On the Characteristic impedance of the TEM horn antenna

Some time ago, Carrel presented an analytical formula, based on conformal mapping, for the characteristic impedance of the transverse electromagnetic horn antenna . Later, results from this formula were shown to be in error, and Lambert et al. offered a new analytical formula, also based on conformal mapping . This formula also contains an error that is easily corrected. Independently, Yang and Lee offered an analytical formula . In this paper, we compare these analytical formulas to a direct numerical solution. Finally, we compare the "microstrip approximation" for the characteristic impedance to the exact solution. Graphs are presented for the characteristic impedance versus the angles of the horn that should be useful for the purpose of design.