VCE VCC I C RC VCE VCB VBE VCB VCE VBE ECE 442 Power Electronics 11 BJT Transistor Switch (continued) I CM VCC VCE VCC VBE
RC RC I BM I CM F ECE 442 Power Electronics 12 BJT in Saturation
I CS VCC VCE ( sat ) RC I BS I CS F IB ODF
I BS forced I CS IB ECE 442 Power Electronics 13 Model with Current Gain
ECE 442 Power Electronics 14 Miller Effect vbe iout vce ECE 442 Power Electronics 15
Miller Effect (continued) d d iout Ccb (vbe vce ) Ccb (vbe Avbe ) dt dt d d iout Ccb [1 A]vbe Ccb [1 A] vbe dt dt Ccb Ccb [1 A]
ECE 442 Power Electronics 16 Miller Effect (continued) Miller Capacitance, CMiller = Ccb(1 A) since A is usually negative (phase inversion), the Miller capacitance can be much greater than the capacitance Ccb This capacitance must charge up to the base-emitter forward bias voltage, causing a delay time before any collector current flows.
ECE 442 Power Electronics 17 Saturating a BJT Normally apply more base current than needed to saturate the transistor This results in charges being stored in the base region To calculate the extra charge (saturating charge), determine the emitter current I cs I e I B
ODF I BS I BS I BS ODF 1 ECE 442 Power Electronics 18 The Saturating Charge The saturating charge, Qs Qs s I e s I BS (ODF 1) storage time constant of the transistor ECE 442 Power Electronics
19 Transistor Switching Times ECE 442 Power Electronics 20 Switching Times turn on Input voltage rises from 0 to V1 Base current rises to IB1 Collector current begins to rise after the delay time, td
Collector current rises to steady-state value ICS This rise time, tr allows the Miller capacitance to charge to V1 turn on time, ton = td + tr ECE 442 Power Electronics 21 Switching Times turn off Input voltage changes from V1 to V2 Base current changes to IB2 Base current remains at IB2 until the Miller capacitance discharges to zero, storage
time, ts Base current falls to zero as Miller capacitance charges to V2, fall time, tf turn off time, toff = ts + tf ECE 442 Power Electronics 22 Charge Storage in Saturated BJTs Charge storage in the Base Charge Profile during turn-off
ECE 442 Power Electronics 23 Example 4.2 ECE 442 Power Electronics 24 Waveforms for the Transistor Switch VCC = 250 V VBE(sat) = 3 V IB = 8 A
VCS(sat) = 2 V ICS = 100 A td = 0.5 s tr = 1 s ts = 5 s tf = 3 s ECE 442 Power Electronics fs = 10 kHz duty cycle k = 50 % 25 ECE 442 Power Electronics
26 Power Loss due to IC for ton = td + tr During the delay time, 0 t td Instantaneous Power Loss Pc (t ) vCE iC VCC I CEO Pc (t ) (250V )(3mA) 0.75W Average Power Loss td td VCC I CEO 1
Pd Pc (t )dt dt VCC I CEO f s td T 0 T 0 Pd (250V )(3mA)(10kHz )(0.5 s ) 3.75mW ECE 442 Power Electronics 27 During the rise time, 0 t tr Pc (t ) vCE ic
t I CS Pc (t ) VCC (Vce ( sat ) VCC ) t tr tr dPc (t ) Vce ( sat ) VCC I CS t I CS t VCC (Vce ( sat ) VCC ) dt tr tr
tr tr Pc (t ) Pmax @ t tm trVCC tm 2[VCC Vce ( sat ) ] ECE 442 Power Electronics 28 (1 s )(250V ) tm 0.504 s 2[250V 2V ]
Pmax 2 CC CS V I 4[VCC VCE ( sat ) ] 2 Pmax (250V ) (100 A)
6300W 4[250V 2V ] ECE 442 Power Electronics 29 Average Power during rise time tr VCC VCE ( sat ) VCC 1 Pr Pc (t )dt f s I CS tr
T 0 3 2 (250V ) (2V 250V ) Pr (10kHz )(100 A)(1 s ) 2 3 Pr 42.33W
ECE 442 Power Electronics 30 Total Power Loss during turn-on Pon Pd Pr Pon 0.00375 42.33 42.33375W Pon 42.33W ECE 442 Power Electronics 31
ECE 442 Power Electronics 32 Power Loss during the Conduction Period 0 t tn ic (t ) I CS 100 A vCE (t ) VCE ( sat ) 2V Pc (t ) ic vCE (100 A)(2V ) 200W tn tn
1 Pn Pc (t )dt VCE ( sat ) I CS f s dt VCE ( sat ) I CS f s tn T 0 0 Pn (2V )(100 A)(10kHz )(48.5 s ) 97W ECE 442 Power Electronics 33 ECE 442 Power Electronics 34
Power Loss during turn off Storage time 0 t ts ic (t ) I CS 100 A vCE (t ) VCE ( sat ) 2V Pc (t ) vCE ic VCE ( sat ) I CS (2V )(100 A) Pc (t ) 200W ts ts 1 Ps Pc (t )dt VCE ( sat ) I CS f s dt VCE ( sat ) I CS f s t s T 0
0 Ps (2V )(100 A)(10kHz )(5 s ) 10W ECE 442 Power Electronics 35 ECE 442 Power Electronics 36 Power Loss during Fall time 0 t t f t
ic (t ) I CS 1 , I CEO 0 tf V vCE (t ) CC t , I CEO 0 tf Pc (t ) vCE ic VCC I CS t t 1 t f t f
1 t t 1 0 t f t f t f 3 s Pc (t ) Pm @ t 1.5 s 2 2 VCC I CS (250V )(100 A) Pm 6250W 4
4 dPc (t ) VCC I CS dt tf ECE 442 Power Electronics 37 Power Loss during Fall time (continued) tf VCC I CS t f f s
1 Pf Pc (t )dt T 0 6 (250V )(100 A)(3 s )(10kHz ) Pf 125W 6 VCC t f Poff Ps Pf I CS f s tsVCE ( sat ) 6
Poff 10 125 135W ECE 442 Power Electronics 38 ECE 442 Power Electronics 39 Power Loss during the off time 0 t to vCE (t ) VCC ic (t ) I CEO Pc (t ) vCE iC VCC I CEO (250V )(3mA) 0.75W
to 1 Po VCC I CEO dt VCC I CEO f s to T 0 Po (250V )(3mA)(10kHz )((50 5 3) s) Po 0.315W ECE 442 Power Electronics 40 The total average power losses PT Pon Pn Poff Po
PT 42.33 97 135 0.315 PT 274.65W ECE 442 Power Electronics 41 Instantaneous Power for Example 4.2 ECE 442 Power Electronics 42 BJT Switch with an Inductive Load
ECE 442 Power Electronics 43 Load Lines ECE 442 Power Electronics 44
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