Variable-frequency Ripple Control Based Switching Converters And Their Stabilities

Ripple control for switching converter is a kind of control technique that employs voltage ripple signal or current ripple signal of the converter as pulse width modulation(PWM)ramp.Compared to conventional voltage-mode control,ripple control has advantages of fast transient response and simplicity of design.Ripple control can be implemented as constant-frequency ripple control(CF-RC)and variable-frequency ripple control(VF-RC).Compared to CF-RC,VF-RC can improve light-load efficiency and its stability is not limited by duty cycle of the converter.Therefore,VF-RC has been widely used in voltage regulator module(VRM)and point of load(POL)converter for powering microprocessor.However,similar to that of CF-RC,the stability of VF-RC can be also affected by some circuit parameters,such as output capacitor and its equivalent series resistance(ESR),etc.Taking VF-RC switching dc-dc converters as the reserch objects,the effects of circuit parameters on the stability and dynamical behaviors are further investigated in this paper,which can extend theoretical analysis of these converters and provide a guideline for designers to choose circuit paramters.Firstly,based on the derivations of five operation modes and four switching borderlines,an asynchronous-switching discrete-time model of fixed off-time(FOT)controlled buck converter is established.With the decrease of output capacitor ESR,instability and modeshifting from continuous conduction mode(CCM)to discontinuous conduction mode(DCM)are discussed.Furthermore,with small ESR of output capacitor,stability effects of load resistance and inductance on dynamical behaviors are investigated,and the approximate stability criteria and the corresponding normalized critical conditions are obtained.The theoretical analyses and experimental results show that the converter operates in DCM chaos via period-doubling and border-collision bifurcation routes,and its instability caused by small ESR can be removed by choosing appropriate load resistance,inductance and voltage transfer ratio,which are very suitable for the circuit design of FOT controlled buck converter.Secondly,by sensing inductor current information for compensating the slope of output voltage,the stable and normal operation of voltage-mode VF-RC buck converter with small output capacitor ESR is obtained.The action mechanism of the ramp compensation technique is analyzed,and the critical slopes of compensation ramp voltage to ensure the FOT controlled buck converter and constant on-time(COT)controlled buck converter stable operation are achieved quantitatively.Take FOT controlled buck converter with ramp compensation as example,its asynchronous-switching discrete-time model is established,upon which the dynamical behaviors of the converter are investigated by taking the slope of compensation ramp voltage as bifurcation parameter.The results indicate that the ramp compensation effectively extends the stable operating range of the output capacitor ESR of the converter,and the ramp compensation technique makes that voltage-mode VF-RC buck converter with small output capacitor ESR can also be in stable and normal operation.Thirdly,to solve the problem that the stability of voltage-mode VF-RC is depependent of output capacitor ESR,variable-frequency capacitor current control technique for switching converter is proposed and its operation principle is elaborated.Using description function method,the small-signal models of COT capacitor current controlled buck converter and FOT capacitor current controlled buck converter are established,upon which their stability are studied by using the Routh-Hurwitz criterion.The study results show that variable-frequency capacitor current control technique has fast transient response characteristic and its stability is independent of output capacitor ESR.Forthly,current-mode VF-RC buck converter is stable and no subharmonic oscillation exists in its current loop when its outer voltage loop is open or its voltage ripple can be ignored.However,when its output capacitance is small or feedback gain is high,subharmonic oscillation may occur in current-mode VF-RC buck converter with proportional-integral(PI)compensator.Take COT current-mode controlled buck converter with PI compensator as an example,considering that compensation capacitor voltage in PI compensator is the linear combination of inductor current and output capacitor voltage,its reduced-order asynchronous-switching discrete-time model is established,upon which instability behaviors caused by output capacitance and feedback gain are investigated.Furthermore,its approximate instability condition is obtained and its design-oriented stability boundaries in different circuit parameter spaces are yielded.Then,the approximate instability condition of FOT current-mode controlled buck converter with PI compensator is given.The analysis results show that the instability of current-mode VF-RC buck converter with PI compensator is mainly affected by output capacitance,output capacitor ESR,feedback gain,current-sensing gain and constant on-time.Finally,it is found that when output capacitor with large ESR is used,subharmonic oscillation may occur in current-mode VF-RC boost converter with PI compensator,causing the converter operating in unstable state,which is completely different from that of current-mode VF-RC buck converter with PI compensator.Take FOT current-mode controlled boost converter with PI compensator as an example,its reduced-order asynchronous-switching discrete-time model is established,up which the effects of feedback gain of outer voltage loop and output capacitor ESR on stability and dynamical behaviors of the converter with PI compensator are studied and the subharmonic oscillation mechanism is investigated.Furthermore,its corresponding approximate critical stability condition is derived.The results indicate that when output capacitor ESR is small,FOT current-mode controlled boost converter with PI compensator is instability by period-doubling bifurcation with variation of feedback gain of PI compensator;whereas the converter is instability by border-collision bifurcation with the variation of output capacitor ESR.Then,the approximate critical stability condition of COT current-mode controlled boost converter with PI compensator is given.From the results,it is known that to avoid subharmonic oscillation in current-mode VF-RC boost converter,output capacitor with small ESR and outer voltage loop with small feedback gain should be chosen.