Contents I. Introduction
The superconductor–insulator–superconductor (SIS) mixer serves as an excellent mixing element for heterodyne receivers in millimeter and sub-millimeter astronomical observations because of its ultra-low intrinsic noise and high sensitivity [1]. Since the introduction of the SIS mixer in the 1970s, the associated circuit design has evolved sequentially from a series-connected lumped junction array device that was easily fabricated and had a high dynamic range [2] to single junction and parallel-connected devices [3], [4], and then to the current series-connected distributed junction (SDJ) mixer design with its potential capability for both a wide intermediate frequency (IF) bandwidth and a high dynamic range [5]. In the design and optimization of these novel SIS mixers, noise performance is a significant parameter that dominates the sensitivity of the mixer. In fact, SIS mixer noise analysis has predominantly developed into two methods based on Tucker's quantum theory of mixing [6]. The first is the highly flexible noise scattering matrix method, which is carried out using SuperMix software [7], and the other is the noise correlation matrix analysis method that was developed by Tong and Blundell [8]. SuperMix is a software library written by the California Institute of Technology for calculation and optimization of the signal and noise performances of high-frequency circuits, and is particularly useful for circuits that include superconductor elements and SIS mixers. The noise analysis based on SuperMix involves converting all matrices into a scattering matrix, and then collapses the entire circuit into a single 3 × 3 scattering noise correlation matrix using a scattering matrix method developed at Caltech by Wedge. The embedding impedances are then applied to give the noise temperature [9]. Since SuperMix is a general Computer-Aided Design (CAD) program, it allows arbitrary circuit connections to be made. The noise correlation matrix analysis method of Tong and Blundell is based on superposition. In this analysis method, the shot noise that is generated at each junction is transformed using the entire mixer circuit to the mixer IF output port. Assuming that the noise generated at one device is not correlated with that generated at other devices, the theorem of superposition is applied to accumulate the noise power that was delivered to the IF port from the individual junctions [8]. The noise analysis methods mentioned above show explicit and fundamental physical thoughts. Nevertheless, they may not be well suited to simulations performed using general mathematics software packages or CAD program.
