Unified Equivalent Circuit Model and Optimal Design of $V^{2}$ Controlled Buck Converters

V² control has advantages of simple implementation and fast transient response and is widely used in industry for point-of-load applications. This control scheme is elegant when output capacitors with large RC time constant are employed, such as OSCON capacitors. However, in most cases using capacitors with small RC time constant, such as ceramic capacitors, instability problem will occur. Previous modeling methods including sampled-data modeling, discrete-time analysis, time-domain analysis, and describing function are all very mathematical and difficult to apply for practical engineers as little physical insight can be extracted. Up to now, no equivalent circuit model is proposed which is able to predict the instability issue and serve as a useful design tool for V² control. This paper proposes a unified equivalent circuit model which is applicable to all types of capacitors by considering the effect of capacitor voltage ripple. The equivalent circuit provides the physical insight of V² control as a nonideal voltage source, a dual concept of previous nonideal current source for current-mode control. The equivalent circuit model is a simple yet accurate complete model and is very helpful for design purpose. Optimal design guidelines for point-of-load applications are provided. The proposed equivalent circuit model is applicable to both variable frequency modulation and constant frequency modulation. The equivalent circuit model and design guidelines are verified with Simplis simulation and experimental results.