# Comb-Line Filter with Coupling Capacitor in Ground Plane

Authors: Toshiaki Kitamura
Journal: Active and Passive Electronic Components
 (2011)

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## Abstract

A comb-line filter with a coupling capacitor in the ground plane is proposed. The filter consists of two quarter-wavelength microstrip resonators. A coupling capacitor is inserted into the ground plane in order to build strong coupling locally along the resonators. The filtering characteristics are investigated through numerical simulations as well as experiments. Filtering characteristics that have attenuation poles at both sides of the passband are obtained. The input susceptances of even and odd modes and coupling coefficients are discussed. The filters using stepped impedance resonators (SIRs) are also discussed, and the effects of the coupling capacitor for an SIR structure are shown.


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## Body

## 1. Introduction

Miniaturization  of microwave filters is highly demanded. For mobile telephones especially, ceramic laminated filters [1–4] have been widely used, and in particular, comb-line filters have extensively made practical use.In this study, comb-line filters in which both sides of the substrate are utilized are considered. Comb-line filters consist of two quarter-wavelength resonators, and attenuation poles can be created in the frequency characteristics of the transmission parameter by changing the coupling locally along the resonators [5]. The stopband characteristics can be improved by arranging the attenuation poles around the passband. In [1, 2], strong coupling between two resonators is obtained by installing a patch conductor on the dielectric substrate above the resonators. The patch conductor is referred to as a coupling capacitor (Cc). The method of installing a coupling capacitor by inserting slots into the ground plane is discussed. By this method, a coupling capacitor can be achieved without using a multilayered structure. As a method of inserting slots into a ground plane, a defected ground structure (DGS) has been attracting much attention [6–8]. In a broad sense, the proposed structure is a kind of DGS. The filtering characteristics are investigated through numerical simulations as well as experiments. The filters using stepped impedance resonators (SIRs) are also discussed, and the effects of the coupling capacitor for an SIR structure are shown.


## 2. Filter Structure

Figure1 shows an overview of the proposed comb-line filter. Two microstrip resonators are arranged on the substrate, and each resonator is terminated through the ground plane at one end using a through hole. As an I/O port, a microstrip line with a characteristic impedance of 50 ohm is directly connected to each resonator. A square-shaped coupling capacitor is fabricated by inserting slots into the ground plane. The coupling capacitor is a patch conductor that is not terminated through the ground plane and produces strong coupling locally along the resonators. The thickness and relative permittivity of the substrate are assumed to be 1.27 mm and 10.2, respectively, and the diameter of the through hole is 0.3 mm.Figure 1
Whole structure of filter.The metallization patterns and dimensions of the filter are shown in Figure2. The dimensions and position of the coupling capacitor are also shown. The coupling capacitor is a×5.2 mm2 and is located d mm from the open ends of the microstrip resonators. The filtering characteristics are investigated with a and d as parameters. The other structural parameters are also shown in Figure 2.Figure 2
Metallization patterns.


## 3. Results and Discussion

The filtering characteristics are investigated through numerical simulations by the full-wave EM simulator Ansoft HFSS Ver. 11. The frequency characteristics of the scattering parameters whena=5.2 mm and d=1.0 mm are shown in Figure 3. For comparison, the results when there is no coupling capacitor (Cc) are also shown. It can be seen that an attenuation pole was created at each side of the passband by installing the coupling capacitor. The center frequency of the passband was also increased slightly by inserting slots into the ground plane. The slots also cause radiation loss, and it is understood from Figure 3 that 1-|S11|2-|S21|2=0.090 at 2.1 GHz when a coupling capacitor is used. Figure 4 illustrates the equivalent circuit of the comb-line filter. Attenuation poles appear at the frequencies where the input susceptances of the even and odd modes are equal to each other.Figure 3
Frequency characteristics of scattering parameters.Figure 4
Equivalent circuit.The frequency characteristics of the input susceptances of the even and odd modesBine and Bino are shown in Figures 5(a) and 5(b), respectively. The structural parameters were the same as those in Figure 3. The input susceptances of the even and odd modes were calculated by setting the magnetic and electric wall, respectively, on the symmetric plane shown in Figure 1. As shown in these figures, the odd-mode susceptances hardly changed, whether or not there was a coupling capacitor. The coupling capacitor does not have much effect on the electromagnetic fields of the odd mode. On the other hand, the even-mode susceptances were decreased by inserting the coupling capacitor, and they intersected with the odd-mode ones at 1.62 and 2.81 GHz, as shown in Figures 5(a) and 5(b), respectively. The frequencies of the intersections correspond with the attenuation-pole frequencies in Figure 3.Frequency characteristics of input susceptances around attenuation-pole frequencies (a) below and (b) above passband.
(a)(b)The frequency characteristics of the scattering parameters withd as a parameter when a=5.2 mm are shown in Figures 6(a) and 6(b). Here, the parameter d corresponds to the position of the coupling capacitor. As shown in Figure 6(a), when d is small (from 0 to 1.0 mm), two attenuation poles appear at both sides of the passband, and the parameter d mainly affects the attenuation-pole frequency above the passband. On the other hand, as shown in Figure 6(b), no attenuation pole appears when d is large (from 4.0 to 6.0 mm). The resonant frequency of the odd mode is about 2.0 GHz and changes very little when changing d. However, the resonant frequency of the even mode decreases as d increases. It was confirmed that the even-mode resonant frequency becomes lower than the odd-mode one when d exceeds about 2.5 mm.Frequency characteristics of scattering parameters when (a)d=0~1.0 mm and (b) d=4.0~6.0 mm (a=5.2 mm).
(a)(b)The frequency characteristics of the input susceptances of an even mode are shown in Figure7. Here, the frequency range is chosen so as to be close to the attenuation-pole frequency above the passband. The structural parameters were the same as in Figure 6(a). As shown in this figure, the input susceptances of an even mode change almost in parallel to each other with changing d. According to this, the attenuation-pole frequencies above the passband change as shown in Figure 6(a).Figure 7
Frequency characteristics of input susceptances of even mode (a=5.2 mm).However, from Figure6, the parameter d also has a large effect on the bandwidth of the passband. The coupling coefficients as a function of d are shown in Figure 8. The coupling coefficient k is calculated using the following equation (1)k=fe2-fo2fe2+fo2.
Here, fe and fo are the resonant frequencies of the even and odd modes, respectively, and they are determined from the zero-crossing points of the input susceptance curves of the even and odd modes. As can be seen, the coupling coefficients decrease steadily as d increases.Figure 8
Coupling coefficients as a function ofd (a=5.2 mm).Figure9 shows the frequency characteristics of the scattering parameters with a as a parameter when d=0 mm. Here, the parameter a is the length of the patch conductor that makes up the coupling capacitor. As shown in this figure, the attenuation-pole frequencies decrease, and, in contrast, the passband frequency shifts slightly higher as a increases. The coupling coefficients as a function of a are shown in Figure 10. It can be seen that the coupling coefficients increase almost linearly as a increases.Figure 9
Frequency characteristics of scattering parameters (d=0 mm).Figure 10
Coupling coefficients as a function ofa (d=0 mm).Next, an SIR filter shown in Figure11 is studied. Filters can be miniaturized by using an SIR structure. The frequency characteristics of scattering parameters are shown in Figure 12. The solid line shows the results of a normal SIR filter (without Cc) when s1=0.1 mm and s2=0.2 mm. It is shown that the passband frequency becomes lower compared with that in Figure 3, meaning that it is possible to miniaturize the filter. In addition, two attenuation poles can be created at both of the passbands by choosing appropriate values for parameters s1 and s2. However, the values of s1 and s2 are quite small. The dotted line shows the results of an SIR filter with Cc when s1=0.4 mm and s2=0.9 mm. It is understood that attenuation poles can be created near the passband by choosing s1 and s2 that are easy to fabricate, and therefore, the structural limitation can be relaxed by using a coupling capacitor [2]. However, a drawback is that the passband frequency becomes higher compared with a normal SIR filter. This is due to the decrease of the effective relative permittivity by the installation of slots in the ground plane. For comparison, the results of the filter shown in Figure 2 (a=5.2 mm, and d=1.0 mm) are also shown (dashed line).Figure 11
Metallization patterns of SIR filter.Figure 12
Frequency characteristics of scattering parameters (solid line:s1=0.1 mm and s2=0.2 mm (without Cc), dotted line: s1=0.4 mm and s2=0.9 mm (with Cc), and dashed line: a=5.2 mm and d=1.0 mm (Figure 2)).Finally, the filtering characteristics of our developed filter are investigated through experiments. The proposed filter shown in Figure2 is manufactured on an RT/duroid 6010LM substrate of 1.27-mm thickness and 10.2 relative permittivity. The frequency characteristics of the scattering parameters when a=5.2 mm and d=1.0 mm are shown in Figure 13. Here, the solid and dashed lines indicate the experimental and numerical results, respectively. As can be seen, bandpass characteristics with an attenuation pole both below and above the passband were achieved. The experimental results were also in good agreement with the numerical ones. From this figure, it is estimated that the influence of process variation may cause the degradation of impedance matching.Figure 13
Frequency characteristics of scattering parameters (a=5.2 mm and d=1.0 mm (Figure 2)).


## 4. Conclusion

A comb-line filter with a coupling capacitor in the ground plane was proposed. The insertion of the coupling capacitor builds strong coupling locally along the resonators in the filter. The filtering characteristics were investigated through numerical simulations as well as experiments, and the filtering characteristics having attenuation poles at both sides of the passband were obtained. The input susceptances of even and odd modes and coupling coefficients were discussed. The filters using SIRs were also discussed, and the effects of the coupling capacitor for an SIR structure were shown.



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*Source: 919240-2011-04-27.xml*