We have proposed here a new structure of printed circuit transmission lines in which the dominant mode leaks power through additional dielectric multilayer without affecting neighboring circuits. Such a structure of a microstrip line has a slot on the ground plane and also has a dielectric multilayer under it. Then the appropriate combination of dielectric constant between dielectric layers produces the leakage into the multilayer. This means that the leaky field does not leak into the substrate of the microstrip line, and then we can get the lossy uniform microstrip line above the critical frequency. We present first the dependence of the structural parameters of the proposed microstrip lines on the leakage properties. We also apply such a structure to slot lines as one of coplanar printed circuit transmission lines and confirm that the leakage effect can be successfully controlled by an additional dielectric multilayer. Finally, we present the experimental results for the microstrip line with the dielectric multilayer to verify the validity of the numerical results.
 We now know that the dominant mode on printed circuit transmission lines is often leaky at high frequencies, and it may even be leaky at all frequencies, depending on the structure [Shigesawa et al., 1988, 1991, 1993; Tsuji et al., 1993; Lin and Itoh, 1993; Zehentner et al., 1997]. The leaky mode carries power in the forms of the surface wave propagating on substrate, and then leakage effects can produce serious performance difficulties in circuits, such as cross talk between neighboring portions. In contrast to these difficulties, if the frequency characteristics of the leakage effect can be utilized well without leaking on dielectric substrate, we can have a filter property (for example, low-pass property) of the dominant mode on a uniform line.
 In this paper, we first investigate the dispersion behavior of a newly modified microstrip line in order to find out the guide structure that has such filter properties due to leakage effect. The proposed guide has a slot on the ground plane and also has dielectric layers under it. When we take the appropriate combination of dielectric constants between dielectric layers, the leakage occurs not through the substrate but through the dielectric multilayer above some critical frequencies or all frequencies. As a result, the transmitted power along the guide decays because of leakage, but the leaky field does not affect the neighboring circuits on the substrate. This means that the leakage effect can be successfully controlled by the dielectric multilayer, although an absorber is practically required at the edges of the dielectric multilayer to suppress the reflection of leakage. In numerical calculations, we investigate such leakage properties of the proposed guide by varying the structural parameters in detail and also find the interesting coupling phenomena around the onset frequency of the leakage. Furthermore, we apply the same structure to a slot line and show its leakage properties. Finally, we present the experimental results for the modified microstrip line to verify the validity of the numerical results.
2. Leakage Mechanism
 The inset of Figure 1 shows a proposed structure of a microstrip line. For the conventional microstrip line with strip width w, the thickness of a substrate h and its dielectric constant ɛr is modified by introducing a slot with width d on the ground plane and also under it, setting two dielectric layers with thickness t1 and t2 and dielectric constants ɛr1 and ɛr2, respectively. We assume here the relation between the dielectric constants to be ɛr2 < ɛr < ɛr1. The leakage of the dominant mode occurs when its phase constant becomes lower than that of the surface wave propagating on the surrounding dielectric layers. In the present guide, we have two surrounding layers; one of them is the conductor-backed slab waveguide with the dielectric thickness h, and the other is the parallel-plate guide with two dielectric layers. Figure 1 shows typical dispersion behaviors of the dominant mode on the conventional microstrip line (slot width d = 0) and two lowest TM0 surface wave modes on surrounding guides. Although the conventional microstrip line has a leaky mode at higher frequencies in addition to the dominant bound mode, we do not plot the leaky mode. In Figure 1, the dielectric constants are chosen to be ɛr = 2.25, ɛr1 = 10.5, and ɛr2 = 1.0, and the strip width w and dielectric thickness t2 are fixed to be w/h = 1.0 and t2/h = 0.2, respectively. Only the dielectric thickness t1 is varied from t1/h = 0.1 to 0.4. The dispersion curve of the dominant mode on the conventional microstrip line indicated by the thick solid line always lies above that of the TM0 surface wave mode on the conductor-backed slab waveguide indicated by the thin dashed line, so that the dominant mode does not leak into the substrate in all frequencies.
 However, if there is a slot on the ground plane (d ≠ 0), the dominant mode becomes purely bound or leaky, depending on the dispersion curve of the TM0 parallel-plate guide mode indicated by the thin solid lines. The dominant mode of the microstrip line with a slot maintains almost the same value of the phase constant with that of the conventional one because the dielectric constant ɛr2 of the dielectric layer faced on the slot is lower than ɛr of the substrate. As a result, the leakage of the dominant mode can be approximately expected from the relation between the dispersion curves for the conventional microstrip line and the parallel-plate guide. That is, you can find from Figure 1 that for t1/h = 0.1, the dominant mode of which the phase constant lies above that of the TM0 parallel-plate guide mode does not leak in the given frequency range. But in a higher frequency range, it leaks above some critical frequency because the phase constant of the TM0 parallel-plate guide mode approaches the square root of ɛr1 = 10.5. As a result, the guide has a low-pass property. While for t1/h = 0.4, the dominant mode curve lies below the parallel-plate guide one, so power leakage always occurs. For t1/h = 0.2, where both curves cross each other at two frequencies, the dispersion behavior of the dominant mode is expected to become very complicated. In section 3, we calculate the dispersion behavior for the various structural parameters by using the spectral domain method [Nghiem et al., 1993].
3. Dispersion Behavior on Proposed Microstrip Lines
3.1. Dependence on Dielectric Thickness t1
Figures 2a and 2b show the normalized phase constant β/k0 and leakage constant α/k0 of the dominant microstrip line mode on the proposed guide. The structural parameters are the same with those given in Figure 1, and the slot width is assumed to be d/h = 1.0. The thick lines indicate the dominant mode of the guide, while the thin line indicates the TM0 parallel-plate mode on two dielectric layers for t1/h = 0.2. As expected from the discussion in the section 2, the dominant mode for t1/h = 0.1 indicated by the dash-dotted line does not leak in the given frequency range, while that for t1/h = 0.4 indicated by the dashed line always leaks as shown in Figure 2b. The dispersion behavior for t1/h = 0.2 indicated by the thick solid lines is very interesting. In this case, the dominant mode becomes purely bound within some frequency range and is leaky at both outside ranges so that the guide has a band-pass property as shown by the solid curves in Figure 2b. This dispersion actually shows more complicated behavior because the bound mode does not directly connect to the leaky mode as seen in Figure 2a. This behavior will be investigated deeply by changing the dielectric thickness t2 in the section 3.2.
3.2. Dependence on Dielectric Thickness t2
Figures 3a–3c show the normalized phase constant β/k0 for the dielectric thickness t2/h = 0.2, 0.24, and 0.4, respectively, when keeping t1/h = 0.2. In Figure 3, the thick solid line indicates the bound mode, the dash-dotted lines are the leaky mode, and the dashed lines are the improper real mode. (The field distribution of an improper real mode grows up transversely, but its phase constant is real, so this mode is nonphysical.) The thin solid line is the TM0 parallel-plate mode. Figure 3d also summarizes the leakage constant α/k0 for the various dielectric thickness t2. Figure 3a depicts in detail the behavior of the phase constant for t1/h = t2/h = 0.2 shown in Figure 2a on the expanded scale. It is obvious from Figure 3a that the mode coupling around frequencies h/λ0 = 0.07 and 0.18 occurs near the transition region from the bound mode to the leaky one. These couplings are very similar to the leakage phenomenon of a coplanar waveguide [Tsuji et al., 1992]. These are caused by the interaction between the dominant microstrip line (MSL) mode and the surface wave–like (SWL) mode lying along the TM0 parallel-plate mode. This phenomenon may be understood well by regarding this guide as a modified coplanar waveguide with an offset center strip. Basically, it may be also regarded as a coupling between the dominant microstrip mode and a dominant parallel-plate mode through a slot. We can see the dispersion curves divided into two separate portions by the coupling. We look first at the top part of Figure 3a (the portion that continues from the bound MSL mode). The dashed line on the left represents the improper real SWL mode, and it continues to the bound MSL dominant mode (the thick solid line) through the lower-frequency coupling region. After that, this bound mode continues again to the improper real SWL mode (the dashed line) on the right through the higher-frequency coupling region. We next examine the bottom part of Figure 3a. On the left and right are the dominant MSL leaky modes indicated by the dash-dotted line. These leaky modes change to SWL leaky ones in both coupling regions, and then they continue to the improper real SWL modes (dashed line), of which the dispersion curve forms the closed loop. The junction points between the improper real and leaky modes also represent the onset of leakage. Therefore, in the coupling region, the leakage constant also moves between both MSL and SWL modes so that its behavior becomes complicated as the small dip is observed at around h/λ0 = 0.2 in Figure 3d.
 The dispersion curves of the dominant mode for t2/h = 0.24 and 0.4 are shown in Figures 3b and 3c. These curves intersect with that of the TM0 parallel-plate mode only in the higher-frequency region so that the guide has a low-pass property although the coupling between the dominant MSL mode and the SWL mode still occurs. The property of the leakage constant for the different values of t2/h in the higher frequency shows the similar behavior with the small dip caused by the coupling as shown in Figure 3d.
3.3. Dependence on Slot Width d
Figures 4a and 4b show the dispersion behaviors for the slot width d/h = 0.5 and 0.25, respectively, when keeping t1/h = t2/h = 0.2. Comparing these Figure 4 with Figure 3a for d/h = 1.0, the phase constant of the dominant MSL mode approaches that of the conventional microstrip line indicated by the thin dashed line as the slot width d is decreased. For d/h = 0.25, both curves overlap each other, but the dominant mode still becomes leaky outside two crossing points. Figure 4c also summarizes the leakage constant α/k0 for the various slot width d. The value of the leakage constant becomes small with decreasing slot width because the microstrip field does not penetrate so much into the parallel-plate guide through the slot.
4. Dispersion Behavior on Slot Lines
 The inset of Figure 5 shows a slot line with slot width d, thickness h of a substrate, and its dielectric constant ɛr, which is modified by introducing two dielectric layers with thickness t1 and t2 and dielectric constants ɛr1 and ɛr2, respectively. We now assume the same relation between the dielectric constants as the microstrip line case. In Figure 5, the dielectric constants are chosen to be ɛr = 2.25, ɛr1 = 10.5, and ɛr2 = 1.0, and the slot width d and dielectric thickness t2 are fixed to be d/h = 0.4 and t2/h = 2.0, respectively. This guide also has the two surrounding layers, which can support the TM0 surface wave mode or the TM0 parallel-plate mode. Therefore we can control the leakage properties by adjusting the thickness of dielectric multilayer as done in section 3. Figure 5 shows typical dispersion behaviors of the dominant mode on the slot line for t1/h = 0.2 and 0.4, indicated by the thick lines. The phase constants of these modes lie above the TM0 surface wave curve indicated by the thin dashed line so that the dominant mode does not leak power through the substrate with thickness h. Furthermore, the dominant mode for t1/h = 0.2 indicated by the dash-dotted line lies above the thin solid line of the TM0 parallel-plate mode. As a result, this mode is purely bound in the given frequency range. The dominant mode for t1/h = 0.4 indicated by the thick solid line intersects with the TM0 parallel-plate mode at around h/λ0 = 0.1, and then this mode leaks power through the parallel-plate guide above the critical frequency as shown in Figure 5b. Although the detailed dispersion behavior of this guide and other guides will be presented elsewhere, the effect of the dielectric multilayer is useful for controlling the leakage properties without affecting the neighboring circuit on the substrate.
Figure 6 shows the measured results for the proposed microstrip line, of which the structural parameters are indicated in the inset. The measurement is performed by varying the thickness t2 of the dielectric layer with ɛr2 = 1. The measured results are obtained from the ratio of the transmitted power between the guides with and without the dielectric layer with ɛr1 because the guide without it supports the bound mode. The thick lines indicate the experimental results, and the thin lines are the theoretical ones. Both results show good agreement. For t2 = 0 and 1 mm, the leakage occurs from zero frequency, while for t2 = 4 mm, the dominant mode is purely bound in the given frequency range, so it is observed experimentally that power does not attenuate. For t2 = 2 mm, the leakage begins occurring at about 14 GHz theoretically. In the experimental data, the power begins to leak gradually from about 10 GHz because of the fabrication error of the guide. In this case, however, we can observe the low-pass property experimentally. These measurements prove that the leakage property of the guide can be controlled by the thickness of the dielectric layer.
 We have investigated the leakage properties of a microstrip line and a slot line with two dielectric layers in addition to dielectric substrate, in which the dominant mode becomes leaky without the surface wave propagation into the substrate. The dispersion behavior has been investigated for various structural parameters. As a result, it is found that the present guide can have the leakage characteristics with a low-pass or a band-pass behavior, and the coupling between the dominant microstrip mode and the surface wave–like mode occurs around the onset frequency of the leakage. Finally, we have verified that the experiment results agree well with the calculated results.
 This work was supported in part by a Grant-in-Aid for Scientific Research (C) (13650439) from Japan Society for the Promotion of Science and by grants from the Research Center for Advanced Science and Technology, Doshisha University.