The Low-Frequency Distortion in D-Class Amplifiers

D-class amplifiers use pulsewidth modulation to transform an input signal u into a rectangular signal p whose duty cycle linearly depends on the input signal u. After low-pass-filtering p to suppress the switching frequency and its harmonics, we obtain the output signal y that is a good approximation of u. This kind of an amplifier is attractive (as compared with the classical A-class and B-class amplifiers) due to its high efficiency. A buck power supply may be regarded as a particular instance of a D-class amplifier. While the operating principle of the D-class amplifier is intuitively clear, a rigorous mathematical analysis of this system is not trivial, as the amplifier is time-varying and nonlinear. We derive a rigorous proof of the fact that the signal p is a good approximation of u in the low-frequency range, and we provide precise error bounds for this approximation.