A theoretical solution for PWM with non-ideal transient response

The ideal theoretical spectral analysis for PWM has been available for decades. However, PWM actually suffers from non-ideal switching characteristics and their effects on the output spectrum have not been thoroughly studied theoretically due to the complexity involved. Transient ringing on both rising and falling edges is a common phenomenon during switching and it has been held responsible for harmonic distortion, judging from experimental results. In this paper, we present a theoretical technique to model the PWM with transient ringing using a second-order circuit. This theoretical solution is the first of its kind available in the literature and it helps us to understand the distortion effects on the spectrum due to transient ringing. Simulations have been carried out to verify the correctness of the theoretical solution.