Generalized Design Technique of Ultra-Wideband Transitions for Quasi-TEM Planar Transmission Lines Based on Analytical Models

Abstract

A generalized design technique of ultra-wideband planar transitions using EM-based analytical models is presented in this paper. Among various planar transmission lines, each transmission line has unique advantages over other line types, and a microwave component in a system can be designed to perform much better if it is implemented on a certain type of transmission line. Therefore, low-loss and high-performance transitions between transmission lines, with easy integrability with the main circuit board, are needed. The proposed transition design technique uses the Schwarz-Christoffel transformation, which is one of conformal mapping methods, and can be applied to design any planar transition between a pair combination of planar transmission lines based on TEM or quasi-TEM waves. To optimally match the characteristic line impedance and smoothly transform the electromagnetic field distribution between the planar transmission lines, entire cross-sections through the planar transition should be analyzed with proper models. In this paper, the crosssections of planar transitions are categorized into 4 cross-sectional models, where each cross-section is divided into multiple regions for the analysis to obtain line capacitance. Therefore, for the 4 cross-sectional models, 7 types of basis structures are identified to obtain their capacitances by applying conformal mapping. By adding capacitances of a combination of the 7 analysis types, the total line capacitance, thus the characteristic line impedance, of any cross-sectional model of the planar transition can be obtained. The characteristic line impedance of each cross-sectional model calculated with the proposed analytical formulas is compared with the 3D EM calculations, and it is found that the deviated values are mostly well under 6%. This proposed technique enables to design various planar transitions efficiently and quickly for the maximum performance without parameter tuning trials, by providing optimal impedance matching and smooth field transformation up to mm-wave frequencies.INDEX TERMS Conformal mapping, cross-sectional model, planar transition, planar transmission line, Schwarz-Christoffel transformation.

Compact Wideband Coplanar Stripline-to-Microstrip Line Transition Using a Bended Structure on a Two-Layered Substrate

“…Figure 5 shows the cross-sectional model with four analysis regions. In [20], which presented a systematic analysis technique for TEM/quasi-TEM planar transitions by the authors group, a similar cross-sectional model (Model II in [20]) was analyzed using the conformal mapping. In the analysis, each region is transformed into parallel conductor plates through the Schwarz-Christoffel transformation.…”

“…where K is the elliptical integral of the first kind with modulus k 1 and complementary modulus k 1 of Type 2 in [20]. Region II is the inner region of the CPS line with a finite bottom ground plate of the upper substrate with relative dielectric constant ε r .…”

“…where k 2 and k 2 are the modulus and complementary modulus of Type 3 in [20], respectively. Region III is considered as a region with the fringing field distributed in the lower substrate with relative dielectric constant ε r .…”

“…where k 3 and k 3 are the modulus and complementary modulus of Type 5 in [20], respectively. Also, as increasing the bottom ground plane, another fringing field distribution in Region IV results in capacitance C 4 expressed by Equation (4):…”

“…where k 4 and k 4 are the modulus and complementary modulus of Type 7 in [20], respectively. Therefore, by summing up the line capacitances of the analysis regions, the characteristic line impedance and effective dielectric constant of the cross-sectional area of the bended transition are obtained as Equations ( 5) and (6), respectively.…”