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Page 1
Buck Converter
When CH is ON ? ? o t DT ??
Voltage across inductor ? ?
L S O
V V V ??
When CH is OFF (DT < t < T)
Voltage across inductor
LO
VV ?
Applying volt-sec balance across inductor
? ? ? ? ? ?
S O O
V V DT V T DT 0 ? ? ? ? ? ?
? ? ? ?
S O O
V V D V 1 D 0 ? ? ? ?
OS
V DV ?
D = duty cycle =
ON
T
T
Where T = switching period =
1
f
f = switching frequency
Page 2
Buck Converter
When CH is ON ? ? o t DT ??
Voltage across inductor ? ?
L S O
V V V ??
When CH is OFF (DT < t < T)
Voltage across inductor
LO
VV ?
Applying volt-sec balance across inductor
? ? ? ? ? ?
S O O
V V DT V T DT 0 ? ? ? ? ? ?
? ? ? ?
S O O
V V D V 1 D 0 ? ? ? ?
OS
V DV ?
D = duty cycle =
ON
T
T
Where T = switching period =
1
f
f = switching frequency
? Average output voltage =
S
DV
? rms output voltage =
S
DV
? Average source current =
O
DI
? Average current of FD = ? ?
O
1 D I ?
Ripple in output current
When CH is ON ? ? 0 t DT ??
? ?
L S O S
V V V 1 D V ? ? ? ?
During this period, since voltage is positive current increase from minimum value to maximum
value.
max min
i I I ? ? ?
t DT 0 DT ? ? ? ?
? ?
? ?
?
? ? ?
S
i
L 1 D V
DT
? ?
S
D 1 D V
i
fL
?
??
? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5
? ?
S
max
V
i
4fL
??
?
L
max O
I
II
2
?
??
?
L
min O
I
II
2
?
??
Critical Inductance (L C)
Value of inductance at which inductor voltage waveform is just discontinuous.
? ?
?
?
c
1 D R
L
2f
Page 3
Buck Converter
When CH is ON ? ? o t DT ??
Voltage across inductor ? ?
L S O
V V V ??
When CH is OFF (DT < t < T)
Voltage across inductor
LO
VV ?
Applying volt-sec balance across inductor
? ? ? ? ? ?
S O O
V V DT V T DT 0 ? ? ? ? ? ?
? ? ? ?
S O O
V V D V 1 D 0 ? ? ? ?
OS
V DV ?
D = duty cycle =
ON
T
T
Where T = switching period =
1
f
f = switching frequency
? Average output voltage =
S
DV
? rms output voltage =
S
DV
? Average source current =
O
DI
? Average current of FD = ? ?
O
1 D I ?
Ripple in output current
When CH is ON ? ? 0 t DT ??
? ?
L S O S
V V V 1 D V ? ? ? ?
During this period, since voltage is positive current increase from minimum value to maximum
value.
max min
i I I ? ? ?
t DT 0 DT ? ? ? ?
? ?
? ?
?
? ? ?
S
i
L 1 D V
DT
? ?
S
D 1 D V
i
fL
?
??
? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5
? ?
S
max
V
i
4fL
??
?
L
max O
I
II
2
?
??
?
L
min O
I
II
2
?
??
Critical Inductance (L C)
Value of inductance at which inductor voltage waveform is just discontinuous.
? ?
?
?
c
1 D R
L
2f
Critical Capacitance (C C)
Value of capacitance at which capacitor voltage waveform is just discontinuous.
C
1
C
8fR
?
Step-up chopper (Boost converter)
? ?
? ? ?
LS
when CHis ON 0 t DT , V V
? ? ? ?
? ? ? ?
L S O
when CHis OFF DT t T , V V V
Applying volt-sec balance across inductor
? ? ? ? ? ?
S S O
V DT V V 1 D T 0 ? ? ? ?
? ?
S
O
V
V
1D
?
?
? Since D < 1,
OS
VV ?
?
? ?
? ? ? ?
CO
when CHis ON 0 t DT , I I
? ?
? ? ? ? ?
C L O
when CHis OFF DT t T , I I I
? ? ? ? ? ?
?
? ? ? ? ?
O L O
Applying Ampere sec balance across capacitor
I DT I I 1 D T 0
? ?
?
?
O
L
I
I
1D
Ripple in inductor current
? ?
??
min max
When CHis ON 0 t DT , current increase from I to I
? ? ?
? ? ? ? ?
S
S L
SL
V DT
DV i
L V i
DT L fL
Page 4
Buck Converter
When CH is ON ? ? o t DT ??
Voltage across inductor ? ?
L S O
V V V ??
When CH is OFF (DT < t < T)
Voltage across inductor
LO
VV ?
Applying volt-sec balance across inductor
? ? ? ? ? ?
S O O
V V DT V T DT 0 ? ? ? ? ? ?
? ? ? ?
S O O
V V D V 1 D 0 ? ? ? ?
OS
V DV ?
D = duty cycle =
ON
T
T
Where T = switching period =
1
f
f = switching frequency
? Average output voltage =
S
DV
? rms output voltage =
S
DV
? Average source current =
O
DI
? Average current of FD = ? ?
O
1 D I ?
Ripple in output current
When CH is ON ? ? 0 t DT ??
? ?
L S O S
V V V 1 D V ? ? ? ?
During this period, since voltage is positive current increase from minimum value to maximum
value.
max min
i I I ? ? ?
t DT 0 DT ? ? ? ?
? ?
? ?
?
? ? ?
S
i
L 1 D V
DT
? ?
S
D 1 D V
i
fL
?
??
? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5
? ?
S
max
V
i
4fL
??
?
L
max O
I
II
2
?
??
?
L
min O
I
II
2
?
??
Critical Inductance (L C)
Value of inductance at which inductor voltage waveform is just discontinuous.
? ?
?
?
c
1 D R
L
2f
Critical Capacitance (C C)
Value of capacitance at which capacitor voltage waveform is just discontinuous.
C
1
C
8fR
?
Step-up chopper (Boost converter)
? ?
? ? ?
LS
when CHis ON 0 t DT , V V
? ? ? ?
? ? ? ?
L S O
when CHis OFF DT t T , V V V
Applying volt-sec balance across inductor
? ? ? ? ? ?
S S O
V DT V V 1 D T 0 ? ? ? ?
? ?
S
O
V
V
1D
?
?
? Since D < 1,
OS
VV ?
?
? ?
? ? ? ?
CO
when CHis ON 0 t DT , I I
? ?
? ? ? ? ?
C L O
when CHis OFF DT t T , I I I
? ? ? ? ? ?
?
? ? ? ? ?
O L O
Applying Ampere sec balance across capacitor
I DT I I 1 D T 0
? ?
?
?
O
L
I
I
1D
Ripple in inductor current
? ?
??
min max
When CHis ON 0 t DT , current increase from I to I
? ? ?
? ? ? ? ?
S
S L
SL
V DT
DV i
L V i
DT L fL
Ripple in output voltage
??
CO
when CHis ON , I I
C
O
V
C. I
DT
?
??
? ?
O
OC
I DT
VV
C
?
? ? ? ?
-ve sign indicates voltage decrease
? ?
O
O
I DT
V
C
? ? ?
Critical Inductance (Lc)
L
L
I
I
2
?
?
? ?
?
?
C
D 1 D R
L
2f
Critical Capacitance (C c)
O
O
V
V
2
?
?
?
C
D
C
2fR
If inductor also has an internal resistance, then
? ?
? ?
OS
2
1D
VV
r
1D
R
??
?
??
?
?? ??
??
r = internal resistance of inductor
R = load resistance
Page 5
Buck Converter
When CH is ON ? ? o t DT ??
Voltage across inductor ? ?
L S O
V V V ??
When CH is OFF (DT < t < T)
Voltage across inductor
LO
VV ?
Applying volt-sec balance across inductor
? ? ? ? ? ?
S O O
V V DT V T DT 0 ? ? ? ? ? ?
? ? ? ?
S O O
V V D V 1 D 0 ? ? ? ?
OS
V DV ?
D = duty cycle =
ON
T
T
Where T = switching period =
1
f
f = switching frequency
? Average output voltage =
S
DV
? rms output voltage =
S
DV
? Average source current =
O
DI
? Average current of FD = ? ?
O
1 D I ?
Ripple in output current
When CH is ON ? ? 0 t DT ??
? ?
L S O S
V V V 1 D V ? ? ? ?
During this period, since voltage is positive current increase from minimum value to maximum
value.
max min
i I I ? ? ?
t DT 0 DT ? ? ? ?
? ?
? ?
?
? ? ?
S
i
L 1 D V
DT
? ?
S
D 1 D V
i
fL
?
??
? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5
? ?
S
max
V
i
4fL
??
?
L
max O
I
II
2
?
??
?
L
min O
I
II
2
?
??
Critical Inductance (L C)
Value of inductance at which inductor voltage waveform is just discontinuous.
? ?
?
?
c
1 D R
L
2f
Critical Capacitance (C C)
Value of capacitance at which capacitor voltage waveform is just discontinuous.
C
1
C
8fR
?
Step-up chopper (Boost converter)
? ?
? ? ?
LS
when CHis ON 0 t DT , V V
? ? ? ?
? ? ? ?
L S O
when CHis OFF DT t T , V V V
Applying volt-sec balance across inductor
? ? ? ? ? ?
S S O
V DT V V 1 D T 0 ? ? ? ?
? ?
S
O
V
V
1D
?
?
? Since D < 1,
OS
VV ?
?
? ?
? ? ? ?
CO
when CHis ON 0 t DT , I I
? ?
? ? ? ? ?
C L O
when CHis OFF DT t T , I I I
? ? ? ? ? ?
?
? ? ? ? ?
O L O
Applying Ampere sec balance across capacitor
I DT I I 1 D T 0
? ?
?
?
O
L
I
I
1D
Ripple in inductor current
? ?
??
min max
When CHis ON 0 t DT , current increase from I to I
? ? ?
? ? ? ? ?
S
S L
SL
V DT
DV i
L V i
DT L fL
Ripple in output voltage
??
CO
when CHis ON , I I
C
O
V
C. I
DT
?
??
? ?
O
OC
I DT
VV
C
?
? ? ? ?
-ve sign indicates voltage decrease
? ?
O
O
I DT
V
C
? ? ?
Critical Inductance (Lc)
L
L
I
I
2
?
?
? ?
?
?
C
D 1 D R
L
2f
Critical Capacitance (C c)
O
O
V
V
2
?
?
?
C
D
C
2fR
If inductor also has an internal resistance, then
? ?
? ?
OS
2
1D
VV
r
1D
R
??
?
??
?
?? ??
??
r = internal resistance of inductor
R = load resistance
Buck-Boost Converter
When CH is ON (O < t < DT)
LS
VV ?
CO
II ??
When CH is OFF (DT < t < T)
LO
VV ?
? ?
C L O
I I I ? ? ?
Applying volt-sec balance across inductor
? ? ? ?
? ? ?
SO
V DT V 1 D T 0
? ?
S
O
DV
V
1D
?
?
?
Applying Ampere-sec balance across inductor
? ? ? ? ? ?
O L O
I DT I I 1 D T 0 ? ? ? ? ?
? ?
O
L
I
I
1D
?
?
?
? ?
? ?
?
??
?
?
2
OS
L
V DV
I
R 1 D
R 1 D
Ripple in inductor current
When CH is ON (O < t < DT)
Inductor current increase from
min max
I to I
?
??
L
S
I
LV
DT
S
L
DV
I
fL
??
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Nov 24, 2024 Last updated |
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