Modeling of ${\rm V}^{2}$ Current-Mode Control

Recently, V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> constant on-time control has been widely used to improve light-load efficiency. In the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> implementation, the nonlinear PWM modulator is much more complicated than usual, since not only is the inductor current information fed back to the modulator but also the capacitor voltage ripple information. Generally speaking, there is no subharmonic oscillation in constant on-time control. However, the delay due to the capacitor ripple results in subharmonic oscillation in V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> constant on-time control. So far, there has been no accurate model to predict the instability issue due to the capacitor ripple. This paper presents a new modeling approach for the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> constant on-time control. The power stage, the switches, and the PWM modulator are treated as a single entity and modeled based on the describing function method. The model for the V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> constant on-time control achieved by the new approach can accurately predict subharmonic oscillations. Two solutions are discussed to solve the instability issue. The extension of the model to other types of V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> current-mode control and multiphase application is also shown in this paper. Simulation and experimental results verify the proposed model.