  We analyse the nonlinear behaviour of a third-order class-D amplifier, and
demonstrate the remarkable effectiveness of the recently introduced ripple
compensation (RC) technique in reducing the audio distortion of the device. The
amplifier converts an input audio signal to a high-frequency train of
rectangular pulses, whose widths are modulated according to the input signal
(pulse-width modulation) and employs negative feedback. After determining the
steady-state operating point for constant input and calculating its stability,
we derive a small-signal model (SSM), which yields in closed form the transfer
function relating (infinitesimal) input and output disturbances. This SSM shows
how the RC technique is able to linearise the small-signal response of the
device. We extend this SSM through a fully nonlinear perturbation calculation
of the dynamics of the amplifier, based on the disparity in time scales between
the pulse train and the audio signal. We obtain the nonlinear response of the
amplifier to a general audio signal, avoiding the linearisation inherent in the
SSM; we thereby more precisely quantify the reduction in distortion achieved
through RC. Finally, simulations corroborate our theoretical predictions and
illustrate the dramatic deterioration in performance that occurs when the
amplifier is operated in an unstable regime. The perturbation calculation is
rather general, and may be adapted to quantify the way in which other nonlinear
negative-feedback pulse-modulated devices track a time-varying input signal
that slowly modulates the system parameters.
