Cad Formulas, Their Inverses and Interrelations for Microstrip, Cpw Lines Without and With a Backing Ground Plane, By Successive Synthetic Asymptotes

Abstract

This paper derives simple CAD formulas of microstrips, coplanar waveguides (CPW) without and with a backing ground plane. Both analysis and design formulas, in pairs, of the three lines, can be derived from just one technique: the synthetic asymptote. This novel asymptotic technique ensures a maximum error of 4% or less with no limits on the possible parameter values. The technique also shows that a combination of the first two pairs of formulas of the above actually forms the third pair of formulas in a bootstrapping succession. It is possible to get smaller errors than above with formulas including a series of artificial coefficients. This is not done so as to maintain the simplicity of the formulas and to emphasize the insights to the interrelations between the different lines over full ranges of parameter values. Physical insights, such as the microstrip and CPW combining into the CPW with conductor backing, are very helpful in the initial design choices and estimates in an RF circuit. They are lacking at the present time.