An exact TEM calculation of loss in a stripline of arbitrary dimensions

Based on a modification of a conformal mapping originally introduced by R.H.T. Bates (1956), an exact expression for the quasi-static conductive attenuation constant α_c, of a general stripline with arbitrary dimensions is obtained. The method is based on a quasi-static formula for α_c which assumes a transverse electromagnetic (TEM) mode and is thus restricted to the case where the skin depth is small compared to the strip thickness. The final formula for α_c involves an integral of only a smoothly varying function, since an analytic extraction of a term representing the singular behavior of the charge density is performed in the analysis. A comparison of the results obtained using the present method and the approximate formulas of S.B. Cohn (1955) shows that a maximum error of about 5-6% occurs in the Cohn formulas at a point where the two approximate formulas are joined