Stability analysis & design of hysteretic current-mode switched-inductor buck DC-DC converters

Battery-supplied systems demand fast, power efficient, and compact power supplies. Although linear regulators are quick and small, tiny batteries cannot sustain their losses for long. Pulse-width-modulated (PWM) switchers are considerably more efficient, but also slower. Luckily, hysteretic converters can respond within one switching cycle. Stabilizing the system for maximum speed with a hysteretic inductor-current loop, however, which is not linear, is not straightforward. This paper shows how load dumps delay the response of the hysteretic oscillator that the current loop implements. Knowing the worse-case dump and the delay it causes reveals the lowest output capacitance that maintains stable operation at maximum speed. The converter designed here can therefore recover, as predicted, from 100-mA load dumps in 2 μs with 10 μF and 45° of phase margin.