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1 Prof. S. Ben-Yaakov , DC-DC Converters [5- 4] Average power = - PDF document

Mar 24, 2023 •15 likes •188 views

Prof. S. Ben-Yaakov , DC-DC Converters [5- 1] Power elements 5.1 Conduction loss calculations 5.2 Diode 5.2.1 Types of diodes 5.2.2 Diode conduction losses 5.2.3 Diode recovery 5.3 Power switches 5.3.1 BJT 5.3.2 MOSFETs 5.3.3 IGBT 5.3.4

  1. Prof. S. Ben-Yaakov , DC-DC Converters [5- 1] Power elements 5.1 Conduction loss calculations 5.2 Diode 5.2.1 Types of diodes 5.2.2 Diode conduction losses 5.2.3 Diode recovery 5.3 Power switches 5.3.1 BJT 5.3.2 MOSFETs 5.3.3 IGBT 5.3.4 Other switches 5.4.4 Switching losses 5.4 Capacitor 5.4.1 Capacitor types 5.4.2 Specifications, model, ESR 5.4.3 Assignments ( ∆ V ESR ) 5.4.4 Capacitor losses Prof. S. Ben-Yaakov , DC-DC Converters [5- 2] Conduction Losses I 1 T Z = ⋅ P V I dt ( time domain ) ∫ T 0 V I t V t I × V P t T Prof. S. Ben-Yaakov , DC-DC Converters [5- 3] Resistor � Periodic waveform = ⋅ V I R R R I R I R T 1 s t off t on = ⋅ P ∫ V I dt t R R R T 0 s V R T T S 1 s 2 = V P R { ∫ ( I ) dt } R R R T s 0 t T 1 s 2 ≡ { ( I ) dt } I ∫ rms R T T S s 0 2 = P I R R R ( rms ) 1

  2. Prof. S. Ben-Yaakov , DC-DC Converters [5- 4] Average power = + ∑ ω I I I cos( t ) av i i i V = V + ∑ V cos( ω t ) av i i i T 1 = ⋅ P ∫ V I dt ( time domain ) T 0 T ω ω = ≠ ∫ Cos ( t ) Cos ( t ) dt 0 if n m n m 0 Conclusion: � Only V,I components of same frequency produce real power. � DC → ω =0 Prof. S. Ben-Yaakov , DC-DC Converters [5- 5] Average power T 1 s 2 = I { ∫ ( I ) dt } rms R T s 0 2 = ∑ I ( I ) rms i i = 2 V ∑ ( V ) rms i i I 1 , I 2 , I 3 … of different frequencies V 1 , V 2 ,…. Prof. S. Ben-Yaakov , DC-DC Converters [5- 6] Example 1 I R I m I R V R t t T S Consider only t on P on = (I m ) 2 R P av = P on t on /T s = P on D on I R I m 2 2 = ⋅ ⋅ = ⋅ P I R D R I av m on rms = I I D t rms m on 2

  3. Prof. S. Ben-Yaakov , DC-DC Converters [5- 7] Example 2 I pk t This is an AC signal I av = 0 ! T T S S 2 2 -I pk T S I pk ⋅ I pk = I t T I T I pk 2 T T  I  I 2 I 2 I 1 t 3 ∫ I =  pk  t dt = pk = pk = pk rms 3 T  T  T 3 3 3 t 0 0 I T I rms = pk 3 2 I R = pk P R 3 Prof. S. Ben-Yaakov , DC-DC Converters [5- 8] Example 2 (Cont.) I pk t T T S S 2 2 -I pk T S I rms = pk I For each of the sub- triangle: 3 I rms = pk � Therefore for complete waveform: I 3 Prof. S. Ben-Yaakov , DC-DC Converters [5- 9] Example 3 I I pk ∆ I t on t off t T S Separate into waveforms of different frequencies I assuming a repeating wave: t on t on t 3

  4. Prof. S. Ben-Yaakov , DC-DC Converters [5- 10] Waveform decomposition I I pk I av ∆ I t on t on t Not like this ! Why ? I DC av DC I t av t ∆ I 2 ∆ I ∆ I 2 t t t on t on Prof. S. Ben-Yaakov , DC-DC Converters [5- 11] Waveform decomposition ∆ I 2 I ∆ I pk = − = I ( I ) I ( av ) I DC av pk rms av 2 t ∆ I 1 = I ( rms ) ∆ I ∆ 2 3 I 2 2 ∆ I 2 ∆ I 1 t I 2 ( t ) = I 2 + ( ) 2 rms on av 2 3 t on Prof. S. Ben-Yaakov , DC-DC Converters [5- 12] Waveform decomposition I ∆ I 1 2 = 2 + 2 I ( t ) I ( ) rms t on t on on av 2 3 t Averaging the power over T : I I pk s ∆ I ∆  I 1  t off 2 = 2 + 2 ⋅ t on I  I ( )  D rms t av on  2 3  T S ∆ I 1 I = D I 2 + ( ) 2 rms on av 2 3 ∆ 2 I ∆ ∆ I I 1 I = D I 2 + = − 2 + 2 I D ( I ) ( ) rms on av 12 rms on pk 2 2 3 = 2 ⋅ P I R R rms 4

  5. Prof. S. Ben-Yaakov , DC-DC Converters [5- 13] Switching Elements 1.Diode 1.1 Types of diodes 1.2 Diode conduction losses 1.3 Diode recovery 2. Power switches 2.1 BJT 2.2 MOSFETs 2.3 IGBT 2.3 Other switches 3. Capacitor 3.1 Capacitor types 3.2 Specifications, model, ESR 3.3 Assignments ( ∆ V ESR ) 3.4 Losses Prof. S. Ben-Yaakov , DC-DC Converters [5- 14] Diodes Schottky Si I D Silicone - Slow → Fast STATIC Schottky - Fast V D 0.4V 0.7V Prof. S. Ben-Yaakov , DC-DC Converters [5- 15] Diode conduction losses I D V D = V F ≈ constant I V F V D P ? V F =DC frequency=0 Only DC components of I are important: P = I av V F 5

  6. Prof. S. Ben-Yaakov , DC-DC Converters [5- 16] Diodes recovery L V x V o V in Reverse current at R C switch turn on Prof. S. Ben-Yaakov , DC-DC Converters [5- 17] Diode recovery I D I F V L t t rr V D ~V F t L - parasitic inductance V O Reverse Recovery of diode Prof. S. Ben-Yaakov , DC-DC Converters [5- 18] Diode recovery I D L 1 <L 2 <L 3 I F I pk , t rr are function of I F , L, T t L 3 L 2 L 1 I pk 6

  7. Prof. S. Ben-Yaakov , DC-DC Converters [5- 19] Diode conduction losses L S I L I av V in C I L R D off D D on I D t I D t I Dav = I av • D off V D P = I Dav • V F t Prof. S. Ben-Yaakov , DC-DC Converters [5- 20] Power Switches D C C B G G S E E BJT MOSFET IGBT C D C N G B G P N E E S Prof. S. Ben-Yaakov , DC-DC Converters [5- 21] BJT STATIC CHARACTERSTICS } I B(ON) I C I B C B E V CE V CE sat I In linear region I = h I → I = C C fe B B h fe I I >> C At saturation B h fe 7

  8. Prof. S. Ben-Yaakov , DC-DC Converters [5- 22] BJT Drive problems � Relatively slow (storage time) � Replaced by MOSFET or IGBT � Still is use in lamp ballasts and in very high power applications (motor drive) Prof. S. Ben-Yaakov , DC-DC Converters [5- 23] MOSFET STATIC CHARACTERSTICS } V GS(ON) I D V GS = ⋅ V I R DS D DS ( ON ) R DS(ON) → Ω − Ω R 10 10 m DS ( ON ) V DS V DS(ON) Power MOSFETS � Parallel connections of many basic MOSFET cells Prof. S. Ben-Yaakov , DC-DC Converters [5- 24] RDSon as a Function of Breakdown Voltage MOSFET R DS ( ON ) V DS 500V 8

  9. Prof. S. Ben-Yaakov , DC-DC Converters [5- 25] RDS(ON) as a Function of Temperature R DS(ON) Temp � Permits parallel connection of MOSFETs Prof. S. Ben-Yaakov , DC-DC Converters [5- 26] MOSFET n channel � Internal diodes � Gate voltage Normal : 15V -15V Logic level: 5V -5V p channel n channel � more popular � less expensive Prof. S. Ben-Yaakov , DC-DC Converters [5- 27] IGBT } C I C V GE G E � Similar to BJT but faster I C � Same gate voltage as MOSFET V CE V CE(sat) V CE(sat) � Slow IGBT - 1V � Fast IGBT - 3V 9

  10. Prof. S. Ben-Yaakov , DC-DC Converters [5- 28] Other Switches � SCR - low frequency no forced turn off � MCT - SCR+FET input � GTO - turn on and off; slow, high current Prof. S. Ben-Yaakov , DC-DC Converters [5- 29] Conduction Losses of Active Switches MOSFET → Rds(on) BJT, IGBT → V CE (sat) Pd(MOSFET) → (I rms ) 2 Rds(on) Pd( BJT, IGBT) → I av V CE (sat) Prof. S. Ben-Yaakov , DC-DC Converters [5- 30] Example: L V x V o L=10uH; f s = 100kHz; V in R R ds (on)= 1 Ω C MOSFET V in =25V; V o =100V; P out =100W = I V P o o o P 100 = o = = I 1 Amp o V 100 o V 1 100 1 o = = V D 25 D in off off = = D 0 . 25 D 0 . 75 off on D D = off = = on = t 2 . 5 uS t 7 . 5 uS off on f f s s 10

  11. Prof. S. Ben-Yaakov , DC-DC Converters [5- 31] Example: I L ∆ I I av V 10 V in ∆ = = = I in t 7 . 5 u 3 Amp t on t off on L 25 u L t T S I S ∆ I = 3 A P I av =1A = = I o 1 Amp av V o t Prof. S. Ben-Yaakov , DC-DC Converters [5- 32] Example: I L ∆ I I av I av =4A ∆ I=1A t on t off R DS(on) =1ohm D on =0.75 t T S  ∆ 2 2 I 1   0 . 5  = + = 2 + = I 2   D 4   0 . 75 3 . 47 A I av rms on  2 3   3  = P 2 R I d rms ds ( on ) I = 3 . 47 A rms P = 12 . 063 W d Prof. S. Ben-Yaakov , DC-DC Converters [5- 33] RDS(ON) as a Function of Temperature Over useful temp: Rds(on) =1.5 x Rds(on)[25 0 C] � The limitation: Junction Temp. T j : 120 0 C- 175 0 C 11

  12. Prof. S. Ben-Yaakov , DC-DC Converters [5- 34] Parallel connection � IMPORTANT Parallel connections of a number of MOSFETs is possible because of the positive temp coefficient of R ds (on) Prof. S. Ben-Yaakov , DC-DC Converters [5- 35] CV 2 Losses 2 C  2  C V dss dss max f → lost to heat   s 2   Linear with f s ! Switching losses (overlap) also linear with f s ! Prof. S. Ben-Yaakov , DC-DC Converters [5- 36] Switching losses control V GS t V V S S I S t J d P switching t Switching losses due to overlap P d linear with f S ! 12

  13. Prof. S. Ben-Yaakov , DC-DC Converters [5- 37] Switching losses V V S S I S t t t r r T S t  I   − 1  I V r ⋅ ∫     = E ≈ E ≈ S t V 1 t dt S S t d on d off S r t t 6     r r 0 E + E 2 E E I V I V = = d on d off ≈ d on ≈ = P d S S t S S t f d r r S T T T 3 T 3 S S S S Switching losses due to overlap P d linear with f S ! Prof. S. Ben-Yaakov , DC-DC Converters [5- 38] Heat conduction Heatsink FET Isolation T T T T ambient j C HS θ θ θ jC CHS HSAIR Equivalent circuit + T θ P P → I T → V → R - ambient ° c w Prof. S. Ben-Yaakov , DC-DC Converters [5- 39] Transistors’ Data θ jC 20 ° c w Very small transistors ° 0 . 5 c w Large Modern MOSFET T247 ÷ ° ~ 0 . 5 1 c w Isolator HS Surface-Airspeed ÷ ° 10 0 . 5 c w θ HS-AIR 13

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