Analysis of a triode oscillator with losses associated with the inductive branch and signal applied in grid circuit

By transforming the nonlinear equations of a triode oscillator, with and without an applied signal, to linear ones with periodically varying coefficients, the complete solutions of oscillator equations to the first power of the tube parameters are obtained, the losses being associated with the inductive branch of the oscillatory circuit and the signal applied in the grid circuit. When the circuit losses are relatively low, the resulting harmonics as well as the fundamental amplitude of oscillation are practically the same as when the losses are represented by a constant conductance shunting the oscillatory circuit, but the frequency of oscillation differs by an amount depending on the resistance representing the losses as well as the amplitude of oscillation. The amplitude-phase-frequency relations of the system within and outside the locking range are obtained and the ranges of synchronization determined.