In this letter, a mathematical model in self-oscillating class-D audio amplifiers is proposed to describe the switching frequency variation as a fuction of the modulation depth. It is alleged in a very simple form which can be applied to any general structure adopting phase-shifting in the feedback filter, time delay of the loop, and the hysteresis window at the comparator. The main focus is set on the analysis of the phase-shifting filter which shows the least dependency on the modulation depth, which is not yet revealed.