1Inclusion of Switching Loss in theAveraged Equivalent Circuit ModelThe methods of Chapter 3 can be extended to include switching loss inthe converter equivalent circuit model• Include switching transitions in the converter waveforms• Model effects of diode reverse recovery, etc.To obtain tractable results, the waveforms during the switchingtransitions must usually be approximatedThings that can substantially change the results:• Ringing caused by parasitic tank circuits• Snubber circuits• These are modeled in ECEN 5817, Resonant and Soft-Switching Phenomena in Power Electronics2The Modeling ApproachExtension of Chapter 3 MethodsSketch the converter waveforms– Including the switching transitions (idealizing assumptionsare made to lead to tractable results)– In particular, sketch inductor voltage, capacitor current, andinput current waveformsThe usual steady-state relationships: vL  = 0,  iC  = 0,  ig  = IgUse the resulting equations to construct an equivalentcircuit model, as usual3Buck Converter Example• Ideal MOSFET, p–n diode with reverse recovery• Neglect semiconductor device capacitances, MOSFETswitching times, etc.• Neglect conduction losses• Neglect ripple in inductor current and capacitor voltage4AssumedwaveformsDiode recovered charge Qr,reverse recovery time trThese waveforms assumethat the diode voltagechanges at the end of thereverse recovery transient• a “snappy” diode• Voltage of soft-recoverydiodes changes sooner• Leads to a pessimisticestimate of inducedswitching loss5Inductor volt-second balanceand capacitor charge balanceAs usual:  vL  = 0 = DVg – VAlso as usual:  iC  = 0 = IL – V/R6Average input current ig  = Ig = (area under curve)/Ts = (DTsIL + trIL + Qr)/Ts = DIL + trIL /Ts + Qr /Ts7Construction of Equivalent Circuit ModelFrom inductor volt-second balance:  vL  = 0 = DVg – VFrom capacitor charge balance:  iC  = 0 = IL – V/R8Input port of model ig  = Ig = DIL + trIL /Ts + Qr /Ts9Combine for complete modelThe two independent current sources consume powerVg (trIL /Ts + Qr /Ts)equal to the switching loss induced by diode reverse recovery10Solution of modelOutput:V = DVgEfficiency:  = Pout / PinPout = VIL Pin = Vg (DIL + trIL /Ts + Qr /Ts)Combine and simplify: = 1 / [1 + fs (tr /D + Qr R /D2Vg )]11Predicted Efficiency vs Duty CycleSwitching frequency 100 kHzInput voltage 24 VLoad resistance 15 Recovered charge 0.75 µCoulReverse recovery time 75 nsec(no attempt is made here tomodel how the reverserecovery process varies withinductor current)• Substantial degradation ofefficiency• Poor efficiency at low dutycycleBuck converter with diode reverse recovery0.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%0 0.2 0.4 0.6 0.8 1Duty cycleEfficiency12Boost Converter ExampleModel same effects as in previous buck converter example:• Ideal MOSFET, p–n diode with reverse recovery• Neglect semiconductor device capacitances, MOSFETswitching times, etc.• Neglect conduction losses• Neglect ripple in inductor current and capacitor voltage13BoostconverterTransistor and diodewaveforms have sameshapes as in buckexample, but dependon different quantities14Inductor volt-second balanceand average input currentAs usual: vL  = 0 = Vg – DVAlso as usual: ig  = IL15Capacitorcharge balance iC  = id  – V/R = 0 = – V/R + IL(DTs – tr)/Ts – Qr /TsCollect terms: V/R = IL(DTs – tr)/Ts – Qr /Ts16Construct modelThe two independent current sources consume powerV (trIL /Ts + Qr /Ts)equal to the switching loss induced by diode reverse recoveryThe result is:17Predicted V/Vg vs duty cycleBoost converter with diode reverse recovery0123456780 0.2 0.4 0.6 0.8 1Duty cycleV/VgSwitching frequency 100 kHzInput voltage 24 VLoad resistance 60 Recovered charge 5 µCoulReverse recovery time 100 nsecInductor resistance RL = 0.3 (inductor resistance also insertedinto averaged model here)With RL onlyWith RL and diode reverse recovery18SummaryThe averaged modeling approach can be extended toinclude effects of switching lossTransistor and diode waveforms are constructed,including the switching transitions. The effects of theswitching transitions on the inductor, capacitor, andinput current waveforms can then be determinedInductor volt-second balance and capacitor chargebalance are appliedConverter input current is averagedEquivalent circuit corresponding to the the averagedequations is