The Degenerate and Quasi-Degenerate Mode of Parametric Amplification

The analysis of this mode of parametric amplification is based on the theory of linear differential equations with periodically varying coefficients. A steady-state (particular integral) solution of Mathieu's equation was obtained and expressions for gain, bandwidth and noise figure were derived for varying signal, pump and resonance frequencies. Similar expressions were derived or the lower-sideband or idler response. The gain and bandwidth of the idler response approaches that of the signal as the variation of capacitance is increased. When the fractional capacitance variation becomes equal to
2/Q
, oscillations at half the pump frequency are excited. Due to the frequency inversion of the idler response, the practical application of the degenerate mode is very limited. In quasi-degenerate mode, when idler and signal responses are sufficiently removed to prevent the intermixing of the sidebands, both the gain and the noise figure deteriorate by approximately 3 db.