An Approximate Dynamic Green´s Function in Three Dimensions for Finite Length Microstripline

A spatial Green´s function in 2-D for straight and infinite microstriplines has been shown to be accurate at frequencies that the dynamic effects cannot be neglected. It is reasonable, therefore, to expect that a similarly accurate spatial Green´s function in 3-D can be constructed for finite and curved microstriplines. Based on the same image model of charges and currents as in 2-D, this paper constructs the 3-D Green´s function. The Green´s function is then applied, through Harrington´s moment rnethod, to calculate the input impedance of a few microstriplines, viz., a matched microstripline, straight and hairpin open-ended stubs. The input impedance of a microstrip stub always has a small resistive component indicating the radiative loss. This resistive component agrees with that calculated from the Lewin´s formula. Finally, as expected, the imaginary part of the input impedance agrees with that calculated from the TEM approach.