Application of voltage-wave S parameters with complex normalisation to 1-port and 2-port coaxial-resistor design

A procedure is described for coaxial-resistor design, employing voltage-wave scattering parameters coupled with the process of matrix renormalisation. The rigour of the theory is demonstrated in the design of 1-port and 2-port coaxial resistors and worked-out examples are given showing the change in the parameters from d.c. to 500 MHz. In addition to 1-port standards for S11, network analysers require 2-port standards to verify the accuracy of S21 measurements. Air-dielectric lines are normally employed for this purpose, but they only provide standards of phase angle because |S21|=1. The analysis undertaken indicates that the 2-port resistor could form the basis of a calculable S21 standard in which |S21|¿1. Practical limitations are discussed, together with the effects caused by discontinuity capacitances and a nonradial electric field that occurs when the surface resistivity is comparatively large compared with the wave impedance. It is shown that the discontinuity capacitances can be taken into account in a rigorous manner by matrix transformation. A proposed design for a 2-port resistor, in which |S21|=1/¿10, is evaluated at 500 MHz, together with the magnitude of the corrections arising from discontinuity capacitances and a nonradial electric field. It is also shown that a pair of such standards, when used in association with a 3-port coaxial junction, could provide a standard in which|S21|<0.01(¿40 dB). One conclusion drawn from the analysis is that the nonradial electric-field effect needs further study.