Shielded Coupled-Strip Transmission Line

TLDR

The paper analyzes odd and even TEM modes of parallel coplanar strips between ground planes, presenting rigorous formulas for zero‑thickness strips and approximate ones for finite‑thickness or opposite‑side printed strips, and demonstrates that their characteristic impedances and phase velocities fully determine the design of directional couplers, coupled‑line filters, and related components. The authors aim to facilitate design work by providing nomograms that relate coupled‑strip cross‑section dimensions to odd‑ and even‑mode characteristic impedances. These nomograms are derived from the characteristic impedance and phase velocity analysis of the coupled‑strip modes. The nomograms achieve better than one‑percent accuracy over a wide range of values sufficient for most purposes.

Abstract

An analysis is made of the odd and even TEM modes on a pair of parallel co-planar strips midway between ground planes. Rigorous formulas are presented for the case of zero-thickness strips, while approximate formulas are given for strips of finite thickness and for strips printed on opposite sides of a thin dielectric sheet supported in air between ground planes (AIL construction). The characteristic impedances and the phase velocities of the two modes are necessary and sufficient information for the design of directional couplers, coupled-line filters, and other components utilizing the coupling between parallel-strip lines. In order to facilitate design work, nomograms are included in the paper which give the dimensions of the coupled-strip cross section in terms of the odd- and even-mode characteristic impedances. The characteristic-impedance scales of these nomograms may be read to an accuracy of better than one per cent over a wide range of values that is sufficient for most purposes.