Dynamic Modeling of Peak Current Mode Controlled Two-phase PWM Converters with Coupled Inductors

This paper presents simple and accurate large-signal and small-signal averaged models for basic two-phase coupled-inductor PWM converters operating in continuous conduction mode with peak current-mode (PCM) control. A large-signal model is developed, which captures the effects of inductor-current slopes using equivalent, duty-cycle-dependent inductances. A small-signal averaged model is then derived, which includes sampled-data effects. The small-signal model is used to explain differences compared to well-known PCM control models for single-phase or uncoupled multi-phase converters. It is shown how subharmonic instability regions depend on the coupling coefficient and the duty cycle. A continuous-time transfer function is derived for the control-to-inductor current response, with the high-frequency resonant pole
$(F_{res})$
that occurs in the range
$[0.5F_{s},\ F_{s}]$
and varies with the coupling coefficient. A new closed-form expression for
$F_{res}$
is then derived, which allows simplification to a design-oriented
$3^{rd}$
order transfer function. The proposed small-signal model can also predict audio-susceptibility, input, and output impedances accurately. Finally, the model is validated using simulations and experiments on a two-phase buck converter prototype with inversely coupled inductors.