Equivalent Circuit Model of High Frequency PWM and Resonant Converters

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Date
2015-09-30
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Virginia Tech
Abstract

Distributed power system (DPS) is widely adopted in Power supplies for the telecom, computer and network applications. Constant on-time current mode control and V2 control are widely used as point-of-load (POL) converters and voltage regulators (VR) in DPS systems. Series resonant converters (SRC) are widely used in aerospace systems and LLC resonant converters are widely used as Front-end converters in DPS systems. The technological innovations bring increasing demand for optimizing the dynamic performance of the switching regulators in these applications. There has been a strong desire to develop simple and accurate equivalent circuit models to facilitate the design of these converters.

Constant on-time current-mode control has been widely used in POL and VRM converters. For multi-phase application, external ramp is required to improve jittering performance using pulse distribution method. Chapter II analyzes the effect of external ramp on small-signal model of constant on-time current mode control. It is found that external ramp brings additional dynamics by introducing a moving pole and a static zero. Next, a three-terminal switch model is proposed based on non-ideal current source concept, where the non-idealness of the current source is presented by a Re2-Le2 branch. Based on the proposed model, design guidelines are proposed based on either worst case design strategy or auto-tuning strategy.

V2 control has advantages of simple implementation and fast transient response and is widely used in industry for POL and VR applications. However, the capacitor voltage sideband effect, which casues the instability problem when ceramic capacitors are employed, also needs to be taken into consideration in modeling. Chapter III proposed a unified equivalent circuit model of V2 control, the model is built based on non-ideal voltage source concept. The model represents capacitor voltage sideband effect with a Re2-Le2 branch, which forms the double pole by resonating with power stage output capacitor. The equivalent circuit model is a complete model and can be used to examine all the transfer functions. Bsed on the unified equivalent circuit model, design guidelines for VR applications and general POL applications are provided in Chapter IV, for both constant on-time V2 control and constant frequency V2 control.

For resonant converters, the small-sginal modelling is very challenging as some of the state variables do not have dc components but contain strong switching frequency component and therefore the average concept breaks down. For SRC, the equivalent circuit model proposed by E. Yang in [E26] based on the results by the extended describing function concept is the most successful model. However, the order of the equivalent circuit model is too high and the transfer functions are still derived based on numerical solution instead of analytical solutions. Chapter V proposes a methodology to simplify the fifth-order equivalent circuit of SRC to a third-order equivalent circuit. The proposed equivalent circuit model can be used to explain the beat frequency dynamics: when switching frequency is far away from resonant frequency, beat frequency will occur; when the two frequencies are close, beat frequency will disappear and another double pole which is determined by equivalent inductor and output capacitor will be formed. For the first time, analytical solutions are provided for all the transfer functions which are very helpful for feedback design.

LLC resonant converters are widely adopted as front-end converter in distributed power system for the telecom, computer and network applications [F2]. Besides, LLC resonant converters are also very popular in other applications, such as LCD, LED and plasma display in TV and flat panels [F3]-[F6]; iron implanter arc power supply[F7]; solar array simulator in photovoltaic application[F8]; fuel cell applications[F9],and so on. For LLC, no simple equivalent circuit model is available and no analytical expressions of transfer functions are presented. Chapter VI proposes an equivalent circuit model for LLC resonant converter. When Fs ≥ Fo, Lm is clamped by the output voltage and LLC behaves very similar as SRC. As a result, the dynamic behavior is similar as SRC: when switching frequency is larger than resonant frequency, the beat frequency double pole show up and the circuit is third-order; when switching frequency is close to resonant frequency, beat frequency double pole disappear and a new double pole formed by equivalent inductor Le and equivalent output capacitor Cf show up. The circuit reduces to second order. When Fs<Fo, Lm participates in resonance during some time periods and the circuit is essentially a multiresonant structure. An approximated model is proposed where the equivalent resonant inductor is modified to include the effect of Lm. As a result, the double pole will move to a little lower frequency. For the first time, analytical solutions are provided for all the transfer functions which are very helpful for feedback design.

In conclusion, the works shown in this dissertation focus on small-signal equivalent circuit modeling for Buck converters with advanced control schemes and also resonant converters. The models are simple and accurate up to very high frequency range (1/2 fsw).

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Keywords
Equivalent Circuit, Design, PWM Converters, Resonant Converters, SRC, LLC
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