The usage of alternative Green's function formulations in the analysis of microstrip transmission lines

As microstrip transmission lines are used in denser circuits and at higher frequencies, conventional quasi-static and scalar potential approximations become inaccurate. One exact analytical formulation uses an electric field integral equation which possesses a dyadic electric-type Hertzian potential Green's function kernel whose scalar components are Sommerfeld-type integrals. These Sommerfeld integrals are slowly convergent and possess singularities in their integrands. An alternative technique using full complex plane analysis is advanced to bypass these problems. It results in an expression for the Green's function as a sum of residues term physically corresponding to surface wave modes plus a branch integral contribution physically corresponding to the radiation spectrum. The alternative formulation integrands exhibit exponential decay, speeding evaluation. These alternative formulations are applied to specific test cases and compared to existing results to illustrate their usefulness.