Closed-form approximations for fin-line eigenmodes

The characteristic equations for bilateral, unilateral and antipodal fin lines are formulated in a convenient form for an approximate evaluation. It is shown that the eigenvalues for all higher-order modes can be calculated from closed-form expressions provided that the two lowest eigenvalues are known. Dispersion relations are developed which are equivalent to those for rectangular waveguides. The analysis also comprehends a simple evaluation of the field configurations of all hybrid eigenmodes. The approximate formulas are checked against exact numerical calculations, the agreement being excellent.