Random Switching for High Performance DC-DC Power Converters

Random Pulse Width Modulation (RPWM) has been successfully applied in power electronics for nearly 30 years. The effects of the various possible RPWM strategies on the Power Spectral Density have been thoroughly studied. Despite the effectiveness of RPWM in spreading harmonic content, an appeal is consistently made to maintain the textbook Pulse Width Modulation scheme ‘on average’. Random Switching (RS) does away with this notion and probabilistically operates the switch. In addition to fulfilling several optimality conditions, including being the only viable switching strategy at the theoretical limit of performance and having lower switching losses than any other RPWM; RS allows for design of the DC behaviour separately from that of the PSD. The pulse amplitude probability affects the DC and total PSD. The first and second moment of the pulse length probability distribution affects the shape of the envelope of the noise of the PSD. The minimum pulse length acts like a selective harmonic filter. The PSD can therefore be shaped without external filtering by changing these probabilities. Gaussian and Huffman pulse length probabilities are shown to be good choices depending on whether real-time PSD control or spectrum usage are the design goal. In addition, it is shown that C'uk’s state space averaging model applies to RS, with $D \to p$, hence no new tools are needed to understand the low frequency behavior or control performance. A benefit of closed loop random switching is that no filtering of the controlled variable is required. Randomly responding in a biased manner dependent on the error is hence shown to be useful. There are several good reasons to consider RS for high performance applications.

💡 Research Summary

The paper presents a comprehensive study of Random Switching (RS) and its generalization, Fully Random Switching (FRS), as alternatives to conventional Pulse Width Modulation (PWM) and Random Pulse Width Modulation (RPWM) for high‑performance DC‑DC converters. The authors begin by highlighting a fundamental limitation of PWM: the duty cycle D must be an integer multiple of a minimum time quantum Δt, which is dictated by the fastest achievable switching transition of the power device. As switching frequencies increase and Δt becomes comparable to the desired pulse width, PWM loses its ability to represent arbitrary duty cycles, and even RPWM, which adds randomness to PWM parameters, suffers from the same constraint because it still relies on a deterministic PWM carrier.

To overcome this, the authors define Random Switching as a binary switching process that, at each elementary time slot of length Δt, selects the “ON” state with probability p and the “OFF” state with probability 1‑p, independent of any underlying carrier waveform. This probabilistic model is expressed mathematically by a sum of rectangular pulses multiplied by a Bernoulli random variable. The key insight is that the time‑average of the switching function is exactly p, so p plays the role of the average duty cycle in conventional PWM. Consequently, the DC output voltage or current can be directly controlled by adjusting p, while the instantaneous switching pattern is completely random.

The paper then investigates the impact of the pulse‑length probability distribution P(L) on the Power Spectral Density (PSD) of the converter. The first moment E