Conditions for optimum noise performance of transistor amplifiers with a reactive source

When driven from a purely reactive source, conventional noise figure is undefined for a two-port network such as an audio amplifier. In order to assess the noise performance of small-signal amplifiers driven from reactive sources such as capacitor microphones, a signal-to-wideband-average-noise ratio is defined. It is shown that for transducers where output is related to internal reactance by a simple transformer relationship and where the Thevenin equivalent internal impedance is a pure series
R
and
L
or
C
, there exists an optimum value of internal reactance for maximum signal-to-noise ratio when used with a given noisy amplifier. The equations for optimum reactance and signal-to-average-noise ratio are general and include low-frequency dependence of the transistor noise generators, equalization or frequency dependence of amplifier gain, and source resistance as well as reactance. Solutions are given for the practical audio case with typical low-noise audio transistors for both inductive and capacitive transducers.