Symmetrical Matrix Analysis of Parametric Amplifiers and Converters

It is shown that the parametric amplifier and frequency converter can be described by four equations whose coefficients form a matrix that is symmetrical. Because of this symmetry, the calculations for gain, bandwidth, and noise figure yield simple and manageable results. By regarding the matrix as a nodal admittance array, an equivalent conductance circuit is constructed. The derived expressions show that, for low noise figure, the idlefrequency should be much higher than the signal-frequency. This is also the requirement for wide bandwidth. Numerical examples of amplifier and converter design are given.