Formulas by synthetic asymptote for TM/sub 0/ surface wave pole locations of a microstrip substrate

It is convenient to have simple formulas to determine the pole locations of the surface wave in the Green's function instead of searching in spectral space. In many practical circuits, to avoid excessive radiation and surface wave losses, the frequency is kept low for a given substrate thickness. This leads to the existence of only one surface wave mode TM/sub 0/. The formula is synthesized from the asymptotes of the original transcendental equations. With the pole located it is easy to find the pole amplitude with existing formulas.