Defected-ground-structure (DGS) cells can serve as effective building blocks for high-performance, high-frequency filters. Microstrip filters are widely used in microwave and millimeterwave systems and, in particular, low-pass filters (LPFs) are essential components in modern communications systems.1 The increasingly challenging requirements of such systems calls for LPFs with increasingly improved performance for in-band and out-of-band responses.2-4 Because of this, filters based on DGS cells are attractive for their reduced size, low insertion loss, and high rejection. Based on research into the use of DGS cells for RF/microwave filters, the authors propose a LPF with cut-off frequency of 3.1 GHz and stopband from 3.4 to 10.0 GHz with 35 dB rejection based on the uneven distribution of DGS cells in a microstrip structure.

Periodic or nonperiodic DGS cells can be realized by etching a slot in the backside of a microstrip circuit??s metallic ground plane. The etched slot effectively disturbs the current distribution in the microstrip ground plane. The disturbance alters the normal characteristics of the microstrip line in terms of line inductance and capacitance.5 For modeling purposes, an inductive-capacitive (LC) equivalent circuit can represent the proposed DGS cell.

When a DGS cell is added to a microstrip line, it causes a modification to the resonant characteristics of the transmission line with a resonant frequency that can be controlled by changing the shape and size of the DGS slot. A variety of different ??defected? DGS shapes have evolved over time, including dumbbell, periodic, fractal, circular, spiral, L-, and H-shaped structures.6-8 In this report, the uneven DGS cells proposed for high-performance LPFs feature a compact geometry. The use of an uneven DGS-cell topology can provide an extremely sharp LPF frequency cut-off response as well as excellent performance in both the passband and the stopband.

Compared with conventional DGS LPF designs,9 the proposed DGS-based LPF boasts a more compact size, a lower number of required DGS cells, lower insertion loss, and a better frequency shift. A circuit model has been developed to characterize the proposed DGSbased LPF. The equivalent-circuit model agrees well with electromagnetic (EM) simulation results from the High-Frequency Structure Simulator (HFSS) software simulation tool from Ansoft Corp. (www.ansoft.com). To demonstrate the effectiveness of the design, the theoretical results will be compared with measurements made on a fabricated prototype.

** Figure 1** shows the proposed DGS cell and its equivalent circuit. The structure of the cell is quite basic, and is simple to adjust and analyze. The rectangular etched shape is ideally suited for achieving compact circuit sizes. For the purposes of the simulation analysis, a permittivity of 3.2 was used for the dielectric printed-circuitboard (PCB) material with thickness, h, of 0.787 mm. The width of microstrip transmission line on the top is 1.88 mm, which corresponds to a 50-ohm characteristic impedance.

There is a close relationship between the etched size of a DGS cell and the electrical parameters of its equivalent-circuit values.10 **Figure 2** shows the frequency responses of an EM simulation performed for DGS cells with different dimensions. When the length, l, of the rectangular cell increases, the attenuation pole shifts from 5.38 GHz to 5.82 GHz as shown in Fig. 2. To derive the equivalent-circuit parameters for the cell, its Sparameters can be calculated at the reference plane using an EM simulator. Then, using the relationship between the DGS cell??s S-parameters and the ABCD matrix, the equivalent-circuit parameters can be extracted.^{5}

As shown in **Tables 1 and 2**, the equivalent-circuit capacitance increases as the slot width, g, decreases. The tables also show that the value of the equivalent-circuit capacitance, C, decreases from 0.379 pF to a value of 0.309 pF as the slot width, g, is increased from 0.2 to 0.5 mm. The equivalent-circuit resistance, R, also decreases from 1.268 kohms to a value of 1.115 kohms, causing a decrease in the value of forward transmission, S_{21}.

It is interesting to note that the change in slot width, g, has relatively little effect on the equivalent-circuit inductance. The equivalentcircuit inductance for the proposed DGS cell changes with the length, l, of the rectangle, increasing as the length is increased from 4 to 7 mm while the other dimensional parameters remain constant. This causes the equivalent-circuit inductance, L, to increase in proportion to the area of the defected rectangle, as does the slot length, s (* Table 2*). The other DGS dimensional parameters have little effect on the series inductance, Ls. This may also explain the shift of cutoff frequency and the attenuation poles with changes in the dimensional parameters for the DGS cell, since changes in the dimensional parameters are reflected by changes in the values of the equivalent-circuit electrical parameters.

The validity of the proposed equivalent-circuit model for DGS-based circuits has been borne out in comparisons between EM simulations on these DGS circuits and circuit simulations performed on DGS cell equivalent-circuit networks using the Advanced Design System (ADS) computer-aided-engineering (CAE) simulation software from Agilent Technologies (www.agilent.com). LPF designs based on the proposed DGS cells show larger attenuation in the stopband and higher harmonic suppression with a lower number of periodic structures than in filters based on conventional DGS cells.

The proposed DGS cell analyzed above is well suited for LPFs with low in-band insertion loss and high spurious suppression, but it also suffers some disadvantages, such as insufficient hamonic suppression at higher frequencies and a slow cutoff frequency slope. Because of these shortcomings, the transfer characteristics of the DGS cells should be optimized by adjusting their dimensional parameters and using them with open-stub tuning. * Figure 3(a)* shows an LPF structure with DGS cells distributed symmetrically at the center of a microstrip line with the proposed uneven DGS cells on the ground plane. For improved out-of-band suppression and sharp cutoff characteristics, open stubs were placed at both sides of the DGS cells on the microstrip transmission line, functioning as shunt capacitors.

*shows the equivalent-circuit representation of this arrangement with uneven DGS cells.*

**Figure 3(b)** For all of the simulations performed in this report, the width, d, of the transmission line on the top is 1.88 mm for a 50-ohm match while the width of the open stubs and the defected triangles, w, is 1 mm. The length of the etched slots, s, is 5 mm, while the distance between the open stubs and the defected triangles is denoted by l. The length of the open stubs on the top, l_{2n}, combined with the microstrip line and the defected triangles on the ground plane, l_{2n - 1}, can be expressed as Eqs. 1 and 2:

l_{2n} = l - 2n(Δ l) (1)

and

l_{2n} = /2 (2)

where

l = the length of the open stub at the center of the topology.

From this, it can be seen that the parameters of the LPF can be controlled and optimized by means of the stub length and distance between open stubs and defected triangles, l and Δ l, respectively. Based on analysis, the LPF could be simulated and designed according to the equivalentcircuit response and the dimensions of the proposed topology. For this purpose, two DGS cells were chosen for the LPF as a basic structure, with dimensions of d = 1.8 mm, g = 0.2 mm, s = 5 mm, w = 1 mm, Δ l = 0.5 mm, and with l varied from 18 to 21 mm. The defected rectangle length, l1, and the open stuns, l2, increase with l following the relationships of Eqs. 1 and 2. * Figure 4* shows the simulated results with two cells, indicating that the cutoff frequency decreases as a function of the equivalent-circuit inductance increasing with l.

To improve out-of-band suppression, the number of DGS cells should be increased with uneven DGS cells. * Figure 5(a)* shows the simulated results using increasing numbers of DGS cells. In these simulations, the number of DGS cells increases from 2 to 6, while the dimensional parameters d, w, s, Δ l, and g are kept constant and parameters l, l1, l2, ..., l2n vary according to Eqs. 1 and 2. By increasing the number of DGS cells, the proposed LPF structure provides an attenuation pole with 58 dB rejection at 3.02 GHz while the in-band insertion loss is as low as 0.31 dB. In comparison, a conventional filter will suffer increased insertion loss with the increase in resonators needed for higher harmonic suppression.

For the DGS LPF??s out-of-band suppression characteristic, it achieved better than -40 dBc harmonic suppression from 3.02 GHz to 8.1 GHz with 6 DGS cells due to the resonance characteristic of DGS and the open stubs which perform as shunt capacitances. * Figure 6(b)* shows the simulated results of an 8-cell LPF with l varied from 16 to 22 mm. The increase in equivalentcircuit inductance increases the sharpness of the cutoff and minimizes return loss to better than 18 dB.

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* Figure 6* shows the LPF based on 8 DGS cells and with optimized dimensional parameters. The main dimensional parameter of interest is l, which is equal to 20 mm; equivalent-circuit simulated results are also presented here. For this 8-cell structure, the return- loss performance throughput the passband frequency range is 25 dB or better while the out-of-band rejection is generally more than 45 dB across a wide frequency range from 2.1 to 10.0 GHz.

The LPF with optimized dimensions based on 8 cells is shown in * Fig. 6*. The main dimensional parameter l is 20 mm and its equivalent circuit simulated results is also presented. The return losses throughout passband range are below -25 dB, while out-band suppression are generally more than 45 dB at a wide range from 3.1 to 10 GHz. Compared with a conventional LPF,

^{9}the proposed filter only uses 8 DGS cells while a conventional design (with similar performance) requires 17 cells. As this demonstrates, the use of uneven DGS cells helps to achieve higher stopband attenuation with greater harmonic suppression using less periodic structures compared to a conventional DGS-based filter.

To validate the proposed LPF, the uneven DGS cells were simulated and fabricated with TLC substrate material from Taconic (www.4taconic.com) with relative permittivity εr = 3.2 and thickness h = 0.787 mm. * Figure 7* shows a photograph of the proposed LPF measuring a compact 30 x 50 mm. Compared with a conventional DGS-based filter, its features an area reduced by 35 percent. Measured results for this filter are in good agreement with the theoretical results. The experiment results show that the fabricated LPF has a 3-dB cutoff frequency at 3.1 GHz with a shift of cutoff frequency about 90 MHz, considerably better than the conventional filter with a shift in cutoff frequency of about 150 MHz. The insertion loss for this prototype DGS-based design is less than that of the conventional DGS filter, and the stopband suppression was better than -35 dBc from 3.4 to 10.0 GHz.

In short, this report has shown the effective use of an uneven distribution of DGS cells to form high-frequency LPFs. In a high-frequency filter, the new structure increases the equivalent- circuit shunt capacitance by using stubs with a cross shape to improve out-of-band suppression. The authors developed an accurate equivalent-circuit model for the DGS filter so that different filter designs could be realized with commercial CAE tools. Following analysis of LPF structures with different numbers of DGS cells and DGS cells with different dimensional parameters, a prototype filter was fabricated with excellent sharp cutoff frequency, low passband insertion loss, and better than 35-dB stopband rejection across a stopband frequency range from 3.4 to 10.0 GHz. The resulting compact design is ideal for a wide range of applications in RF and microwave systems.

*REFERENCES*

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