# Proposed Multi-Frequency Model (2004)

It is well known that a state-space averaging technique can be used to model the switching converter up to half of the switching frequency. However, unexplained phase delay often can be observed when the modulation frequency approaches one-half of the switching frequency and causes an additional phase delay. This could not be explained with the current average model. Research at CPES recently developed a more accurate model than can extend the accuracy beyond half the switching frequency to allow this model to be used up to the switching frequency. The model incorporates additional modulation signal that is centered around the switching frequency. Normally, the sideband frequency is ignored in the small-signal low-frequency average model. However, the modulation side-band centered at the switching frequency will create considerable phase delay when modulation frequency is approaching half the switching frequency. By incorporating sideband effect, a more accurate model can be created with capability of predicting both magnitude and phase with accuracy close to the switching frequency. This tool is especially useful for designing multi-phase voltage regulator modules, whereby high bandwidth is desired.