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EET 423
POWER ELECTRONICS -2
Prof R T Kennedy
POWER ELECTRONICS 2
1
BUCK CONVERTER CIRCUIT CURRENTS
Ii n
Ids a IL
Ifwd
IL b Iout
L
IC
Ids
Ei n
Ifwd
Prof R T Kennedy
C
POWER ELECTRONICS 2
R Vout
2
BUCK CONVERTER CIRCUIT VOLTAGES
Vds
a
VL,a-b
b
L
Ei n
Prof R T Kennedy
Vfwd
C
POWER ELECTRONICS 2
R Vout
3
SUB INTERVAL EQUIVALENT CIRCUITS
VL,a-b= Ein-Vout
Vds = 0
a
L
rds,on
MOSFET
Ei n
ON
Vfwd = -Ein
b
C
R
Vout
RECTIFIER
OFF
Prof R T Kennedy
POWER ELECTRONICS 2
4
SUB INTERVAL EQUIVALENT CIRCUITS
Vds = Ein
VL,a-b= -Vout
a
b
L
MOSFET
Ei n
C
OFF
R Vout
Vfwd= 0
RECTIFIER
ON
Prof R T Kennedy
POWER ELECTRONICS 2
5
Vgs
0
Ein
0
Vds
Ein =Vds +(- Vfwd)
0
0
Vfwd
0
VL
Vout
VL + Vout = -Vfwd
0
0
Prof R T Kennedy
POWER ELECTRONICS 2
6
Vgs
0
Ein
Ein = Vds + (-Vfwd)
0
-Vfwd
Vds
0
0
Vfwd
0
VL
Vout
0
0
Prof R T Kennedy
POWER ELECTRONICS 2
7
SMPS OPERATION
QUANTIZED POWER/ENERGY TRANSFER
VOLTAGE REGULATION
Prof R T Kennedy
POWER ELECTRONICS 2
8
VOLTAGE TRANSFER FUNCTION ANALYSIS
• ENERGY BALANCE
• POWER BALANCE
• VOLT-TIME INTEGRAL
Prof R T Kennedy
POWER ELECTRONICS 2
9
‘IDEAL’ BUCK ANALYSIS CCM
ENERGY BALANCE APPROACH
IL,M
INDUCTOR CURRENT
I L  I out
I L
2
IL,av = Iout
I L
2
I L, M

I out 
I L
2
I L, m

I out 
I l
2
I L, M  I L, m

2  I out
I L, M  I L, m

I L  I out
I L, M 2Prof
 I LR, mT2Kennedy
 2  I out  I L
IL,m
0
t
POWER ELECTRONICS 2
10
SUB INTERVAL -1: MOSFET ON
JL

1
L( I L, M 2  I L, m 2 ) 
2
ON
Ei n
a
ENERGY
STORED
L
L  I out  I L
b
C
OFF
R
LOAD ENERGY
from source
INPUT
ENERGY
J load , s
J in
 Pin  ton
Prof R T Kennedy

Pout  ton  Vout  I out  Dsw  T
 Ein  I out  Dsw  T
POWER ELECTRONICS 2
11
SUB INTERVAL -2: RECTIFIER ON
NO INPUT
ENERGY
Ei n
OFF
ON
ENERGY
Discharge
a
b
L
C
R
J load, L
Jload, L
Prof R T Kennedy
 Vout  I out  D fwd  T
LOAD ENERGY
from inductor

L  I out  I L
 Vout  I out  (1  Dsw )  T
POWER ELECTRONICS 2
12
J load , s  J load, L
total load energy
(Vout  I out  Dsw  T )  (Vout  I out  (1  Dsw )  T )
J load, s  J load, L
Dsw Ein
Prof R T Kennedy
 (Vout  I out  T )
total load energy

input energy
Vout  I out  T


Ein  I out  Dsw  T
Vout
Vout
 Dsw
Ein
POWER ELECTRONICS 2
13
‘IDEAL’ BUCK ANALYSIS CCM
POWER BALANCE APPROACH
INPUT CURRENT = MOSFET CURRENT
IL,M
Iout
IL,m
Iin
Iin,av = Ids,av
0
Dsw T
Pout

Pin
Vout  I out

Ein  I in, av
Vout  I out

Ein  Dsw  I out
Vout

Prof R T Kennedy
Ein
Dsw
Dfwd T
POWER ELECTRONICS 2
t
14
FARADAY’S VOLT-TIME INTEGRAL
IM
INDUCTOR CURRENT
Im
current start and finish at same value
0
t
V1
INDUCTOR VOLTAGE
0
t1
t
V2
t2
VL, av

1 T  di 
L
dt
T 0  dt 
VL, av

1 T
L di
T 0
VL, av

L T
I 
T 0
VL, av

L
I 0  IT   0
T
T
EQUAL AREAS
T
0 v(t ) dt
V1  t1
Prof R T Kennedy
0
 V2  t2
POWER ELECTRONICS 2
15
‘IDEAL’ BUCK ANALYSIS CCM
VOLT-TIME INTEGRAL APPROACH
INDUCTOR VOLTAGE
IL
0
Ein -Vout
VL area A
0
area B
Dsw T
Prof R T Kennedy
-Vout
Dfwd T
POWER ELECTRONICS 2
t
16
‘IDEAL’ BUCK ANALYSIS CCM
VOLT-TIME INTEGRAL APPROACH
INDUCTOR VOLTAGE
area A

area B
 0
( Ein  Vout )  Dsw  T 

 Vout  (1  Dsw )  T 
 0
( Ein  Vout )  Dsw  T

Vout  (1  Dsw )  T
Vout
Ein

Dsw
Prof R T Kennedy
POWER ELECTRONICS 2
17
BUCK CONVERTER CCM
voltage & current waveforms
‘ideal’
• refer to msw notelet
Prof R T Kennedy
POWER ELECTRONICS 2
18
Vgs
I L , rise Ein (1  Dsw )

dt
L
0
I out 
Iout
I C , rms 
0
Ic
Dsw Ein
R
I L 
I L
12
d
D E  (1  Dsw ) R 
I L, M  sw in 1 

R
2 L f sw 

0
( Ein  Vout ) Dsw
 I C
L f sw
I L , fall
dt
s
D E
 sw in
L
k
a
I out
Vout
IL
0
I L, m 
Dsw Ein
R
 (1  Dsw ) R 
1 

2 L f sw 

I L, rms 
Dsw ( Ein  Vout )
12 L f sw
2

1  I  
I ds, rms  I out Dsw 1   L  
 12  I out  


I ds, av  Dsw  I out
I out
Ids
0
I out
Ifwd
I fwd, av  D fwd  I out
0
d
s
k
2

1  I  
I fwd , rms  I out D fwd 1   L  
 12  I out  


a
Ein
Ein
0
Ein
Ids Vds
Vds
0
0
Vfwd
Ei n
 Ein
Ein  Vout
Vgs
fsw
VL
L
IL Iout
IC
Vfwd C
Ifwd
Iout
R
VL 0
 Vout
Vout
Vout  Dsw Ein
0
Dfwd = 1-Dsw
DfwdT
swTT Kennedy
ProfDR
POWER ELECTRONICS 2
19
INDUCTOR CURRENT WAVEFORMS
• CCM or DCM operational mode
• component current stress
• capacitor ripple current
• output voltage ripple
• converter efficiency
• closed loop regulation performance
Prof R T Kennedy
POWER ELECTRONICS 2
20
INDUCTOR CURRENT v INDUCTANCE
REDUCTION in L
IL
Iout
0
EinVout
VL
0
-Vout
t
DswT
Prof R T Kennedy
Dfwd T
POWER ELECTRONICS 2
21
INDUCTOR CURRENT v INDUCTANCE
increased
REDUCTION in L
Isw,max
IL
Ifwd,max
Iout
0
IC,ripple
Ein-Vout
VL
Vout,ripple
0
-Vout
t
DswT
dI L, rise
dI L, fall
dt
dt
Dfwd T
Prof R T Kennedy
POWER ELECTRONICS 2
22
INDUCTOR CURRENT
I L, M

I L, M

I out 
I L
2
I L
Vout Vout  (1  Dsw )

R
2  L  f sw

Vout (1  Dsw ) Ein  Dsw  (1  Dsw )

L  f sw
L  f sw
V 1  M 
I L  out 

R  L 
 (1  Dsw )  R 
1 

2

L

f
sw


I L, M

Vout
R
I L, M

Dsw  Ein
R
 (1  Dsw )  R 
1 

2

L

f
sw 

I L, m 
V  1 M 
I L, M  out 1 

R 
2 L 
Dsw  Ein
R
 (1  Dsw )  R 
1 

2

L

f
sw 

V  1 M 
I L, m  out 1 

R 
2 L 
V
M  out
Ein
L f sw
L

RR
Tsw
R
Prof
T Kennedy
L 
POWER ELECTRONICS 2
23
INDUCTOR CURRENT
Dsw > 0.5
Dsw= 0.5
I L
IL
Iout
I L
Dsw < 0.5
I L
0
Dsw = 0.2
Dsw = 0.5
Dsw = 0.8
Prof R T Kennedy
t
POWER ELECTRONICS 2
24
INDUCTOR CURRENT
dI L, rise
dt

Ein (1  Dsw )
L
dI L, fall
dt

Ein Dsw
L
DOWNSLOPE
UPSLOPE
I L
IL
I L
I L
0
t
Prof R T Kennedy
POWER ELECTRONICS 2
25
INDUCTOR
PEAK-PEAK RIPPLE CURRENT
I L

Ein  Dsw  (1  Dsw )
L  f sw
I L  f n Dsw (1  Dsw )
I L, max
I L
0
Prof R T Kennedy
0.5
Dsw
POWER ELECTRONICS 2
1
26
J
IL
t
0
IL
t
0
IL
t
0
Prof R T Kennedy
POWER ELECTRONICS 2
27
L
IL
t
0
IL
t
0
IL
t
0
Prof R T Kennedy
POWER ELECTRONICS 2
28
L
IL
t
0
IL
t
0
IL
t
0
Prof R T Kennedy
POWER ELECTRONICS 2
29
‘IDEAL’ BUCK CCM DEVICE CURRENT
I out
IL
I sw, M
I sw
I sw, rms
I sw, av
I fwd
I fwd, M
I fwd, rms
I fwd, av
Dsw
Prof R T Kennedy
D fwd
POWER ELECTRONICS 2
30
‘IDEAL’ BUCK CCM DEVICE CURRENT
I out
IL
I sw, M
I sw
I sw, rms
I sw, av
I fwd
I fwd, M
I fwd, rms
I fwd, av
Dsw
Prof R T Kennedy
D fwd
POWER ELECTRONICS 2
31
‘IDEAL’ BUCK CCM TRANSISTOR CURRENT
CCM TRANSISTOR CURRENT
IM
Vout   1  Dsw  R 


1  
R   2  L f sw 
Vout   1  M 

1  
R   2  L 
Iav
Vout
Dsw 
R
Vout
M 
R
Irms
 Dsw (1  Dsw ) 2  R  2 Vout
Vout

 
Dsw  
Dsw



R
12
Lf
R

 sw 
IL
2
Vout  1  1  M   Vout
 
M 1  
M

R
 12  2  L   R


 R 
Vout
1  Dsw  
R
 L f sw 
Vout  1  M 


R  L 
V
M  out
Ein
Prof R T Kennedy
POWER ELECTRONICS 2
L 
L f sw
R
32
‘IDEAL’ BUCK CCM RECTIFIER CURRENT
CCM RECTIFIER CURRENT
Vout   D fwd
1  
R   2
IM

Vout
D fwd
R
Iav
Irms

rms
av
 R 
Vout

D fwd 
R
L
f
 sw 

 D fwd
 
D fwd  12
1
Vout   1  M 

1  
R   2  L 
Vout
1  M 
R
 ( D fwd ) 3  R  2 V
Vout

out

D fwd  

D fwd



R
R
 12  L f sw 


IL
ffi 
 R 


 L f 
 sw 

 1 1 M 2  V
Vout
   out M
M 1  
R
 12  2  L   R


Vout  1  M 


R   L 
M
1 M
2
 R 
1



 L f 
D fwd
 sw 
V
M  out
Ein
Prof R T Kennedy
POWER ELECTRONICS 2
L 
L f sw
R
33
OUTPUT
EFFECTS
L
Ei n
Iin
0
Prof R T Kennedy
C
s/c
Vout= 0
dI in Ein

dt
L
t
POWER ELECTRONICS 2
34
OUTPUT
EFFECTS
L
Ei n
C
o/c
VoutEin
Prof R T Kennedy
POWER ELECTRONICS 2
35
POWER - UP EFFECT
L
Ei n
Prof R T Kennedy
C
POWER ELECTRONICS 2
Vc = 0
R
Vout
36
POWER - DOWN EFFECT
L
Ei n
Prof R T Kennedy
C
POWER ELECTRONICS 2
R
Vout
37
CCM-DCM BOUNDARY
I L
 I out
2
IL
I out
0
t
Dsw T
L  f sw 1  Dsw

R
2
I L
2
I out

Vout
R
Vout (1  Dsw )

2  L  f sw
L  Lcritical
Prof R T Kennedy
I L
 I out
2
POWER ELECTRONICS 2

(1  Dsw )  R
2  f sw
38
CCM-DCM BOUNDARY
0.5
0.45
0.4
CCM :
0.35
0.3
L  f sw 1  Dsw

R
2
boundary
L  f sw 1  Dsw

R
2
L  f sw
0.25
R
0.2
0.15
DCM :
0.1
0.05
0
L
Tsw
0
L  f sw 1  Dsw

R
2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Dsw

normalised

L f sw
Prof R R
T Kennedy
inductor
time
constant
POWER ELECTRONICS 2
39
CCM-DCM BOUNDARY
0.5
0.45
0.4
CCM
0.35
0.3
L  f sw
0.25
R
boundary
0.2
0.15
0.1
0.05
0
DCM
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
Dsw
CCM
Prof R T Kennedy
POWER ELECTRONICS 2
40
CCM-DCM BOUNDARY
L Dsw fsw
0.5
0.45
0.4
constant
CCM / DCM
determined by R
CCM
0.35
0.3
L  f sw
0.25 INCREASE R
R
0.2 ‘light loading’
0.15
0.1
0.05
0
to ensure a desired CCM
DCM
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
does not transfer to DCM
1
Dsw
specify a minimum load current
(maximum R)
avoid open circuit operation
Prof R T Kennedy
POWER ELECTRONICS 2
41
CCM-DCM BOUNDARY
R Dsw fsw
0.5
0.45
0.4
constant
CCM / DCM
determined by L
CCM
0.35
0.3
L  f sw
0.25 DECREASE L
R
0.2
0.15
0.1
0.05
to ensure a desired CCM
0
DCM
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
does not transfer to DCM
1
Dsw
design for CMM
at lowest inductance
including  L v  I
Prof R T Kennedy
POWER ELECTRONICS 2
42
CCM-DCM BOUNDARY
R Dsw fsw
0.5
0.45
0.4
constant
CCM / DCM
determined by fsw
CCM
0.35
0.3
L  f sw
0.25 DECREASE fsw
R
0.2
0.15
0.1
0.05
to ensure a desired CCM
0
DCM
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
does not transfer to DCM
1
Dsw
design for CMM
at lowest frequency
Prof R T Kennedy
POWER ELECTRONICS 2
43
CCM-DCM BOUNDARY
L R fsw
0.5
0.45
0.4
constant
CCM / DCM
determined by
Dsw
CCM
0.35
0.3
L  f sw
0.25 DECREASE Dsw
R
0.2
0.15
0.1
0.05
to ensure a desired CCM
0
DCM
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
does not transfer to DCM
1
Dsw
design for CMM
at lowest duty cycle
Prof R T Kennedy
POWER ELECTRONICS 2
44
LINE & LOAD REGULATION
1
M DCM
M DCM
M CCM
V
M  out
Ein
DCM
0.9
L f sw

R
0.8
0.7
CCM
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3 0.4
0.5
0.6 0.7
Dsw
Prof R T Kennedy
POWER ELECTRONICS 2
0.8
0.9
1
Dsw
45
LINE & LOAD REGULATION
1
V
M  out
Ein
DCM
0.9
L f sw

R
0.8
0.7
CCM
0.6
M
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3 0.4
Dsw, dcm
Prof R T Kennedy
0.5
0.6 0.7
0.8
D sw, ccm
POWER ELECTRONICS 2
0.9
1
Dsw
46