Synthesis of optimum smooth transition in microstrip through line on microwave integrated circuit

A problem in designing microstrip trough lines as transmission lines for microwave hybrid-film integrated circuits is the synthesis of the optimum smooth widening of the center conductor on the dielectric substrate. Such a transition is described by the relation c(z)= Phi b(z) sub Z (sub0)(z) = const or , more explicitly c(z)= Phi b(z) sub C (sub1)(z) = const (z- longitudinal coordinate, 1- length, 2b- width of center conductor, 2c- clearance between outer conductors, Z sub O- wave impedance, C sub 1 - capacitance per unit length). It can be accurately synthesized according to the single-model T-approximation of the electrodynamic process, on the basis of quasi-steady solutions to the corresponding singular integral equations and with conformal mapping. This is demonstrated by calculations made for a typical trough line as well as for a coplanar one.