Noise Figure and Gain of Linear Systems Containing a Single Sinusoidally Varying Element

A method for determining the noise figure and gain of an important class of time-varying linear systems is presented. The voltage-current relationships within the system are determined by a continued fraction solution of a second-order difference equation. The resulting of noise figure and gain can be determined as precisely as desired by truncating a convergent series. Numerical examples comparing these resuits with the two-frequency methods are presented for a parametric amplifier and a noninverting upconverter.