In-depth stability analysis of degenerate parametric amplifiers

A relevant instability phenomenon in degenerate parametric power amplifiers is the division by two of the pump frequency. Because of the existence of an input source at the same frequency of the instability, the degenerate parametric power amplifier will exhibit a specific bifurcation behavior, inherent to this type of circuit. The anomalous shape of the solution curves with high slope and generation of new paths will be associated with an imperfect Pitchfork bifurcation. Its understanding will be essential for a proper interpretation of the simulated and measured results. For illustration, a global stability analysis of a broadband phase-coherent degenerate parametric amplifier is presented. Good agreement has been obtained with the measurement results.