Microstrip filters formed with defected ground structures (DGSs) offer high performance levels at microwave and millimeter-wave frequencies. By building upon that technology, it has been possible to develop a novel symmetrical split ring resonator (SSRR) DGS that has been used to fabricate lowpass microwave filters with wide rejection bands. Several filters were simulated and fabricated based on SSRR DGS units, with good agreement between simulated and measured results.

DGS units are suitable for both microwave and millimeterwave applications.^{1-4} Known as a subcategory of electromagnetic- bandgap (EBG) structures, a DGS allows modifications in a circuit's guided wave properties by etching lattice shapes in the ground plane of a microstrip line.^{5,6} Any defect etched in the ground plane of a microstrip line disturbs its current distribution, increasing the effective capacitance and inductance. Researchers have explored numerous types of DGS shapes, including dumbbell, periodic, U-shaped, and SSRR types, with a variety of effects.^{7-9}

However, all of these structures exhibit relatively narrow filter stopbands, making them unsuitable for filter design, harmonic suppression, or broad out-ofband rejection without the use of loaded open stubs or compensated microstrip line.10 Conventional lowpass filters (LPFs) using shunt stubs and stepped impedance lines have narrow stopbands and poor cutoff responses. But these could be improved by increasing the number of filter elements at the cost of increased size and degraded passband characteristics.

To overcome the limitations of conventional SSRR DGS approaches, a novel SSRR DGS LPF has been developed that is compact and features wide stopband performance with two transmission zeros and sharp falling edge at the cutoff frequency. Even wider stopbands are possible by cascading two or three of the novel SSRR DGS units together. To demonstrate the effectiveness of the new approach, several LPFs were simulated and fabricated, with close agreement between modeled and measured performance.

Figure 1 shows the layout of the proposed circular SSRR (a) and its equivalent circuit (b). The circular SSRR DGS has two symmetrical splits in each ring and there is an additional etched slot connected with the inner ring in the middle that is different from a conventional SSRR DGS.^{10} For the equivalent circuit of the proposed SRSS, two series resonators with inductor L1 and capacitor C_{1} result from the two symmetrical half defected circles of the outer ring; the inner ring with the additional slot corresponds to a resonator formed by capacitor C_{2} and inductor L_{2}. While the coupling of the two half outer circuits and between the outer and the inner rings results in capacitor C_{p}.

For the purpose of performing an electromagnetic (EM) computer-aided- engineering (CAE) simulation, two resonant frequencies were applied. Frequency f1 = 5.13 GHz is the high resonant frequency for the outer ring and f2 = 4.48 GHz is the low resonant frequency for the inner ring (*Fig. 2*). Simulations were performed using the Advanced Design System (ADS) suite of software tools from Agilent Technologies as well as the High-Frequency Structure Simulator (HFSS) EM software from Ansoft with the results from both software tools agreeing quite closely. The values of the circuit models extracted from the EM simulations are C_{1} = 0.979 pF, L_{1} =1.667 nH, C_{2} = 0.75 pF, L_{2} = 1.683 nH, and Cp=0.487 pF for R1 = 5 mm, R_{2} = 3.5 mm, r = 1 mm, d = 0.5 mm, g = 0.5 mm, and w = 1.88 mm.

Compared with conventional dumbbell DGS and SSRR DGS units, the new SSRR DGS unit offers several advantages, including flatter lowpass properties and a sharper filter cutoff response. It also provides an even wider bandgap due to the introduction of two elliptic- function transmission zeros (*Fig. 3*).

Figure 4 offers a comparison of the resonant properties of a circular SSRR with and without an additional slot. The slot greatly increases the effective capacitance C2, which is closely related to the slot width, g. When g increases, the equivalent capacitance C2 decreases, and the resonant frequency, f2, moves upward in frequency. The additional slot effectively improves the width of the stopband without increasing the open stubs. The new SSRR DGS unit has two different resonant frequencies, since each ring corresponds to a specific resonant frequency. Both resonant frequencies could be controlled by adjusting the radius of each ring (*Fig. 5*).

For filter designs, such as LPFs, the proposed SSRR DGS offers several advantages compared to conventional DGS units, including flatter lowpass response and a sharper cutoff response. The novel SSRR DGS units can even achieve a LPF with a wider bandgap than conventional DGS units, due to the two transmission zeros compared to only one for the conventional SSRR or dumbbell DGS units. To demonstrate the effectiveness of using multiple DGS units, Fig. 6 shows the out-ofband suppression possible when using a periodic array of DGS units, using as many as three SSRR DGS units. In all cases, a dielectric circuit board with permittivity (dielectric constant) of 3.2 and height of 0.787 mm was used. The width of the conductor line was w = 1.88 mm, which corresponds to a characteristic impedance of 50 Ohms. The circular SSRR DGS unit has a radius of R1 = 4.8 mm (outer), R2 = 3.3 mm (inner) and a split-gap of d = 1 mm. The width of the ring is r = 1 mm and the width of the loaded slot in the middle is g = 0.5 mm. The distance between the centers of each of the two SSRR units is l = 13.5 mm. The length of the input and output line is s = 10.2 mm for LPFs formed of two SSRR DGS units, while l = 15 mm and s = 7.7 mm for the LPFs formed of three SSRR DGS units. The slow-wave and coupling effects between the neighboring DGS units lead to the suppression of higher harmonics and consequently a wide rejection band.

As shown in Fig. 6, the stopband and the cutoff characteristics of the LPFs improve as the number of DGSs is increased, without adding any compensatory stubs. This indicates that coupling effects can improve the filter's characteristics, but when a large number of coupled resonators are used, the radiation losses in the passband become significant.

To validate the theoretical analysis, LPFs with different SSRR DGS units were designed and fabricated. Figure 7 shows the measured results of a LPF based on a single SSRR DGS unit together with EM software simulated results. It has a 3-dB cutoff frequency of 4.3 GHz with resonant frequencies of 4.49 and 5.14 GHz. As can clearly be seen, the proposed LPF has a sharp transition domain and a wide stopband response.

Figure 8 shows the simulated and measured results of a LPF formed with three cascaded DGS units. The results show low insertion loss of 0.695 dB, with more than 32-dB filter attenuation from 5.02 to 10.00 GHz. The measured results are consistent with the simulated results, revealing only a small frequency offset and different insertion-loss values due to fabrication tolerances. This basic LF design is adaptable to a wide range of microwave and millimeter-wave applications.

**REFERENCES**

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