maps the z-plane of PCPW bounded inside the dielectric material onto the upper-half t-plane, where sn(u, [r.sub.1]) is the Jacobian elliptic function with a variable u and a modulus [r.sub.1] determined by
capacitance Co0 of air-filled PCPW can be obtained by
Figure 3 shows a PCPW structure embedded in a set of infinite number of dielectric layers.
This section will present the calculated results by conformal mapping analysis to verify the derived expressions as well as to investigate the properties of PCPW. Comprehensive comparisons with the results of full-wave analysis and available experimental data in literatures will be presented in this section and demonstrate that the derived formulas are accurate for most of the application range of physical dimensions and available dielectric materials.
Figure 4 shows the characteristic impedance of single layered PCPW operating in even mode.
Figure 5 shows the characteristic impedance of PCPW on two-layered substrate, where the calculations are carried out with the parameters listed in Figure 5 and large lateral ground width of [W.sub.g] 10(W + 2 S).
The corresponding PCPW CAD model consists of nine unit cells of CPW.
Figures 6 and 7 show the even- and odd-mode impedance of PCPW embedded in two dielectric materials of different heights and on top of two-layered substrate, respectively, with parameters listed in the figures.
Figures 8 and 9 show the even- and odd-mode characteristic impedance of PCPW on top of GaAs ([[epsilon].sub.rb1] = 12.9).
For a given W and [W.sub.g], the reduction of [h.sub.b1] decreases the effective dielectric constants of the structure hence increases both the even and odd-mode characteristic impedance of PCPW. It is worth to notice that both even- and odd-mode characteristic impedance reach saturation values for a thick substrate, where the field distribution can be considered as well-confined inside the substrate and not experienced the dielectric boundary.