SNS: Analytic Receiver Analysis Software Using Electrical Scattering Matrices

Abstract

SNS is a MATLAB-based software library written to aid in the design and analysis of receiver architectures. It uses electrical scattering matrices and noise wave vectors to describe receiver architectures of arbitrary topology and complexity. It differs from existing freely-available software mainly in that the scattering matrices used to describe the receiver and its components are analytic rather than numeric. This allows different types of modeling and analysis of receivers to be performed. Non-ideal behavior of receiver components can be parameterized in their scattering matrices. SNS enables the instrument designer to then derive analytic expressions for the signal and noise at the receiver outputs in terms of parameterized component imperfections, and predict their contribution to receiver systematic errors precisely. This can drive the receiver design process by, for instance, allowing the instrument designer to identify which component imperfections contribute most to receiver systematic errors, and hence place firm specifications on individual components. Using SNS to perform this analysis is preferable to traditional Jones matrix-based analysis as it includes internal reflections and is able to model noise: two effects which Jones matrix analysis is unable to describe. SNS can be used to model any receiver in which the components can be described by scattering matrices. Of particular interest to the sub-mm and terahertz frequency regime is the choice between coherent and direct detection technologies. Steady improvements in mm and sub-mm Low Noise Amplifiers (LNAs) mean that coherent receivers with LNAs as their first active element are becoming increasingly competitive, in terms of sensitivity, with bolometer-based receivers at frequencies above ~100 GHz. As an example of the utility of SNS, we use it to compare two polarimeter architectures commonly used to perform measurements of the polarized Cosmic Microwave Background: differencing polarimeters, an architecture commonly used in polarization sensitive bolometer-based polarimeters; and pseudo-correlation polarimeters, an architecture commonly used in coherent, LNA-based, polarimeters. We parameterize common sources of receiver systematic errors in both architectures and compare them through their Mueller matrices, which encode how well the instruments measure the Stokes parameters of the incident radiation. These analytic Mueller matrices are used to demonstrate the different sources of systematic errors in differencing and correlation polarimeters.