Astronomical receiver modelling using scattering matrices

Proper modelling of astronomical receivers is vital: it describes the systematic errors in the raw data, guides the receiver design process, and assists data calibration. In this paper, we describe a method of analytically modelling the full signal and noise behaviour of arbitrarily complex radio receivers. We use electrical scattering matrices to describe the signal behaviour of individual components in the receiver, and noise correlation matrices to describe their noise behaviour. These are combined to produce the full receiver model. We apply this approach to a specified receiver architecture: a hybrid of a continuous comparison radiometer and correlation polarimeter designed for the C-Band All-Sky Survey. We produce analytic descriptions of the receiver Mueller matrix and noise temperature, and discuss how imperfections in crucial components affect the raw data. Many of the conclusions drawn are generally applicable to correlation polarimeters and continuous comparison radiometers.