Derivation of the System Equation for Null-Balanced Total-Power Radiometer System NCS1

A system equation of a recently developed null-balanced, total-power radiometer system is rigorously derived. Delivered noise power and temperature is related to available power (temperature) through an extension of the mismatch factor to broadband systems. The available power ratio α_g, the available gain G and the delivered power ratio (efficiency) η₁ are defined. Properties of idealized, but in principle realizable components such as an infinitely directive isolator and a lossless matched waveguide-below-cutoff attenuator are used. A cascading technique is repeatedly applied to the fundamental noise equation. Mathematically modeling the experimental procedure of sequentially attaching the two noise standards and the unknown source to the system input, we obtain the system of three equations that can be solved for the noise temperature of the unknown noise source.