Unified Equivalent Circuit Model and Optimal Design of <inline-formula><tex-math>$V^{2}$</tex-math> </inline-formula> Controlled Buck Converters

Abstract

V 2 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 instability issue and serve as a useful design tool for V 2 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 physical insight of V 2 control as a non-ideal voltage source, a dual concept of previous non-ideal 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.Index Terms---Equivalent circuit model, V 2 control, ripplebased control, enhanced V 2 control and optimal design guidelines. d vo Driver iL RCo Co RL Ls Pulse Width Modulator vc V ref Hv Vin + -

Derivative-Free Direct Search Optimization Method for Enhancing Performance of Analytical Design Approach-Based Digital Controller for Switching Regulator

“…The specifications of the buck converter to be considered throughout the paper are as the following: [22,23], are expressed by: As can be observed from Figure 1, the output voltage variationv out (s) is a linear combination of the input voltage variationv in (s), the load current variationî out (s) and the small-signal duty cycle perturbationd(s), propagated through the transfer functions, namely the line-to-output transfer function G vg (s), the converter output impedance of the loaded power converter Z o (s) and the control-to-output transfer function G vd (s), respectively. That is to say:…”

“…The three transfer functions G vd (s), G vg (s), and Z o (s), derived using the state-space averaging technique [22,23], are expressed by:…”

Optimized Digital Controllers for Switching-Mode DC-DC Step-Down Converter

“…where ω ω The buck converter's dynamics (transfer function) imperative for the controller design can be derived through its small-signal AC-equivalent circuit model (see Figure 2), where the nonlinear power switches Q 1 and Q 2 are replaced by their equivalent linear small-signal models [21]. By applying the averaging and linearization technique adopted in [22] to the small-signal model, the small-signal transfer functions, such as duty cycle-to-output voltage G vd (s), input voltage-to-output voltage G vg (s), and load current-to-output voltage (loaded power converter output impedance Z o (s)), can be computed and are described by Equations (1)-(3), respectively [22,23].…”

Linearized Discrete Charge Balance Control with Simplified Algorithm for DCM Buck Converter

“…Therefore, a lot of control strategies are proposed for different DC-DC power converters. Among many strategies, the well-known V 2 controls have been widely used in industrial applications, and they can achieve a great control loop bandwidth [1][2][3]. Predictive controls acquire state variables ahead of time, which allow earlier actions to stabilize the system [4,5].…”