Steady-state perturbative theory for nonlinear circuits

We study the steady-state behavior of a damped, driven nonlinear LRC oscillator, where the nonlinearity arises due to voltage-dependent capacitance. The driving or input signal is assumed to be a pure tone. Using an iterative, perturbative solution technique combined with an energy conservation argument, we show that the oscillator transfers energy from the fundamental to higher harmonics. We determine a series expansion of the two-norm of the steady-state output signal and show that in a large region of parameter space, the two-norm depends superlinearly on the input amplitude. We also use the two-norm calculation to devise a performance goal that the infinity-norm of the steady-state output signal should satisfy, in order for the nonlinear system to have a genuine boost over the corresponding linear system. Taken together, these results are a step toward the automatic design of nonlinear systems that have an optimal boost over corresponding linear systems.