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 alpha /sub c/, of a general stripline with arbitrary dimensions is obtained. The method is based on a quasi-static formula for alpha /sub 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 alpha /sub 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.<
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