  We study the origins of period doubling and chaos in the driven series
resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that
resonators driven at frequencies much higher than the diode reverse recovery
rate do not show period doubling, and that models of chaos based on the
nonlinear capacitance of the varactor diode display a reverse-recovery-like
effect, and this effect strongly resembles reverse recovery of real diodes. We
find for the first time that in addition to the known dependence of the reverse
recovery time on past current maxima, there are also important nonlinear
dependencies on pulse frequency, duty-cycle, and DC voltage bias. Similar
nonlinearities are present in the nonlinear capacitance models of these diodes.
We conclude that a history-dependent and nonlinear reverse recovery time is an
essential ingredient for chaotic behavior of this circuit, and demonstrate for
the first time that all major competing models have this effect, either
explicitly or implicitly. Besides unifying the two major models of RLD chaos,
our work reveals that the nonlinearities of the reverse recovery time must be
included for a complete understanding of period doubling and chaos in this
circuit.
