Precision Calculations of the Characteristic Impedance of Complex Coaxial Waveguides Used in Wideband Thermal Converters of AC Voltage and Current

The article presents precision and numerically stable method of calculation of the characteristic impedance of cylindrical multilayer waveguides used in high-precision wideband measuring instruments and standards, especially calculable thermal converters of AC voltage and precision wideband current shunts. Most of currently existing algorithms of characteristic impedance calculation of such waveguides are based upon approximations. Unfortunately, application of such methods is limited to waveguides composed of a specific, usually low number of layers. The accuracy of approximation methods as well as the number of layers is sometimes not sufficient, especially when the coaxial waveguide is a part of precision measurement equipment. The article presents the numerically stable matrix analytical formula using exponentially scaled modified Bessel functions to compute characteristic impedance and its components of the cylindrical coaxial multilayer waveguides. Results obtained with the developed method were compared with results of simulations made using the Finite Element Method (FEM) software simulations. Very good agreement between results of those two methods were achieved.