Envelope stability of low-frequency transistor oscillators

Small departures from a constant envelope of LC oscillators using the normal self-bias circuits for stabilization may be described by a second-order linear differential equation. Besides some general conclusions, detailed results are presented for two usual emitter-base diode characteristics. More complicated bias arrangements and the modulation response are briefly considered. Large departures from equilibrium lead to a pair of non-linear differential equations. Some graphical solutions of these equations are sketched on the phase plane and lead to an understanding of the `large¿ behaviour of the envelope. It is tentatively concluded that `small¿ stability ensures `large¿ stability. An analogue computer has been used to confirm some of the theory.