R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder The Modeling Approach Extension of Chapter 3 Methods Sketch the converter waveforms – Including the switching transitions (idealizing assumptions are made to lead to tractable results) – In particular, sketch inductor voltage, capacitor current, and input current waveforms The usual steady-state relationships: vL = 0, iC = 0, ig = Ig Use the resulting equations to construct an equivalent circuit model, as usual 2 Buck Converter Example • • • • Ideal MOSFET, p–n diode with reverse recovery Neglect semiconductor device capacitances, MOSFET switching times, etc. Neglect conduction losses Neglect ripple in inductor current and capacitor voltage 3 Assumed waveforms Diode recovered charge Qr, reverse recovery time tr These waveforms assume that the diode voltage changes at the end of the reverse recovery transient • a “snappy” diode • Voltage of soft-recovery diodes changes sooner • Leads to a pessimistic estimate of induced switching loss 4 Combine for complete model The two independent current sources consume power Vg (trIL /Ts + Qr /Ts) equal to the switching loss induced by diode reverse recovery 9 Solution of model Output: V = DVg Efﬁciency: = Pout / Pin Pout = VIL Pin = Vg (DIL + trIL /Ts + Qr /Ts) Combine and simplify: = 1 / [1 + fs (tr /D + Qr R /D2Vg )] 10 Predicted Efficiency vs Duty Cycle Switching frequency 100 kHz Input voltage 24 V Load resistance 15 Recovered charge 0.75 µCoul Reverse recovery time 75 nsec Buck converter with diode reverse recovery 100.00% 90.00% 80.00% (no attempt is made here to model how the reverse recovery process varies with inductor current) • Substantial degradation of efﬁciency • Poor efﬁciency at low duty cycle Efficiency 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0 0.2 0.4 0.6 Duty cycle 11 0.8 1 Boost Converter Example Model same effects as in previous buck converter example: • Ideal MOSFET, p–n diode with reverse recovery • Neglect semiconductor device capacitances, MOSFET switching times, etc. • Neglect conduction losses • Neglect ripple in inductor current and capacitor voltage 12 Boost converter Transistor and diode waveforms have same shapes as in buck example, but depend on different quantities 13 Inductor volt-second balance and average input current As usual: vL = 0 = Vg – D V Also as usual: ig = IL 14 Capacitor charge balance iC = id – V/R = 0 = – V/R + IL(D Ts – tr)/Ts – Qr /Ts Collect terms: V/R = IL(D Ts – tr)/Ts – Qr /Ts 15 Construct model The result is: The two independent current sources consume power V (trIL /Ts + Qr /Ts) equal to the switching loss induced by diode reverse recovery 16 Predicted V/Vg vs duty cycle Boost converter with diode reverse recovery 8 7 With RL only 6 5 V/Vg Switching frequency 100 kHz Input voltage 24 V Load resistance 60 Recovered charge 5 µCoul Reverse recovery time 100 nsec Inductor resistance RL = 0.3 (inductor resistance also inserted into averaged model here) 4 3 2 1 With RL and diode reverse recovery 0 0 0.2 0.4 0.6 Duty cycle 17 0.8 1 Summary The averaged modeling approach can be extended to include effects of switching loss Transistor and diode waveforms are constructed, including the switching transitions. The effects of the switching transitions on the inductor, capacitor, and input current waveforms can then be determined Inductor volt-second balance and capacitor charge balance are applied Converter input current is averaged Equivalent circuit corresponding to the the averaged equations is constructed 18 4.2.1. Power diodes! A power diode, under reverse-biased conditions:! v + – p + + + { { low doping concentration n- – E v + n – – – depletion region, reverse-biased Fundamentals of Power Electronics! 9! Chapter 4: Switch realization! Forward-biased power diode! v + – i { conductivity modulation n- p + – + + + n + – + – minority carrier injection Fundamentals of Power Electronics! 10! Chapter 4: Switch realization! Diode in OFF state:" reversed-biased, blocking voltage! v(t) v + – t n– p n E v i(t) + 0 { – t Depletion region, reverse-biased • Diode is reverse-biased! • No stored minority charge: q = 0! (1) • Depletion region blocks applied reverse voltage; charge is stored in capacitance of depletion region! Fundamentals of Power Electronics! 12! Chapter 4: Switch realization! Turn-on transient! v(t) Diode conducts with low on-resistance t • charge to increase voltage across depletion region! Diode is forward-biased. Supply minority charge to n– region to reduce on-resistance Charge depletion region i(t) On-state current determined by converter circuit t (1) (2) Fundamentals of Power Electronics! 13! The current i(t) is determined by the converter circuit. This current supplies: ! • charge needed to support the on-state current! • charge to reduce onresistance of n– region! Chapter 4: Switch realization! Turn-off transient! v + – i (< 0) n- p n + + + + + + + + } Removal of stored minority charge q Fundamentals of Power Electronics! 14! Chapter 4: Switch realization! Diode turn-off transient" continued! v(t) t (4) Diode remains forward-biased. Remove stored charge in n– region (5) Diode is reverse-biased. Charge depletion region capacitance. i(t) tr 0 t di dt Area –Qr (1) (2) Fundamentals of Power Electronics! (3) (4) 15! (5) (6) Chapter 4: Switch realization! The diode switching transients induce switching loss in the transistor! iA + vA fast transistor + – – + – Vg iL(t) – vB + L Qr Vg silicon diode 0 0 t diode waveforms • Diode recovered stored charge Qr flows through transistor during transistor turn-on transition, inducing switching loss! • Qr depends on diode on-state forward current, and on the rate-of-change of diode current during diode turn-off transition! iL vA(t) iB Fundamentals of Power Electronics! see Section 4.3.2! iA(t) transistor waveforms iL iB(t) vB(t) 0 0 t area –Qr –Vg tr pA(t) = vA iA area ~QrVg area ~iLVgtr 16! t0 t1 t2 t Chapter 4: Switch realization! Types of power diodes! Standard recovery! Reverse recovery time not specified, intended for 50/60Hz! Fast recovery and ultra-fast recovery! Reverse recovery time and recovered charge specified! Intended for converter applications! Schottky diode! A majority carrier device! Essentially no recovered charge! Model with equilibrium i-v characteristic, in parallel with depletion region capacitance! Restricted to low voltage (few devices can block 100V or more)! Fundamentals of Power Electronics! 18! Chapter 4: Switch realization! Paralleling diodes! Attempts to parallel diodes, and share the current so that i1 = i2 = i/2, generally don t work.! i i1 i2 Reason: thermal instability caused by temperature dependence of the diode equation.! + + v1 v2 Increased temperature leads to increased current, or reduced voltage.! – – One diode will hog the current.! To get the diodes to share the current, heroic measures are required:! • Select matched devices! • Package on common thermal substrate! • Build external circuitry that forces the currents to balance! Fundamentals of Power Electronics! 20! Chapter 4: Switch realization! Ringing induced by diode stored charge! see Section 4.3.3! iL(t) L vi(t) + – vL(t) vi(t) + – silicon diode iB(t) + vB(t) – V1 t 0 –V2 C iL(t) • Diode is forward-biased while iL(t) > 0! • Negative inductor current removes diode stored charge Qr! • When diode becomes reverse-biased, negative inductor current flows through capacitor C.! • Ringing of L-C network is damped by parasitic losses. Ringing energy is lost.! Fundamentals of Power Electronics! 21! 0 t area – Qr vB(t) t 0 –V2 t1 t2 t3 Chapter 4: Switch realization! Energy associated with ringing! Recovered charge is! Qr = – t3 t2 iL(t) dt vi(t) V1 t 0 Energy stored in inductor during interval t2 ≤ t ≤ t3 :! t3 WL = vL(t) iL(t) dt t2 Applied inductor voltage during interval t2 ≤ t ≤ t3 :! di (t) vL(t) = L L = – V2 dt Hence,! t3 t3 di (t) WL = L L iL(t) dt = ( – V2) iL(t) dt dt t2 t2 –V2 iL(t) 0 vB(t) t 0 –V2 W L = 12 L i 2L(t 3) = V2 Qr t1 Fundamentals of Power Electronics! t area – Qr 22! t2 t3 Chapter 4: Switch realization!

Download PDF

- Similar pages
- Lecture 10 slide deck
- Lecture 9 slide deck
- Inclusion of Switching Loss in the Averaged Equivalent Circuit Model
- jfs050_ mtbf
- Fostex FT207D User's Manual
- Delta Electronics HMU1345 User's Manual
- 0.1” Spacing T.H. with 0.05” offset (201-0001-01)-Top Side
- Delta Electronics HAH1330 User's Manual
- Delta Electronics HAL1340 User's Manual
- datasheet for PE-63588 by Pulse Electronics
- K12013-1
- IRF6892STR/TR1PbF
- Chapter 4. Switch Realization 4.1. Switch applications
- Chapter 4. Switch Realization 4.1. Switch applications