Small Signal Modeling And Loop-gain Measurement Of DC-DC Converters

DC-DC converter contains nonlinear elements such as power switches, diodes,pulse-width modulation (PWM) modulator, thus it belongs to a typical nonlinear system.For such a system, there are still some problems needed to explain and solve, such as theaccuracy of the converter’s model at the frequencies close to half of the switchingfrequency, the different characteristics with different modulation schemes, differentmeasured loop gain with different measurement methods. By analyzing the frequencyspectrum of the signals in the closed loop, the difference of different loop gainmeasurement methods is discussed, and the accurate method is given. Based on the aboveanalysis, a new measurement method is proposed in this thesis, which is used to verify theaccuracy of the models. Considering the properties of natural sampling PWM system, thediscrete model of PWM modulator and converter power stage is derived in this thesis, andit is applied to analysis the impact of modulation scheme on the converter.Chapter II introduces two existing loop gain measurement methods, namely the analogperturbation injection method and the digital perturbation injection method. Using thediscrete small signal block diagram of PWM modulator, the frequency spectrum of thesignals in the closed loop are analyzed, based on which, the relationship of the two loopgain measurement methods is revealed, and it is pointed out that the digital perturbationinjection method can obtain the actual loop gain. An intercept point sample loop gainmeasurement method is proposed, which is equivalent to the digital perturbation injectionmethod, but it is easier to be implemented. The theoretical analyses are verified by thesimulation results.In Chapter III, the discrete models of the PWM modulator and the power stage arederived at the intercept point of carrier and modulating signals under different modulationschemes. Then, the control to output transfer functions of three basic DC-DC converters,i.e., buck, boost and buck-boost, are derived and simplified, so as to improve thepracticability of the model on the precondition of accuracy. Based on the discrete models,the effect of modulation scheme on the PWM modulator is discussed and the distribution ofthe zeros of the control to output transfer function Gvd(z) of the three basic dc-dc converters under different modulation schemes is given. Finally, the above conclusions are verified bythe loop gain measurement simulation results.In Chapter IV, the experiment prototypes of the three basic dc-dc converters are built.The loop gains of the three converters under different modulation schemes are meausuredwith the proposed intercept point sample loop gain measurement method. The measuredresults verify the correctness of the theoretical analysis.