R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

Transcription

1 R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

2 pn junction! Junction diode consisting of! p-doped silicon! n-doped silicon! A p-n junction where the p- and n-material meet! v p n p material contains mobile holes! pn junction! n material contains mobile electrons! Fundamentals of Power Electronics! 1! Chapter 4: Switch realization!

3 Formation of depletion region" also called space charge layer! At the junction, the concentrations of holes and electrons changes abruptly! The holes and electrons diffuse in the direction of reducing concentration! Fundamentals of Power Electronics! p Electron diffusion! v o E 2! Hole diffusion! These holes and electrons leave behind charged atoms a depletion region! An electric field forms in the vicinity of the junction! This electric field constitutes an energy barrier that opposes diffusion! The device comes to equilibrium when the voltage v o across the depletion region is enough to stop further diffusion of charges across the junction! n Chapter 4: Switch realization!

4 The diode under reverse bias conditions! Application of an external reverse voltage to the diode causes the depletion region to increase! The external voltage is blocked by the depletion region! Increasing the reverse voltage requires that charge is added to the depletion region! v o p n E Junction capacitance : depletion region charge vs. voltage characteristic! Fundamentals of Power Electronics! 3! Chapter 4: Switch realization!

5 The diode under forward bias conditions! When the diode voltage is positive, the depletion region voltage is not large enough to prevent diffusion of charge across the junction! Holes from the p-region diffuse across the junction, and become minority carriers in the n-region, whose energy state is high enough to enable them to conduct! Similarly, electrons from n-region diffuse across the junction and become minority carriers in the p-region! v o p n E Fundamentals of Power Electronics! 4! Chapter 4: Switch realization!

6 Minority-carrier stored charge in forward-biased diode! Under forward-biased conditions, a hole enters the p-material from the external circuit. It then either (a) diffuses across junction, then recombines with an electron in the n-region, or (b) recombines in the p-region with a minority-carrier electron! p v o n Electron concentration Hole concentration The forward current of the diode consists entirely of recombination, either in the p- or n-region. The forward current continues as long as there is minority charge. To turn off the diode, the minority charge must be eliminated.! Fundamentals of Power Electronics! 5! Chapter 4: Switch realization!

7 Charge-controlled behavior of the diode! The diode equation:! q(t)=q 0 e v(t) 1 Charge control equation:! dq(t) dt with:! = i(t) q(t) L = 1/(26 mv) at 300 K! L = minority carrier lifetime! (above equations don t include current that charges depletion region capacitance)! (lumped-element charge control model with 1 lump)! p i Electron concentration In equilibrium: dq/dt = 0, and hence! v i(t)= q(t) L = Q 0 L e v(t) 1 = I 0 e v(t) 1 Hole concentration Area = total stored minority charge q! n Fundamentals of Power Electronics! 6! Chapter 4: Switch realization!

8 Removal of stored charge during reverse recovery! Distribution of minority charge on one side of p-n junction during reverse recovery! v(t) t 0 t 1 t 2 t 3 t 4 Minority charge t = t 0 V off t t 1 t 2 i(t) I on 0 x 0 x 3 t = t 3 Slope determines diffusion rate and hence current! x 0 Fundamentals of Power Electronics! 7! Chapter 4: Switch realization!

9 Charge-control in the diode:" Discussion! The familiar iv curve of the diode is an equilibrium relationship that can be violated during transient conditions! During the turn-on and turn-off switching transients, the current deviates substantially from the equilibrium iv curve, because of change in the stored charge and change in the charge within the reverse-bias depletion region! The reverse-recovery time t r is the time required to remove the stored charge in the diode and enable it to block the full applied negative voltage. The area of the negative diode current during reverse recovery is the recovered charge Q r! Fundamentals of Power Electronics! 8! Chapter 4: Switch realization!

10 Inclusion of Switching Loss in the Averaged Equivalent Circuit Model The methods of Chapter 3 can be extended to include switching loss in the 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 switching transitions must usually be approximated Things 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 Electronics 1

11 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: v L = 0, i C = 0, i g = I g Use the resulting equations to construct an equivalent circuit model, as usual 2

12 Buck Converter Example Ideal MOSFET, pn diode with reverse recovery Neglect semiconductor device capacitances, MOSFET switching times, etc. Neglect conduction losses Neglect ripple in inductor current and capacitor voltage 3

13 Assumed waveforms Diode recovered charge Q r, reverse recovery time t r 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

14 Inductor volt-second balance and capacitor charge balance As usual: v L = 0 = DV g V Also as usual: i C = 0 = I L V/R 5

15 Average input current i g = I g = (area under curve)/t s = (DT s I L t r I L Q r )/T s = DI L t r I L /T s Q r /T s 6

16 Construction of Equivalent Circuit Model From inductor volt-second balance: v L = 0 = DV g V From capacitor charge balance: i C = 0 = I L V/R 7

17 Input port of model i g = I g = DI L t r I L /T s Q r /T s 8

18 Combine for complete model The two independent current sources consume power V g (t r I L /T s Q r /T s ) equal to the switching loss induced by diode reverse recovery 9

19 Solution of model Output: V = DV g Efficiency: = P out / P in P out = VI L P in = V g (DI L t r I L /T s Q r /T s ) Combine and simplify: = 1 / [1 f s (t r /D Q r R /D 2 V g )] 10

20 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 (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 Buck converter with diode reverse recovery % 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Duty cycle 11

21 Boost Converter Example Model same effects as in previous buck converter example: Ideal MOSFET, pn diode with reverse recovery Neglect semiconductor device capacitances, MOSFET switching times, etc. Neglect conduction losses Neglect ripple in inductor current and capacitor voltage 12

22 Boost converter Transistor and diode waveforms have same shapes as in buck example, but depend on different quantities 13

23 Inductor volt-second balance and average input current As usual: v L = 0 = V g D V Also as usual: i g = I L 14

24 Capacitor charge balance i C = i d V/R = 0 = V/R I L (D T s t r )/T s Q r /T s Collect terms: V/R = I L (D T s t r )/T s Q r /T s 15

25 Construct model The result is: The two independent current sources consume power V (t r I L /T s Q r /T s ) equal to the switching loss induced by diode reverse recovery 16

26 Predicted V/V g vs duty cycle Switching frequency 100 khz Input voltage 24 V Load resistance 60 Recovered charge 5 µcoul Reverse recovery time 100 nsec Inductor resistance R L = 0.3 (inductor resistance also inserted into averaged model here) V/Vg Boost converter with diode reverse recovery With R L only With R L and diode reverse recovery Duty cycle 17

27 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

28 { Power diodes! A power diode, under reverse-biased conditions:! v low doping concentration p n - n E v { depletion region, reverse-biased Fundamentals of Power Electronics! 9! Chapter 4: Switch realization!

29 Forward-biased power diode! i v conductivity modulation { p n - n minority carrier injection Fundamentals of Power Electronics! 10! Chapter 4: Switch realization!

30 Diode in OFF state:" reversed-biased, blocking voltage! v v(t) t p n n E v { Depletion region, reverse-biased i(t) 0 t Diode is reverse-biased! No stored minority charge: q = 0! Depletion region blocks applied reverse voltage; charge is stored in capacitance of depletion region! (1) Fundamentals of Power Electronics! 12! Chapter 4: Switch realization!

31 Turn-on transient! v(t) i(t) Charge depletion region (1) (2) Diode conducts with low on-resistance Diode is forward-biased. Supply minority charge to n region to reduce on-resistance On-state current determined by converter circuit t t The current i(t) is determined by the converter circuit. This current supplies:! charge to increase voltage across depletion region! charge needed to support the on-state current! charge to reduce onresistance of n region! Fundamentals of Power Electronics! 13! Chapter 4: Switch realization!

32 Turn-off transient! i (< 0) v p n - n } Removal of stored minority charge q Fundamentals of Power Electronics! 14! Chapter 4: Switch realization!

33 Diode turn-off transient" continued! v(t) t i(t) (4) Diode remains forward-biased. Remove stored charge in n region di dt t r (5) Diode is reverse-biased. Charge depletion region capacitance. 0 t Area Q r (1) (2) (3) (4) (5) (6) Fundamentals of Power Electronics! 15! Chapter 4: Switch realization!

34 The diode switching transients induce switching loss in the transistor! V g i A fast transistor v A v B i L (t) silicon diode i B L transistor waveforms i A (t) Q r V g v A (t) 0 i L 0 t see Section 4.3.2! Diode recovered stored charge Q r flows through transistor during transistor turn-on transition, inducing switching loss! Q r depends on diode on-state forward current, and on the rate-of-change of diode current during diode turn-off transition! Fundamentals of Power Electronics! diode waveforms 16! p A (t) = v A i A i L 0 area Q r i B (t) v B (t) t r area ~Q r V g area t 0 t 1 t 2 0 V g ~i L V g t r t t Chapter 4: Switch realization!

35 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!

36 Paralleling diodes! Attempts to parallel diodes, and share the current so that i 1 = i 2 = i/2, generally don t work.! Reason: thermal instability caused by temperature dependence of the diode equation.! v 1 i 1 i 2 i v 2 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!

37 Ringing induced by diode stored charge! see Section 4.3.3! v i (t) i L (t) L v L (t) silicon diode i B (t) v B (t) C v i (t) 0 i L (t) V 1 V 2 t Diode is forward-biased while i L (t) > 0! Negative inductor current removes diode stored charge Q r! 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 v B (t) 0 V 2 area Q r t 1 t 2 t 3 Chapter 4: Switch realization! t t

38 Energy associated with ringing! Recovered charge is! Q r = t 3 t 2 i L (t) dt Energy stored in inductor during interval t 2 t t 3 :! W L = v L (t) i L (t) dt t 3 t 2 v i (t) 0 i L (t) V 1 V 2 t Applied inductor voltage during interval t 2 t t 3 :! v L (t)=l di L(t) =V dt 2 Hence,! t 3 W L = L di t L(t) 3 i dt L (t) dt = (V 2 ) i L (t) dt t 2 t 2 0 v B (t) 0 area Q r t t W L = 1 2 Li 2 L(t 3 )=V 2 Q r V 2 t 1 t 2 t 3 Fundamentals of Power Electronics! 22! Chapter 4: Switch realization!