Short Notes: Chopper | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 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
??
  
Read More
69 docs

Top Courses for Electrical Engineering (EE)

69 docs
Download as PDF
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Short Notes: Chopper | Short Notes for Electrical Engineering - Electrical Engineering (EE)

,

mock tests for examination

,

Viva Questions

,

Short Notes: Chopper | Short Notes for Electrical Engineering - Electrical Engineering (EE)

,

ppt

,

Exam

,

practice quizzes

,

MCQs

,

Semester Notes

,

shortcuts and tricks

,

Extra Questions

,

video lectures

,

Free

,

past year papers

,

Objective type Questions

,

Short Notes: Chopper | Short Notes for Electrical Engineering - Electrical Engineering (EE)

,

study material

,

Summary

,

pdf

,

Sample Paper

,

Previous Year Questions with Solutions

,

Important questions

;