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

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

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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

slide-1
SLIDE 1

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 (∆VESR) 5.4.4 Capacitor losses

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 2]

Conduction Losses

) domain time ( dt I V T 1 P

T

∫ ⋅ =

Z I V I t V t t V I× T P

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 3]

Resistor

Periodic waveform

R I P I } dt ) I ( T 1 { } dt ) I ( T 1 { R P dt I V T 1 P R I V

2 ) rms ( R R rms T 2 R s T 2 R s R T R R s R R R

s s s

= ≡ ∫ ∫ = ∫ ⋅ = ⋅ = IR VR

t

R

I ton toff TS t

R

V TS

slide-2
SLIDE 2

2

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 4]

) t cos( V V V ) t cos( I I I

i i i av i i i av

∑ ω + = ∑ ω + = ) domain time ( dt I V T 1 P

T

∫ ⋅ = Conclusion:

Only V,I components of same frequency produce

real power.

DC → ω=0

m n if dt ) t ( Cos ) t ( Cos

T m n

≠ = ∫ ω ω

Average power

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 5]

} dt ) I ( T 1 { I

s

T 2 R s rms

∫ = ∑ =

i 2 i rms

) I ( I ∑ =

i 2 i rms

) V ( V I1, I2, I3 …

  • f different frequencies

V1, V2,….

Average power

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 6]

Consider only ton Pon= (Im)2 R Pav= Pon ton/Ts= PonDon

  • n

m rms 2 rms

  • n

2 m av

D I I I R D R I P = ⋅ = ⋅ ⋅ =

IR VR t TS IR Im t IR Im t

Example 1

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SLIDE 3

3

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 7]

Example 2

R 3 I P

2 pk R =

t T I I

pk ⋅

= This is an AC signal Iav = 0 !

3 I 3 I 3 t T I dt t T I T 1 I

pk 2 pk T 3 3 2 pk T 2 pk rms

= = =       =

∫

t Ipk

  • Ipk

TS

2 TS 2 T

S

t T

T Ipk

Ipk I

3 I I

pk rms =

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 8]

Example 2 (Cont.)

t Ipk

  • Ipk

TS

2 T

S

2 T

S

3 I I

pk rms =

For each of the sub- triangle:

Therefore for complete waveform:

3 I I

pk rms =

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 9]

Example 3

Separate into waveforms

  • f different frequencies

assuming a repeating wave: t toff TS Ipk I ∆ ton I t ton ton I

slide-4
SLIDE 4

4

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 10]

t t

av

I

ton DC I ∆

Not like this !

Why ?

t ton ton I Ipk I ∆ Iav

t t

av

I

ton DC 2 I ∆ 2 I ∆

Waveform decomposition

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 11]

3 1 2 I ) rms ( I ) av ( I ) 2 I I ( I

2 I rms pk av

∆ = = ∆ − =

∆ 2 2 av

  • n

rms 2

) 3 1 2 I ( I ) t ( I ∆ + = t t

av

I

ton DC 2 I ∆ 2 I ∆ 2 I ∆

pk

I

Waveform decomposition

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 12]

  • n

2 2 av rms 2

D ) 3 1 2 I ( I I ⋅       ∆ + =

2 2 av

  • n

rms

) 3 1 2 I ( I D I ∆ + =

2 2 pk

  • n

rms

) 3 1 2 I ( ) 2 I I ( D I ∆ + ∆ − = R I P

2 rms R

⋅ =

s

T :

  • ver

power the Averaging t toff TS Ipk I ∆ ton I

2 2 av

  • n

rms 2

) 3 1 2 I ( I ) t ( I ∆ + = t ton ton I 12 I I D I

2 2 av

  • n

rms

∆ + =

Waveform decomposition

slide-5
SLIDE 5

5

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 13]

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 (∆VESR) 3.4 Losses

Switching Elements

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 14]

Diodes

Silicone - Slow →Fast Schottky - Fast

STATIC Si Schottky ID VD 0.7V 0.4V

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 15]

Diode conduction losses

ID VD

VD = VF ≈ constant

VF I

P ?

VF=DC frequency=0 Only DC components of I are important: P = Iav VF

slide-6
SLIDE 6

6

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 16]

Reverse current at switch turn on

Diodes recovery

Vin L C R Vx Vo

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 17]

L - parasitic inductance Reverse Recovery of diode

t t ID IF L V trr VD ~VF VO

Diode recovery

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 18]

L1<L2<L3 Ipk, trr are function of IF, L, T

t ID IF Ipk L1 L2 L3

Diode recovery

slide-7
SLIDE 7

7

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 19]

Diode conduction losses

IDav = Iav • Doff P = IDav• VF

t Doff Don ID t IL Iav t VD

S Vin D L C R IL ID

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 20]

Power Switches

BJT MOSFET IGBT G C E G D S C B E G C E G D S N P N C B E

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 21]

In linear region At saturation

}

IB IC IB(ON) VCE VCE sat

fe C B B fe C

h I I I h I = → =

fe C B

h I I >> C B E

BJT STATIC CHARACTERSTICS

slide-8
SLIDE 8

8

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 22]

Relatively slow (storage time)

Replaced by MOSFET or IGBT Still is use in lamp ballasts and in very high

power applications (motor drive)

BJT Drive problems

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 23]

) ON ( DS D DS

R I V ⋅ = Ω − Ω → m 10 10 R

) ON ( DS

}

VGS VGS(ON) ID VDS VDS(ON) RDS(ON)

Power MOSFETS

Parallel connections of many basic MOSFET cells

MOSFET STATIC CHARACTERSTICS

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 24]

) ON ( DS

R

DS

V MOSFET 500V

RDSon as a Function of Breakdown Voltage

slide-9
SLIDE 9

9

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 25]

Temp RDS(ON)

Permits parallel connection of MOSFETs

RDS(ON) as a Function of Temperature

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 26]

p channel

Gate voltage

Normal : 15V -15V Logic level: 5V -5V n channel

more popular less expensive

MOSFET

n channel

Internal diodes

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 27]

IGBT

Similar to BJT but faster Same gate voltage as

MOSFET VCE(sat)

Slow IGBT - 1V Fast IGBT - 3V

}

IC VCE VGE VCE(sat) IC

G C E

slide-10
SLIDE 10

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]

MOSFET → Rds(on) BJT, IGBT →VCE (sat) Pd(MOSFET) →(Irms)2 Rds(on) Pd( BJT, IGBT) → Iav VCE (sat)

Conduction Losses of Active Switches

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 30]

Example:

L=10uH; fs= 100kHz; Rds(on)= 1 Ω Vin=25V; Vo=100V; Pout=100W

uS 5 . 7 f D t uS 5 . 2 f D t 75 . D 25 . D D 1 25 100 D 1 V V Amp 1 100 100 V P I P V I

s

  • n
  • n

s

  • ff
  • ff
  • n
  • ff
  • ff
  • ff

in

  • =

= = = = = = = = = = =

MOSFET Vin L C R Vx Vo

slide-11
SLIDE 11

11

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 31]

t TS IL L Vin Iav I ∆ ton toff

Amp 3 u 5 . 7 u 25 10 t L V I

  • n

in

= = = ∆ Amp 1 V P I

  • av

= = t IS Iav=1A A 3 I = ∆

Example:

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 32]

W 063 . 12 P A 47 . 3 I R I P A 47 . 3 75 . 3 5 . 4 D 3 1 2 I I I

d rms )

  • n

( ds 2 rms d 2 2

  • n

2 2 av rms

= = = =       + =       ∆ + = Iav=4A ∆I=1A RDS(on)=1ohm Don=0.75 t TS IL Iav I ∆ ton toff

Example:

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 33]

Over useful temp: Rds(on) =1.5 x Rds(on)[250C]

The limitation:

Junction Temp. Tj: 1200C- 1750C

RDS(ON) as a Function of Temperature

slide-12
SLIDE 12

12

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 34]

IMPORTANT

Parallel connections of a number of MOSFETs is possible because of the positive temp coefficient of Rds(on)

Parallel connection

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 35]

2 CV2

dss

C heat to lost f 2 V C

s 2 max dss

→       Switching losses (overlap) also linear with fs! Linear with fs!

Losses

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 36]

control

GS

V

S

V

S

V

S

I

d

J

switching

P t t t

Switching losses due to overlap Pd linear with fS !

Switching losses

slide-13
SLIDE 13

13

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 37] S

V

S

V

S

I t

r

t

r

t

S

T

r S S r S t r S

t 6 V I dt t t 1 1 V t t I E E

r

  • ff

d

  • n

d

=       −      

∫

⋅

≈ ≈

S r S S r S S S S

  • n

d S

  • ff

d

  • n

d S d d

f t 3 V I t T 3 V I T E 2 T E E T E P = ≈ ≈ + = =

Switching losses due to overlap Pd linear with fS !

Switching losses

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 38]

Heat conduction

Equivalent circuit P→ I T→ V → R

w c °

θ

FET Isolation Heatsink P

+

  • j

T

C

T

HS

T

ambient

T

ambient

T

HSAIR

θ

CHS

θ

jC

θ

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 39]

jC

θ Very small transistors Large Modern MOSFET T247 Isolator HS Surface-Airspeed θ HS-AIR w c 20° w c 5 . ° w c 1 5 . ~ ° ÷ w c 5 . 10 ° ÷

Transistors’ Data

slide-14
SLIDE 14

14

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 40]

15(θjC+θCHS+θHSAIR)+25=110 ºC 15(1+1+x)=85 θHSAIR= - 2 = 15 85 W C 6 . 3 °

Example

Pd=15 , Tjmax=110 θjC =1 , Tamb(max)=50 θCHS=1 , Find θHS-AIR w c ° w c ° c ° c ° w

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 41]

Assignment

V2 TD = 0 TF = 0.01u PW = 10u PER = 20u V1 = 0 TR = 0.01u V2 = 15 Dbreak D1

  • ut_gnd

gate L2 {L1*(n*n)} RL {Load} drain V1 {Vin} R4 10meg

  • ut

C1 220u IC = 6 K K1 COUPLING = 1 K_Linear L1 = l1 L2 = l2 PARAM ET ERS: n = 0.5 Vin = 12 Load = 10 L1 = 300u

+

  • +
  • Sbreak

S1 L1 {L1}

Modify circuit to include RS=500mΩ. Find by simulation losses on switch and overall efficiency.

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 42]

Capacitors

Materials: Tantalum Aluminum Paper Plastic Teflon Polypropylene Minerals Mica Polarized (electrolytic) Non Polarized C < 10µF

slide-15
SLIDE 15

15

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 43]

Capacitors

Constructions:

dielectric metal metal Wrapped Sintered metal dielectric metal metal

  • xide

electrolyte Comb structure

metal electrode porous body electrolyte

Sintered Electrolyte Capacitor

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 44]

Capacitors

fC 2 1 C 1 Z π = ω = idea l f 20lg(|Z|)

  • 20db/dec

Wrapped capacitors

will tend to have higher inductance C L R Capacitance Series inductance Equivalent series resistance (ESR)

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 45]

Practical C

f1 f2 f 20lg(|Z|) ESR C1 C2 db(Z2) db(Z1)

1 2

C C >

1 1 2 1

C f 2 1 C f 2 1 π < π

1 2 2 2

C f 2 1 C f 2 1 π > π

slide-16
SLIDE 16

16

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 46]

Philips ceramic capacitors

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 47]

100µ 0.1µ +

Why?

At f1: At f2:

f1 fm f 20lg(|Z|)

C1 C2

f2 dB C f 2 1

1 1

      π dB C f 2 1

2 1

      π dB C f 2 1

1 2

      π dB C f 2 1

2 2

      π dB C f 2 1 Z

2 1 1

      π ≈ dB C f 2 1 Z

2 2 2

      π ≈

Electrolytic Ceramic (comb)

Parallel connection of Capacitors

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 48]

Specifications of capacitor

Capacitance Maximum voltage Maximum current Inductance or plot ESR, Sometime:

) frequency test ( CR tg

ESR

= ω ω = δ

slide-17
SLIDE 17

17

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 49]

Implication- Load Step

Ideal response

tS Vo t tS Vo t ) ESR ( V ∆

Practical response

C1 C2 R1 R2 S

  • Prof. S. Ben-Yaakov , DC-DC Converters

[5- 50]

Capacitor losses

S Vin D L C R IL IC IR control IL t Iav t Iav IR IC t AC DC I ∆ I ∆

ESR I P

2 Crms ⋅

=

3 1 2 I ICrms ∆ =