Presentation on theme: "Midterm Exam One-week take-home exam, to cover material of HW#1-6"— Presentation transcript:
1Midterm Exam One-week take-home exam, to cover material of HW#1-6 Averaged switch modelingSimulationExtra element theoremInput filter designN-extra element theoremFeedback theoremDCM modelingOn-campus: handed out this Friday March 6, due at beginning of class of Friday March 13Off-campus: start exam at time of your choosing, after you at least have completed HW#6.
15Zero-order hold: frequency responses fs = 1 MHzMATLAB file: zohfr.m
16How does any of this apply to converter modeling?
17PWM is a small-signal sampler! PWM sampling occurs at tp (i.e. at dTs, periodically, in each switching period)
18General sampled-data model Sampled-data model valid at all frequenciesEquivalent hold describes the converter small-signal response to the sampled duty-cycle perturbations [Billy Lau, PESC 1986]State-space averaging or averaged-switch models are low-frequency continuous-time approximations to this sampled-data model
19Application to DCM high-frequency modeling iLcdTsd2TsTs
20Application to DCM high-frequency modeling iLcdTsd2TsTs
21DCM inductor current high-frequency response High-frequency pole due to the inductor current dynamics in DCM, see (11.77) in Section 11.3
22Conclusions PWM is a small-signal sampler Switching converter is a sampled-data systemDuty-cycle perturbations act as a string of impulsesConverter response to the duty-cycle perturbations can be modeled as an equivalent holdAveraged small-signal models are low-frequency approximations to the equivalent holdIn DCM, at high frequencies, the inductor-current dynamic response is described by an equivalent hold that behaves as zero-order hold of length D2TsApproximate continuous-time model based on the DCM sampled-data model correlates with the analysis of Section 11.3: the same high-frequency pole at fs/(pD2) is obtainedNext: current-mode control (Chapter 12)