# A Compact Wideband DGS Bandpass Filter Based on Half Mode Substrate Integrated Waveguide Technology

Nabil Cherif, Mehadji Abri, Benzerga Fellah, Junwu Tao, Hadjira Badaoui

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Nabil Cherif, Mehadji Abri, Benzerga Fellah, Junwu Tao, Hadjira Badaoui. A Compact Wideband DGS Bandpass Filter Based on Half Mode Substrate Integrated Waveguide Technology. International journal of Microwave and Optical Technology, 2021, 16 (2), pp.142-147. hal-03822117

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Submitted on 22 Oct 2022

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# A Compact Wideband DGS Bandpass Filter Based on Half Mode Substrate Integrated Waveguide Technology

Nabil Cherif<fnref n="1" />,*, Mehadji Abri<fnref n="2" />, Benzerga Fellah<fnref n="1" />, Hadjira Badaoui<fnref n="2" /> and Junwu Tao<fnref n="3" />

**Abstract**- In this paper a defected ground structure (DGS) bandpass filter based on half mode substrate integrated waveguide (HMSIW) technology is proposed. We used vertical double circle complimentary split ring resonator (CSRR) as DGS etched on the top plane of the SIW cavity to constitute a multiple mode resonator and dumbbell DGS etched on the ground plane of the SIW cavity for enhance the filter performance. The taper line is used for transition between microstrip to SIW The simulation results obtained by CST and HFSS show that the proposed filter has a large transmitted bandwidth from 6.2 to 12.7 GHz. The higher simulated insertion loss is about -0.5 dB and the lower return loss is about -48 dB. The size of the designed filter is 60 × 9.8 mm<fnref n="2" /> which make it more compact compared to other published research works with a size reduction of about 50%. Good rejection are achieved under 6 GHz and upper 13 GHz. The good calculation of taper, the empirical parameters of the filter and the use many DGS cells in the bottom plane allowed us to obtain the good results. Good agreement between CST and HFSS simulation results.

**Index Terms**- bandpass filter, complimentary split ring resonator, defected ground structure, half mode, substrate integrated waveguide.

## I. INTRODUCTION

Modern development of telecommunication systems based on minimized the microwave components size with high performance. The design of these components, such as filter, antenna, coupler

and oscillators have great importance in industrial and academic research [1-2]. Among the most used components as transmission line is the rectangular waveguide however due to its voluminous structure it was difficult to be fabricated at low cost and integrate it into planar circuit. To solve this problem scientists have opted for the development of substrate integrated waveguide (SIW) technology [3-4]. The SIW technologies are used for the design of various components serving microwave systems such as antipodal antenna [5], leaky wave antenna [6], DGS filter [7] and power divider [8].

To overcome the challenges of size miniaturizing and performance raising different promising approaches have been recently proposed such as periodic DGS and HMSIW. The defected ground structure (DGS), based on engraved the cells in the ground plane of planar circuit board to generate resonance, among the most used cells is CSRR and dumbbell [9-10].

The HMSIW is based on the modification of the SIW structure, it has similar propagation characteristics compared to the SIW and smaller size. Several filters based on half mode have proposed since its introduction [11-12].

In the literature many works have been presented about bandpass filter (BPF) design, the problems were in the size of the component, the losses and the cost. In [12] a compact bandpass filter using dual-plane resonant cells is presented with a good return loss. However the filter rejection is not good

<footnote n="1">¹LSTE Laboratory, Department of Electrotechnical, Mustapha Stambouli University,
Mascara 29000, Algeria</footnote>

<footnote>E-mail: nabil.cherif@univ-mascara.dz and fellahbenzerga@gmail.com</footnote>

<footnote n="2">²STIC Laboratory, Department of Telecommunications, Abou Bekr Belkaid University,
Tlemcen 13000, Algeria</footnote>

<footnote>E-mail: abrim2002@yahoo.fr and elnbh@yahoo.fr</footnote>

<footnote n="3">³Laplace Laboratory, Ensheeiht, University of Toulouse, France</footnote>

<footnote>E-mail: tao@laplace.univ-tlse.fr</footnote>
enough. In [13] a dual-mode SIW bandpass filter is presented with a good stop band performance but the filter size is large. In [14] a BPF is proposed using CSRR with a good analysis of the parameter effect over the filter output characteristics. However the filter is poorly adapted. In this work we have proposed a compact BPF for the TE10 mode based on HMSIW technology and by using the vertical double CSRR and the dumbbell as DGS cells we have obtained very good results compared to other works.

The organization of this paper is as follows: first we present rules and design method. After that we present simulation results of SIW line transmission which has the high-pass characteristics, then we present simulation result of DGS bandpass filter using a vertically periodic double CSRR as DGS in the top plane of HMSIW cavity and we use dumbbell as DGS for ground plane and we end our work by conclusion.

## II. SIW TRANSMISSION LINE DESIGN

The problems in the design of SIW circuits are the high losses and for minimize it we have to adapt the circuit impedances. The SIW is features by substrate type and its thickness “h”, the diameter “d” of the metal vias, the distance “p” between centers of two successive via and the transverse spacing “w” between the centers of opposite vias, which is given by the same TE mode with the equivalent waveguide [1].

<figure><img src="image_2.png" /><figcaption>Fig.1. Dielectric filled waveguide and SIW geometry</figcaption></figure>

For dielectric filled waveguide DFW, the dimension “ad” of the waveguide is calculated by Equation 1 where εr is the relative dielectric constant of the dielectric that fills the waveguide and “a” is dimension of classic waveguide [3].

$$a_d = \frac{a}{\sqrt{\varepsilon_r}} \qquad (1)$$

The same cut-off frequency (f_c) for the dominant TE10 mode for a DFW can be obtained by equation 2[3].

$$f_c = \frac{c}{2a_d} \qquad (2)$$

By working at the same cut-off frequency the first empirical design equation of a SIW is related to its width “w”, and it is given by equation 3 [4].

$$w = a_d + \frac{d^2}{0.95p} \qquad (3)$$

To minimize the radiation and return loss due to the field leakage from the gaps between vias two conditions are required: d < 0.2λg and p ≤ 2d where λg is the guided wavelength [1].

$$\lambda_g = \frac{2\pi}{\sqrt{\frac{(2\pi f)^2 \varepsilon_r}{c^2} - \left(\frac{\pi}{a}\right)^2}} \qquad (4)$$

We have to adapt our filter to get better transmission. For that, it is necessary to calculate the impedance of the guide SIW which is given by the following equation: [6].

$$Z_{pi} = Z_{TE} \frac{\pi^2 h}{8w} \qquad (5)$$

$Z_{TE}$: represent the wave impedance for the TE10 mode it's given by following equation [6].

$$Z_{TE} = j \frac{\omega}{\gamma} = j \omega \frac{u}{\beta} = \sqrt{\frac{\mu}{\varepsilon_r}} \times \frac{\lambda_g}{\lambda} \qquad (6)$$

Using the CST and HFSS we design a half mode SIW on a Rogers RT5880 based substrate having a
loss tangent approximately 0.0009, a relative permittivity of 2.2 a thickness h of 0.508 mm and the thickness of the conductor equal to 0.05 mm. the optimization of the SIW parameters was done by CST using the parametric study.

<figure><img src="image_3.png" /><figcaption>Fig.2. HMSIW Transmission line geometry.</figcaption></figure>

<table><caption>Table 1: The optimized parameters value of the SIW line transmission</caption><thead><tr><td>Parameters</td><td>Value (mm)</td><td>Parameters</td><td>Value (mm)</td></tr></thead><tbody><tr><td>Win</td><td>0.75</td><td>w</td><td>9.2</td></tr><tr><td>Wout</td><td>2.5</td><td>p</td><td>2</td></tr><tr><td>Lin</td><td>5.0</td><td>d</td><td>1</td></tr><tr><td>Lout</td><td>7.5</td><td>h</td><td>0.508</td></tr></tbody></table>

The simulation result of the HMSIW shown in following figures respectively transmission coefficient and reflection coefficient.

<figure><img src="image_4.png" /><figcaption>Fig.3. Transmission coefficient of SIW.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig.4. Return loss of SIW.</figcaption></figure>

From the figures 3 and 4 we notice that the HMSIW is well adapted and it covers large bandwidth ranging from 6 to 16 GHz with an insertion loss about of -0.5 dB in all band we can also see the appearance of several resonance frequencies the best reached -48 dB at the frequency of 9 GHz. We obtained a good agreement between CST and HFSS simulation results which demonstrates our proposal. A gap of several dB is observed because each simulator use different numerical methods.

<figure><img src="image_6.png" /><figcaption>Fig.5. Distribution of the electric field at the frequency of 13 GHz.</figcaption></figure>

The phenomenon of the electric field distribution of the frequency of 13 GHz is illustrated in the figure 5.We notice that the dominant mode of the HMSIW filter is approximately half of the TE10 and it is well delimited.
### III. HMSIW BANDPASS FILTER DISGN

In this part we propose a novel configuration of bandpass filter with two vertically periodic double circle CSRR as DGS cells etch in the top plane with a distance between them equal to 1.0 mm and three cascading dumbbell DGS cells etched in the ground plane with a distance between them equal to 0.5 mm. the parameters of CSRR and dumbbell are optimized using the parametric study with CST simulator.

<figure><img src="image_7.png" /><figcaption>Fig.6. Structure of the DGS bandpass filter, (a) top view (b) bottom view.</figcaption></figure>

The simulation result of the HMSIW shown in following figures respectively transmission coefficient and reflection coefficient.

<table><caption>Table 2: The optimized parameters value of the DGS bandpass filter.</caption><thead><tr><td>Parameters</td><td>Value (mm)</td><td>Parameters</td><td>Value (mm)</td></tr></thead><tbody><tr><td>E1</td><td>0.5</td><td>b</td><td>0.5</td></tr><tr><td>E2</td><td>0.5</td><td>j</td><td>0.8</td></tr><tr><td>D1</td><td>3.0</td><td>k</td><td>4.5</td></tr><tr><td>D2</td><td>1.4</td><td>m</td><td>2.9</td></tr><tr><td>a</td><td>0.4</td><td>n</td><td>2.7</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Fig.7. Transmission coefficient of HMSIW DGS filter</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig.8. Transmission coefficient of HMSIW DGS filter</figcaption></figure>
From the previous figures we observe that the filtering band range from 6.2 to 12.7 GHz, with an insertion loss around of -0.5 dB and about the return loss, we notice the appearance of many peaks, the best reached -48 dB at the frequency of 6.8 GHz. The rejection is very good and it range from 2 to 6 GHz and from 13 to 16 GHz with the attenuation below -20 dB, and the maximum rejection even reaches -50 dB at the frequencies of 3.1 GHz and 15.1 GHz.

<figure><img src="image_10.png" /><figcaption>Fig.9. Distribution of the electric field at the frequency of 9 GHz, (a) top view (b) bottom view.</figcaption></figure>

<table><caption>Table 3: HMSIW DGS bandpass filter performances compared with other published works</caption><thead><tr><th>Ref</th><th>Center frequency (GHz)</th><th>Insertion loss (dB)</th><th>Return loss (dB)</th><th>Size (mm²)</th><th>Results type</th></tr></thead><tbody><tr><td>[12]</td><td>9.2</td><td>&lt;1.05</td><td>&gt;22</td><td>43.6X16.0</td><td>Meas</td></tr><tr><td>[13]</td><td>11.0</td><td>&lt;0.95</td><td>&gt;35</td><td>66.3X19.8</td><td>Sim</td></tr><tr><td>[14]</td><td>9.3</td><td>&lt;2.85</td><td>&gt;20</td><td>60X14</td><td>Sim</td></tr><tr><td>This work</td><td>9.5</td><td>&lt;0.80</td><td>&gt;40</td><td>60X9.8</td><td>Sim</td></tr></tbody></table>

## V. CONCLUSION

In this work a DGS SIW bandpass filter is designed and simulated using CST and HFSS simulators, the design method is discussed. The proposed filter has

large transmitted bandwidth that extends from 6.2 to 12.7 GHz and he has better overall performance in insertion loss, return loss and size. The HMSIW filter has a size reduction of 50% compared to a similar SIW filter. This type of filter is easy for integration with other planar circuit compared by using conventional waveguide. This SIW DGS bandpass filter has high-rejection so it is suitable for practical applications. The results from our work are in good agreement with previous research done on this topic and we will work to miniaturize the size of this filter and improve its rejection.

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