A general catalog of gain, bandwidth and noise temperature expressions for four-frequency parametric devices

During the last five years, papers on parametric devices have profusely filled the literature. In parametric devices there are many possible arrangements of ports and spectrum modes. Most authors have concentrated upon configurations which yield useful gain together with low-noise performance; however, the degree of rigor, the various assumptions, and the nomenclature used by various authors make the systematic comparison of parametric devices laborious. The intent of this paper has been to compile a comprehensive tabulation of performance expressions for four-frequency parametric devices. Within the bounds of the assumptions and with a consistent nomenclature, expressions are written for: available and transducer power gain, bandwidth, gain-bandwidth product, input and output conductance, midband effective noise temperature, and phase relations. The four-frequency devices are considered because they encompass both the negative conductance and the frequency ratio mechanisms of parametric amplification. These performance expressions are written for the nine possible configurations of ports and spectrum modes of the four-frequency devices which enables an orderly comparison. By proper termination of the idler port in these expressions, eight additional cases arise for the three- and two-frequency parametric devices. As an introduction to the tabulations, the special nomenclature, the terminology, and the assumptions are defined. Only the procedure to derive the various types of expressions is illustrated. The catalog has been intentionally prepared to compare the various operational modes of parametric devices without rigorous inclusion of the nonlinear reactance element losses or without specific emphasis on low-noise operation which obscures the distinctive features of each operational mode.