These enhanced DGS cells support the design and fabrication of broadband lowpass filters with miniature dimensions and high out-of-band rejection.

Defected-ground-structure (DGS) circuit elements show great promise for reducing the size of circuit designs at microwave and millimeter-wave frequencies. 1 For active circuits, such as amplifiers, and passive component designs, such as couplers, DGS elements provide circuits with excellent performance at high frequencies. In particular, miniature filter designs can benefit from the use of DGS circuit elements.^{1,2} To demonstrate the possibilities for compact, lowpass microwave filters (LPFs), a novel elliptic-shaped DGS was developed for use in resonant circuits. Its characteristics will be analyzed and presented, along with an equivalent-circuit (EC) network derived from measured S-parameters. The elliptic DGS circuit elements were used to construct a miniature LPF that offers low insertion loss and compact size, with out-of-band suppression of better than 32 dB from 5.17 to 10.0 GHz. This prototype DGS-based LPF was created with the help of computer simulation results that agree closely with measurements performed on this experimental filter.

A wide range of DGS-based microstrip filters have already been proposed and designed by numerous researchers. Periodic or non-periodic DGS elements can be realized by etching a slot in a backside metallic ground plane. The etched slot effectively disturbs the current distribution in a microstrip line's ground plane, resulting in strong, well-behaved resonant characteristics.^{3, 4} This combination of DGS elements and microstrip lines yields sharp resonances at microwave frequencies that can be controlled by changing the shape and size of the slot.

A great deal of experimentation has been conducted on DGS circuit elements to understand the resonances possible with different forms, with the resulting evolution of a wide range of defected shapes, including dumbbell, periodic, fractal, circular, spiral, and L-shaped structures.5-8 This report will examine an elliptic-shaped DGS for use in LPF designs. Elliptic-shaped DGS circuit elements have been shown to provide sharp cutoff-frequency responses along with good performance in both the passband and stopband regions. To better understand the behavior of DGS elements in LPF designs, an analysis will be presented for different DGS dimensional parameters. In addition, an EC model will be presented that agrees closely with electromagnetic (EM) computer-aided simulation results. Measurements on a fabricated DGS-based LPF also agree closely with performance expected from theory.

These novel elliptic DGS cells are obtained by etching a slot that connects two elliptic DGS shapes in a microstrip ground plane (*Fig. 1*). The width of microstrip line on the top is 1.88 mm, which corresponds to a characteristic impedance of 50 ohms. In order to apply DGS cells to the design of LPFs and other components, it is necessary to develop an equivalent-circuit representation. To derive the equivalent- circuit network parameters, the S-parameters of a DGS cell at the reference plane should be calculated inducusing an EM simulator. Then, by analyzing the relationships among the S-parameters, it should be possible to extract the equivalent-circuit network parameters using Eqs. 1,2, and 3,^{4}

where

Ω_{0} = the angular resonance frequency,

Ω_{c} = the 3-dB cutoff frequency, and

Z_{0} = the characteristic impedance of the microstrip transmission line.

There is a close relationship between the etched shapes of a DGS circuit element and its frequency characteristics. To better understand this relationship between physical and electrical parameters, three different types of DGS structures, including dumbbell, circular, and elliptic shapes, were carried out and simulated to identify their characteristics. The DGS cells were simulated using the High-Frequency Structure Simulator (HFSS) EM simulation software from Ansoft Corp. The permittivity of the dielectric circuit board is 3.2 and the thickness (h) of the circuit board is 0.787 mm.

For the purpose of comparing the three different DGS cell shapes, the three DGS cells that were analyzed have the same defected areas of 15.1 mm2, slot length, s, of 12 mm, and slot width, g, of 0.2 mm. As part of the comparison, an elliptic shape with radius of a = 2 mm and b = 2.4 mm was replaced by a circular shape with radius of 2.19 mm and a dumbbell shape with square length of 3.88 mm. The S-parameters for the three different-shaped DGS cells (*Fig. 2*) show similar characteristics. The cutoff frequency changes slightly, while the resonance frequency of the proposed elliptic DGS is lower than that of the other two DGS shapes. The S-parameters indicate that a sharper cutoff frequency and slow wave performance could be obtained by using the elliptic DGS shape.

The resonant characteristics of the elliptic DGS cell were found to be mainly affected by its radius variables, a and b. To better understand this relationship, the frequency responses from EM simulations were analyzed for elliptic DGS cells with different values of a and b. The radius b was varied from 1 to 4 mm while the radius a was set equal to 2 mm, with a slot length, s, set to 12 mm and slot width, g, kept constant at 0.2 mm. The variation of the characteristics could be explained by its equivalent-circuit model. It demonstrates that the value of the equivalent inductance, L, increases as the radius b increases from 1 to 4 mm, while having relatively little effect on the equivalent capacitance, C. In addition, the attenuation pole shifts from 6.28 GHz to 4.32 GHz. This causes the equivalent inductance to increase in proportion to the areas of the defected rectangle. All the DGS dimensional parameters have little effect on the series inductance, Ls. These results explain the shift of the cutoff frequency and the attenuation poles when the dimensional parameters of the DGS cell are altered. The physical dimensions of the DGS cell have a direct bearing on its equivalent-circuit parameters.

These elliptic-shaped DGS cells can be used for fabricated compact LPF designs with good spurious passband suppression. But these DGS cells also have some disadvantages, such as insufficient spurious suppression in the high-frequency range and slow-wave cutoff characteristics. To enhance the performance possible with an ellipticshaped DGS cell, it was thought to use H-shaped open stubs in a single DGS cell to increase the coupling capacitance between the microstrip line and the DGS cell. This would also reduce the size of the resulting LPF and improve the stopband performance. The proposed enhanced elliptic structure employs H-shaped open stubs (*Fig. 4*). For analysis purposes, the following parameters for this novel DGS cell, c = 2.6 mm, w = 1 mm, a = 1 mm, b = 1.5 mm, and d = 1.88 mm, were assumed constant.

By analyzing the behavior of single DGS cells, they were optimized in terms of physical dimensions for use in the design of a LPF with low inband insertion loss and high out-ofband suppression. The structure of the filter depends on multiple DGS cells with different-length slots; an equivalent circuit of the filter was also developed for analysis purposes (*Fig. 5*). The dimension parameters are all constant except the open stub, l2. The values of these parameters are a = 1 mm, b = 1.5 mm, b_{1} = 2 mm, w = 1 mm, g = 0.2 mm, s_{1} = 12 mm, s_{2} = l_{1} = 10 mm, l_{3} = 5 mm, and l_{4} = 8 mm.

In designing this LPF, the equivalent parallel capacitance, C_{3}, should be chosen carefully. The electrical performance of the LPF can be controlled and optimized by adjusting stub length l_{2}. By performing EM and EC computer simulations to optimize the parameters, a stub length l_{2} of 3 mm was used for three elliptic DGS cells (*Fig. 6*). The values of the various parameters in the equivalent network for the LPF are: C0 = 0.43 pF, L0 = 2.21 nH, R0 = 2.192 k , C2 = 0.21 pF, L2 = 0.93 nH, R2 = 1.642 k , Ls1 = 1.13 nH, Ls2 = 2.38 nH, C1 = 1.41 pF, and C3 = 0.56 pF. The results obtained by the EM and EC simulations are in good agreement and show the validity of the EC model simulation using the Advanced Design System (ADS) software from Agilent Technologies. The return losses throughout the passband range are better than 24 dB, while out-of-band suppression was generally better than 32 dB across a wide frequency range from 5.17 to 10 GHz. The use of open stubs achieves larger attenuation in the stopband and obtains higher harmonic suppressions with fewer periodic structures compared to a conventional DGS filter.

To validate the proposed LPF, it was simulated and fabricated with Taconic TLC dielectric circuitboard material from Taconic Corp. The dielectric circuit board has relative permittivity e_{r} = 3.2 and thickness h = 0.787 mm. The fabricated LPF *Fig. 7(a*)> measures just 25 x 40 mm. The measured results for this fabricated filter agree closely with theoretical results for the filter on material with those dielectric properties. Experimental results reveal that the LPF has a 3-dB cutoff frequency of 4.5 GHz, with a shift in the actual cutoff frequency from the modeled value of about 50 MHz. Passband insertion loss remains low while signals in the stopband are suppressed by at least 32 dB from 5.17 GHz to 10 GHz.

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### Page Title

In summary, a compact microstrip LPF was fabricated using elliptic DGS cells which, when combined with microstrip lines on standard high-frequency dielectric materials, form well-behaved and miniature resonant structures. By employing a novel H-shaped open stub with the elliptic DGS cells, it was possible to increase the equivalent parallel capacitance and improve the out-ofband suppression for the compact filter. In order to better understand the dynamics of the DGS LPF, an equivalent-circuit model was developed for analysis purposes. Using the equivalent circuit as a design guide, a prototype DGS-based LPF was fabricated and tested. The measurements of this filter show close agreement with simulated results for the model. The DGS-based LPF features sharp cutoff frequency response, low insertion loss, and high rejection in the stopband from 5.17 to 10.0 GHz, with better than 32-dB out-of-band suppression.

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