Type I

(a) (b)

(c)

Fig. 5-1. Proposed coupled microstrip lines of type I. (a) Top view. (b) Bottom view. (c) Cross-sectional view.

Fig. 5-1 shows the top, bottom, and cross-sectional views of the proposed coupled mi- crostrip lines of type I. The proposed structure, where there are two inserted signal strips in the ground plane, is basically an extension of the modified coupled lines shown in Fig. 1-2(b).

Note that two via-holes are added on each end of the inserted signal strip on the bottom layer, penetrate through the substrate, and appear on both ends of each signal strip on the top layer.

Therefore, the strip conductor A1 is connected to A2 and B1 is connected to B2. To separate the inserted signal strip from the microstrip ground plane on the bottom layer, there is a narrow gap between them. In the proposed structure, the width of two microstrip lines on the top layer is W and the spacing between them is S. The width of two inserted signal strips with

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a spacing SG on the bottom layer is WS. The spacing between the inserted signal strips and the microstrip ground plane is SR. Accordingly, the width of the ground-plane aperture is W_R = 2 (× W_S +S_R)+S_G. In the quasi-static analysis, the coupling strength of the symmetric coupled lines is determined by the even- and odd-mode capacitances Ce and Co or by the even- and odd-mode impedances Ze and Zo. The voltage coupling factor C for the coupled lines is given by [20]

e o

e o

Z Z

C Z Z

= −

+ . (5.1)

Consequently, the larger the difference between the even- and odd-mode impedances is, the stronger the coupling between the lines will be.

Fig. 5-2 shows the even- and odd-mode excitations of the proposed coupled-line structure. For the even-mode excitation shown in Fig. 5-2(a), the normal component of the electric field at the symmetry plane is zero, which results in a magnetic wall. On the other hand, under the odd-mode excitation, the symmetry plane behaves like an electric wall, as indicated in Fig. 5-2(b). In Fig. 5-2, Cp denotes the parallel-plate capacitance per unit length located vertically between the signal and ground planes. Cf is the fringe capacitance per unit length from the edge of an uncoupled microstrip line. Csa and Csd represent the fringe capacitances per unit length across the gap between the inserted signal strip and the ground plane in the air and dielectric regions, respectively. For the odd-mode excitation in Fig. 5-2(b), Cta and Ctd are the fringe capacitances per unit length across the coupling gap in the air and dielectric regions, respectively, on the top layer, whereas Cga and Cgd are those on the bottom layer. Therefore, the even- and odd-mode capacitances (Ce, Co) of either of the coupled lines are given by

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(a)

(b)

Fig. 5-2. Quasi-TEM modes of the proposed coupled microstrip lines (type I). (a) Even mode.

(b) Odd mode.

e f p sa sd

C =C +C +C +C (5.2)

o f p sa sd ta td ga gd.

C =C +C +C +C +C +C +C +C (5.3)

To compare the characteristics of the conventional and proposed coupled lines shown in Figs. 1-2 and 5-1, first of all, it is necessary to obtain the even- and odd-mode impedances of coupled lines. We first perform the full-wave EM simulation for coupled lines by using Sonnet software, and then load the four-port S-parameter file in AWR Microwave Office to obtain the even- and odd-mode impedances. During the simulation, a lossless metal is assumed, and a substrate with a dielectric constant ε_r =3.58 and a thickness h=0.508 mm

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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0 0.1 0.2 0.3 0.4 0.5 0.6

Line width W (mm)

Coupling factor C

Fig. 5-3. Coupling factor C versus microstrip line width W for two aperture sizes W_R =1.65 mm (circle ○) and 2.85 mm (triangle △). Conventional (Fig. 1-2(a)): dashed-dotted line.

Modified with the ground-plane aperture (Fig. 1-2(b)): dashed line. Proposed: solid line.

is used. Since the capability of the available fabrication process is taken into account, each via-hole is 0.3 mm in diameter, and the minimum line width and gap spacing are limited to be 0.15 mm. Since there are too many physical parameters in the proposed structure, the dimen- sions S, SG, and SR are fixed at 0.15 mm.

Fig. 5-3 plots the coupling factor C versus microstrip line width W for two different aperture sizes W_R =1.65 mm and 2.85 mm, corresponding to W_S =0.6 mm and 1.2 mm.

The lengths of the coupled lines and the ground-plane aperture are 33.75 and 33.15 mm, respectively. The figure shows that as W varies from 0.5 to 5 mm, the proposed structure always has the largest coupling factor compared to the conventional parallel coupled lines with or without the ground-plane aperture under the same physical dimensions. Furthermore, the wider the width WR of the ground-plane aperture is, the larger the coupling factor C will be. The increasing percentage of the coupling factor is especially larger for wide lines. This property is very advantageous since, for the filter application, it is very difficult to obtain

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strong coupling for wide lines.

To explain the mechanism behind the proposed structure in Fig. 5-3, first, consider the conventional coupled lines with and without the ground-plane aperture, as shown in Fig. 1-2.

For the coupled lines without the ground-plane aperture, the even-mode impedance Ze is larger than the odd-mode impedance Zo since the even-mode capacitance Ce is smaller than the odd-mode capacitance Co. For the coupled lines with the ground-plane aperture in Fig.

1-2(b), the decreasing percentage of Ce is greater than that of Co owing to the ground-plane aperture. For this reason, the increasing percentage of Ze is greater than that of Zo, which results in a stronger coupling compared to the conventional structure in Fig. 1-2(a). On the basis of the structure in Fig. 1-2(b), now consider the proposed structure shown in Fig. 5-1 and the even- and odd-mode excitations given in Fig. 5-2. It is seen that the inserted signal strip in the ground-plane aperture increases Ce and Co simultaneously due to capacitances Csa

and Csd in both even- and odd-mode excitations. As the width WS of the inserted signal strip increases, both capacitances Ce and Co increase due to the increases of Csa and Csd. Addi- tionally, the inserted signal strip introduces Cga and Cgd in the odd-mode excitation. Thus, the increasing percentage of Co is much greater than that of Ce. In other words, the proposed structure decreases Ze and Zo at the same time, and the decreasing percentage of Ze is much smaller than that of Zo. This method effectively enhances the coupling strength compared to the structure in Fig. 1-2(b).

It is interesting to compare the proposed coupled lines with and without via-holes and the coupled-line structure with a floating ground-plane conductor in [62]. Here, the dimensions in Fig. 5-3 are used as an example so that W_R =1.65 mm and 2.85 mm correspond to the width of the floating ground-plane conductor 1.35 and 2.55 mm in [62], respectively. Since the coupling enhancement is concerned in this study, Fig. 5-4 shows the coupling factor C for these three structures. As shown in the figure, the structure in Fig. 5-1 always has the largest coupling factor, and via-holes are necessary for strong coupling. The via-holes in the proposed

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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.1 0.2 0.3 0.4 0.5 0.6

Line width W (mm)

Coupling factor C

Fig. 5-4. Comparison of the coupling factor C for three different coupled lines with two aperture sizes W_R =1.65 mm (circle ○) and 2.85 mm (triangle △). Structure in [62]:

dashed-dotted line. Proposed without via-holes: dashed line. Proposed with via-holes: solid line.

structure have an extremely small size and are primarily used for maintaining equal potentials on the top and bottom signal strips. In other words, they are not used to connect the signal strip to the ground plane. Accordingly, the current on the coupled lines is mainly along the longitudinal direction so that the inductive effect of via-holes is not severe and can be neglected. In the following circuit design, we ignore the effect of via-holes and consider them just as an interconnection between the top and bottom signal strips.