value of C2 is negative. For dimensionsshown in Fig. 1(b), The extracted circuit parameters are as follows: L = 5.3 nH, C1 = 0.54 pF,C2 = −1.3 pF, d = 3 mm. Note that the value of C2 is negative. Fig. 2 shows the predictedcharacteristics of the equivalent-circuit and the full wave simulation agree very well.

Figure 2: Full wave simulation (solid line) and equivalent circuit (dotted line) results of CSRR.

The shunt negative capacitance is undesirable for the design of high-pass and band-stop filterssince it forbids the transmission at high frequency band. This can be avoided by widening themicrostrip lines above the CSRR. Fig. 3 shows the layout and the equivalent circuits. The additionalpatches of the widened microstrip line provide the needed capacitance to offset the negative one.

Figure 3: Offsetting the negative capacitance with extra patches (layout and equivalent circuit).

Figure 4 shows the corresponding results of the full wave simulation and the equivalent circuits.It’s seen that the performance at high frequency band is improved with the patches. The modified

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Figure 4: Full wave simulation and equivalent circuit results of CSRR with extra patches.

structure serves as a parallel connected series LC resonator embedded between two segments ofmicrostrip lines. The little difference of the resonant frequency (Fig. 4) may result from the couplingof the patches and the CSRR.

3. DESIGN OF NOVEL HIGHPASS FILTERS:

Figure 5 shows the photograph of the proposed highpass filter. It comprises of two CSRR sectionswith additional microstrip patches. The interdigital capacitors are introduced to prevent transmis-

(a) Top view (b) Bottom view

Figure 5: The photograph of the highpass filter.

sion at lower frequency. The length of the transmission line embedded between the two sections canbe adjusted to optimize the response of the total structure which is similar to the elliptic functioncircuit. The total length of the filter is 2.4 mm. Fig. 6 shows the experimental performance of the

Figure 6: The measured S parameters of the highpass filter (The solid line is for S21, The dotted line is forS11).

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proposed filter. The measured 3dB cutoff frequency is 3 GHz and the suppression is more than25 dB below 2.6 GHz.

4. CONCLUSION

An equivalent circuit model for the CSRR-based microstrip is developed with the parameter extrac-tion method. A novel microstrip highpass filter with CSRRs is proposed. The numerical simulationand the measurement confirm the validity of the highpass filter configuration and the efficient anal-ysis and design procedure. It’s seen that the proposed highpass filter exhibits more steep rejectionas compared to the conventional structure.

ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China under GrantNo (60501018, 60271027), and the National Basic Research Program of China under Grant No2004CB719800.

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