Limit Cycle Phenomenon In Buck Converter

Buck converters are widely used in electrical equipment.In order to ensure the safe and stable operation of various types of Buck converters,the potential risks in the converters need to be fully considered.However,when deriving the mathematical model of the converter which is usually the small-signal linear model,the nonlinear elements in the converter are usually ignored.With the small-signal linear model,the controller parameters are soundly tuned to ensure the Buck converter stably operate.However,the small-signal linear model cannot feature the unstable operation.In fact,limit cycle phenomenon would occur in the unstable Buck converters,and it is an oscillation with equal amplitude.Limit cycle may degrade the performance and the service life of the converter,so it is necessary to uncover the generation of limit cycle.In some applications,the limit cycle is applied to meet the specific control requirements,and thus the information of limit cycle,such as oscillation amplitude and frequency should be concerned.In this thesis,the small-signal linear model of the Buck converter is established firstly,and all the nonlinear saturation elements in the converter are studied.It shows that they results from the discontinuous inductor current and the duty cycle.Referring to the constant gain element in linear system,the nonlinear saturation can be regarded as the variable gain element.As a result,the knowledge of linear control can be applied to analyze the effect of nonlinear saturations.In other words,the root locus and Nyquist stability criterion can be used.The model with these nonlinear saturations can successfully predict the limit cycle phenomenon.Moreover,it can confirm the relevant information of the limit cycle.It was found that as long as the small-signal model is unstable,the stable limit cycle will arise in the converter.The dual-input describing function(DIDF)is used to derive the expression of the nonlinear saturations.As a result,the characteristic equation which considers the nonlinear saturations can be used to calculate the frequency and amplitude of the limit cycle.These calculated results are totally in agreement with the synchronous rectifier Buck converter,but a bit of errors occurs in the conventional Buck converter.It is due to the occurrence of the discontinuous current mode.A 100 W experimental prototype is built in the laboratory and theoretical analysis are verified by simulation and experimental results.