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Power Electronics and Drives (Version 3-2003) Dr. Zainal Salam, UTM-JB 1 Chapter 3 DC to DC CONVERTER (CHOPPER) General Buck converter Boost converter Buck-Boost converter Switched-mode power supply Bridge converter Notes on electromagnetic compatibility (EMC) and solutions.
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Page 1: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

1

Chapter 3

DC to DC CONVERTER(CHOPPER)

• General• Buck converter• Boost converter• Buck-Boost converter• Switched-mode power supply• Bridge converter• Notes on electromagnetic compatibility

(EMC) and solutions.

Page 2: Chopper

DC-DC Converter (Chopper)

DEFINITION:Converting the unregulated DC input to a controlled DC output with a desired voltage level.

• General block diagram:

LOAD

Vcontrol(derived from

feedback circuit)

DC supply(from rectifier-filter, battery,fuel cell etc.)

DC output

• APPLICATIONS: – Switched-mode power supply (SMPS), DC

motor control, battery chargers

Page 3: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

3

Linear regulator• Transistor is operated

in linear (active) mode.

• Output voltage

• The transistor can be conveniently modelled by an equivalent variable resistor, as shown.

• Power loss is high at high current due to:

Lceo

TLo

IVP

RIP

×=

×=or

2

+

VoRL

+ VCEce − IL

LINEAR REGULATOR

RT

EQUIVALENTCIRCUIT

Vin

RL

+ Vce −IL

VinVo

+

ceino VVV −=

Page 4: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

4

Switching Regulator

• Transistor is operated in switched-mode:

– Switch closed: Fully on (saturated)

– Switch opened: Fully off (cut-off)

– When switch is open, no current flow in it

– When switch is closed no voltage drop across it.

• Since P=V.I, no lossesoccurs in the switch.

– Power is 100% transferred from source to load.

– Power loss is zero (for ideal switch):

• Switching regulator is the basis of all DC-DC converters

+

Vo

RL

+ Vce − IL

SWITCHING REGULATOR

EQUIVALENT CIRCUIT

Vin

RL

IL

VinVo

+

(ON)closed

(OFF)open

(ON)closed

DT T

OUTPUT VOLTAGE

Vo

SWITCH

Vin

Page 5: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

5

Buck (step-down) converter

Vd

L

D C RL

S

+

Vo

Vo

+

CIRCUIT OF BUCK CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

Vo

+

iL

Vd D RL

S

Vd D RL

S

+ −vL

+ vL −

iL

Page 6: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

6

Switch is turned on (closed)

• Diode is reversed biased.

• Switch conducts inductor current

• This results in positive inductor voltage, i.e:

• It causes linear increase in the inductor current

odL VVv −=

�=�

=

dtvL

i

dtdi

Lv

LL

LL

1

Vd VD

+ vL -

C RL

+

Vo

Vd−Vo

−Vo

closedopened

closedopened

t

DT Tt

iLmin

iLmax

IL

vL

iL

iL

+

S

Page 7: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

7

Switch turned off (opened)

• Because of inductive energy storage, iL continues to flow.

• Diode is forward biased

• Current now flows (freewheeling) through the diode.

• The inductor voltage can be derived as:

oL Vv −=

Vd

+ vL -

C RL

+

Vo

Vd−Vo

−Vo

closedopened

closedopened

t

DT Tt

iLmin

iLmax

IL

vL

iL

iL

S

D

(1-D)T

Page 8: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

8

Analysis

( )

( ) TDLV

i

LV

TDi

ti

dtdi

LV

dtdi

dtdi

LVv

DTL

VVi

LVV

DTi

ti

dtdi

i

iL

VVdt

didt

diLVVv

oopenedL

oLLL

oL

LoL

odclosedL

odLLL

L

L

odL

LodL

)1(

)1(

opened,switch For

Figure From linearly. increased

must hereforeconstant.T

positive a is of Derivative

:(on) closed isswitch When the

−⋅��

���

� −=∆�

−=−∆=

∆∆=∴

−=�

=−=

⋅��

���

� −=∆�

−=∆=∆

∆=

−=�

=−=

IL

iL max

DT T

iL

Vd− Vo

vL

t

t

iL min

closed

∆iL

Page 9: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

9

Steady-state operation

( ) ( )

do

so

sod

openedLclosedL

L

L

DVV

TDLV

DTL

VV

ii

i

i

=�

=−⋅��

���

�−−⋅��

���

� −

=∆+∆

0)1(

0

:i.e zero, is period oneover of change theisThat cycle.next theof begining

at the same theis cycle switching of end

at the that requiresoperation state-Steady

iL Unstable current

Decaying current

Steady-state current

t

t

t

iL

iL

Page 10: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

10

minmax

min

max

L

:ripplecurrent Inductor

2)1(1

2

:current Minimum

2)1(1

)1(21

2

:current Maximum

Rin current Average currentinductor Average

IIi

LfD

RV

iII

LfD

RV

TDL

VR

ViII

RV

II

L

oL

L

o

ooLL

oRL

−=∆

��

���

� −−=∆−=

��

���

� −+=

��

���

� −+=∆+=

==�

=

Average, Maximum and Minimum Inductor Current

IL

Imax

Imin

iL

∆iL

t

Page 11: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

11

Continuous Current Mode (CCM)

min

min

min

min

be bchosen is Normally operation. of mode continous ensure

current toinductor minimum theis This2

)1(

02

)1(1

,0 operation, continuousFor

2)1(1

2

analysis, previous From

LL

RfD

LL

LfD

RV

I

LfD

RV

iII

o

oL

L

>>

⋅−=≥�

≥��

���

� −−

��

���

� −−=∆−=

iL

Imax

Imint

0

Page 12: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

12

Output voltage ripple

size.capacitor Increasing 3)sizeinductor Increasing 2)frequency switching Increasing 1)

:by reduced becan Ripple :Note8

)1(

factor, ripple theSo,8

)1(8

peak) to-(Peak voltageRipple8

2221

:formula area triangleUse

:as witten becan charge The

:currentCapacitor KCL,

2

2

LCf

DVV

r

LCf

DCiT

V

iT

iTQ

CQ

V

VCQ

CVQ

iii

o

o

Lo

L

L

oo

o

RLc

−=∆=

−=∆=∆∴

∆=

��

���

�∆��

���

�=∆

∆=∆�

∆=∆�

=

+=

iL

iL=IR

imax

imin

0

0

Vo

+

Vo/R

iRL iL

iC

iC

Page 13: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

13

Basic design procedures

Vd(inputspec.)

SWITCH

f = ?D = ?TYPE ?

D

L

Lmin= ?L = 10Lmin

Cripple ?

RLPo = ?Io = ?

• Calculate D to obtain required output voltage.

• Select a particular switching frequency (f) and device– preferably f>20KHz for negligible acoustic noise– higher fs results in smaller L and C. But results in higher losses.

Reduced efficiency, larger heat sink. – Possible devices: MOSFET, IGBT and BJT. Low power MOSFET can

reach MHz range.• Calculate Lmin. Choose L>>10 Lmin• Calculate C for ripple factor requirement.

– Capacitor ratings:• must withstand peak output voltage• must carry required RMS current. Note RMS current for

triangular w/f is Ip/3, where Ip is the peak capacitor current given by ∆iL/2.

• ECAPs can be used

• Wire size consideration:– Normally rated in RMS. But iL is known as peak. RMS value

for iL is given as:2

2, 3

2��

���

�∆+= LLRMSL

iII

Page 14: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

14

Examples• A buck converter is supplied from a 50V battery source. Given

L=400uH, C=100uF, R=20 Ohm, f=20KHz and D=0.4. Calculate: (a) output voltage (b) maximum and minimum inductor current, (c) output voltage ripple.

• A buck converter has an input voltage of 50V and output of 25V. The switching frequency is 10KHz. The power output is 125W. (a) Determine the duty cycle, (b) value of L to limit the peak inductor current to 6.25A, (c) value of capacitance to limit the output voltage ripple factor to 0.5%.

• Design a buck converter such that the output voltage is 28V when the input is 48V. The load is 8Ohm. Design the converter such that it will be in continuous current mode. The output voltage ripple must not be more than 0.5%. Specify the frequency and the values of each component. Suggest the power switch also.

Page 15: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

15

Boost (step-up) converter

Vd

L D

C

RL

S

Vd

L D

CRL

S

Vd

LD

C RLS

+ vL −

+

Vo

+ vL -

Vo

+

CIRCUIT OF BOOST CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

Vo

+

iL

Page 16: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

16

Boost analysis:switch closed

( )LDTV

i

LV

dtdi

DTi

ti

dtdi

LV

dtdi

dtdi

L

Vv

dclosedL

dL

LLL

dL

L

dL

=∆

=�

∆=∆

∆=

=�

=

=

DT T

iL

vL CLOSED

t

t

Vd

Vd− Vo

∆iL

Vd

L D

CS

+ vL −

iL

+vo−

Page 17: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

17

Switch opened

( ) ( )L

DTVVi

LVV

dtdi

TDi

ti

dtdi

LVV

dtdi

dtdi

L

VVv

odopenedL

odL

L

LL

odL

L

odL

)1(

)1(

−−=∆�

−=�

−∆=

∆∆=

−=�

=

−=

DT T

( 1-D )T

iL

vL OPENED

t

t

Vd

Vd− Vo

∆iL

Vd

D

CS

+ vL -

iL

+vo

-

Page 18: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

18

Steady-state operation

( ) ( )( )

DV

V

LTDVV

LDTV

ii

do

odd

openedLclosedL

−=�

=−−+

=∆+∆

1

0)1(

0

• Boost converter produces output voltage that is greater or equal to the input voltage.

• Alternative explanation:– when switch is closed, diode is reversed. Thus

output is isolated. The input supplies energy to inductor.

– When switch is opened, the output stage receives energy from the input as well as from the inductor. Hence output is large.

– Output voltage is maintained constant by virtue of large C.

Page 19: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

19

Average, Maximum, Minimum Inductor Current

LDTV

RD

ViII

LDTV

RD

ViII

RD

VI

RD

VRD

V

IV

RV

IV

ddLL

ddLL

dL

d

d

Ld

odd

2)1(

2

:currentinductor Minimum

2)1(

2

:currentinductor Maximum)1(

:currentinductor Average)1(

)1(

powerOutput powerInput

2min

2max

2

2

2

2

2

−−

=∆−=�

+−

=∆+=�

−=�

−=

��

���

−=

=

=

Page 20: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

20

L and C values

( )

( )

RCfD

VV

r

RCfDV

RCfDTV

V

VCDTR

VQ

fRDD

TRDDL

LDTV

RD

V

I

o

o

ooo

oo

dd

=∆=

==∆

∆=��

���

�=∆

−=

−=

≥−−

factor Ripple

21

21

02)1(

0CCM,For

2

2

min

2

min

Imax

Imin

Imin

Imax

ic

iD

iL

Vd

vL

Vd−Vo

Io=Vo / R

DT T

∆Q

Page 21: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

21

Examples

• The boost converter has the following parameters: Vd=20V, D=0.6, R=12.5ohm, L=65uH, C=200uF, fs=40KHz. Determine (a) output voltage, (b) average, maximum and minimum inductor current, (c) output voltage ripple.

• Design a boost converter to provide an output voltage of 36V from a 24V source. The load is 50W. The voltage ripple factor must be less than 0.5%. Specify the duty cycle ratio, switching frequency, inductor and capacitor size, and power device.

Page 22: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

22

Buck-Boost converter

Vd L

D

C RL

S+

Vo

Vo

+

CIRCUIT OF BUCK-BOOST CONVERTER

CIRCUIT WHEN SWITCH IS CLOSED

CIRCUIT WHEN SWITCH IS OPENED

Vo

+

iLVd vL

+

iLVd vL

+

D

DS

S

Page 23: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

23

Buck-boost analysis

DT T

Imin

Imax

ic

iD

iL

Vd

vL

∆Q

Vd−Vo

Io=Vo / R

Imax

Imin

LTDV

i

LV

TDi

ti

LV

dtdi

dtdi

LVv

LDTV

i

LV

DTi

ti

LV

dtdi

dtdi

LVdv

oopenedL

oLL

oL

LoL

dclosedL

dLL

dL

LL

)1()(

)1(

openedSwitch

)(

closedSwitch

−=∆�

=−∆=

∆∆

=�

==

=∆�

=∆=∆

=�

==

Page 24: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

24

Output voltage

• NOTE: Output of a buck-boost converter either be higher or lower than input.– If D>0.5, output is higher than input– If D<0.5, output is lower input

• Output voltage is always negative.

• Note that output is never directly connected to load.

• Energy is stored in inductor when switch is closed and transferred to load when switch is opened.

��

���

�−

−=�

=−+�

=∆+∆

DD

V

LTDV

LDTV

s

od

openediLclosediL

1V

:tageOutput vol

0)1(

0:operation stateSteady

o

)()(

Page 25: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

25

Average inductor current

2

2

2

2

)1(

,for ngSubstituti

:ascurrent inductor average torelated iscurrent source averageBut

i.e. source,by thesuppliedpower equalmust load by the absorbedpower

converter, in the losspower no Assuming

DR

DVDV

PRDV

VI

V

DIVR

V

DII

IVR

V

PP

d

d

o

d

oL

o

Ldo

Ls

sdo

so

−===�

=�

=

=

=

Page 26: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

26

L and C values

RCfD

VV

r

RCfDV

RCDTV

V

VCDTR

V

fRD

L

LDTV

DR

D

LDTV

DR

DViII

LDTV

DR

DViII

o

o

ooo

oo

d

ddLL

ddLL

=∆=

==∆

∆=��

���

�=∆

−=�

=+−

−−

=∆−=�

+−

=∆+=�

Q

ripple, tageOutput vol2

)1(

02)1(

V

CCMFor

2)1(2

2)1(2

current,inductor min andMax

2

min

2d

2min

2max

Page 27: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

27

Converters in CCM: Summary

Vd

L

DC RL

S

+Vo

fRD

L

LCf

DVV

DVV

o

o

d

o

2)1(

8

1

Buck

min

2

−=

−=∆

=

fRDD

L

RCfD

VV

DVV

o

o

d

o

2)1(

11

Boost

2

min−=

=∆−

=

fRD

L

RCfD

VV

DD

VV

o

o

d

o

2)1(

1

BoostBuck

2

min−=

=∆−

−=

Vd

L

D C RL

S+Vo

Vd

L D

CRL

S

+Vo

Page 28: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

28

Control of DC-DC converter:pulse width modulation (PWM)

Comparator

Vcontrol

SawtoothWaveform

Vo (desired)

Vo (actual)

+

-

Switch control signal

SawtoothWaveform

Vcontrol 1

Switchcontrolsignalton 2

T

Vcontrol 2

ton 1

Page 29: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

29

Isolated DC-DC Converter

• Isolated DC-DC requires isolation transformer• Two types: Linear and Switched-mode

• Advantages of switched mode over linear power supply-Efficient (70-95%)-Weight and size reduction

• Disadvantages -Complex design-EMI problems

• However above certain ratings,SMPS is the only feasible choice

• Types of SMPS-Flyback-forward-Push-pull-Bridge (half and full)

Page 30: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

30

Linear and SMPS block diagramBasic Block diagram of linear power supply

Basic Block diagram of SMPS

Base/gateDrive

ErrorAmp.

LineInput

φφ 3/1

50/60 HzIsolation

Transformer

Rectifier/Filter

+

Vd

-

Vce=Vd-Vo

C E

B

Vo

Vref

RL

+Vo

+

Vo

-

DC UnregulatedDC Regulated

EMIFILTER

RECTIFIERAND

FILTER

HighFrequency

rectifierandfilter

Base/gatedrive

PWMController

errorAmp

Vo

Vref

DCRegulated

DC-DC CONVERSITION ANDISOLATIONDC

Unregulated

Page 31: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

31

High frequency transformer

: Models

;

iprelationshoutput -input Basic voltage varying- meup/down ti step 2)

isolation electricaloutput -Input 1):function Basic

1

2

2

1

2

1

2

1

NN

ii

NN

vv

=

=

V1V2

+

+

i1 i2N1 N2

Ideal model

V1V2

+

+

i1 i2N1 N2

Model used formost PE application

Lm

Page 32: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

32

Flyback Converter

Vd

+

−Vo

Vd

N1 N2i1

i2

+

−v2v1

+

iLM

iD

+ −vDiC

iR

C R

vSW+ −

+

iS

LM

Vo

Flyback converter circuit

Model with magnetisinginductance

Page 33: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

33

Operation: switch closed

Vd

Vo

N2

+

0

0

v1

v1=Vs

iLM

is=iLM+

N1

+

−v2

( )

0 and 0Therefore,

off turneddiode i.e. ,0

er, transform theof side load On the

12

1

2

1

2

1

212

1

==

<���

����

�−−=

���

����

�=���

����

�=

=∆�

=∆=∆=

==

ii

NN

VVv

NN

VNN

vv

LDTV

i

LV

DTiL

dtiL

dtdiL

dtdi

LVv

doD

d

m

dclosedL

m

dmmm

Lmmd

m

Page 34: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

34

Switch opened

Vs

+ −

v1

+

−iLM

N1 N2

v2= −VS

+

− +

−Vo

iD

vSW

( )

( )

���

����

�+=

���

����

�−−=∆�

���

����

�−=−∆

=∆

=

���

����

�−==

���

����

�−=���

����

�=�

−=

���

����

�−=

2

1

2

1

2

1

2

11

2

1

2

121

2

2

11

:switch theacross Voltage

)1(

1

But

NN

VVv

NN

LTDV

i

NN

LV

TD

i

dt

i

dt

di

NN

Vdt

diLv

NN

VNN

vv

Vv

NN

Vv

odSW

m

oopenmL

m

omLmLmL

omL

m

o

o

o

Page 35: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

35

Output voltage

( ) ( )( )

���

����

���

���

�−

=�

=���

����

�−−�

=∆+∆

1

2

2

1

1

01

0operation, state-steadyFor

NN

DD

VV

NN

LTDV

LDTV

ii

do

m

o

m

d

openedLclosedL mm

• Input output relationship is similar to buck-boost converter.

• Output can be greater of less than input,depending upon D.

• Additional term, i.e. transformer ratio is present.

Page 36: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

36

Flyback waveforms

iLm

is

t

t

iD

iC

v1

-V(N1 /N2)

−Vo/ R

V s

DT T

∆iLM( )

( )

���

����

−=

���

����

−=

=�

=

==

=

=

1

20

2

1

22

20

20

20

0

)1(

)1(

:asn can writte

for Solving

:as torelated is

NN

RDV

NN

RD

DVI

I

DRVV

I

RV

DIV

I

DIT

DTII

IIR

VIV

PP

dL

L

dL

Ld

L

LL

s

Ls

sd

s

m

m

m

m

m

mm

m

Page 37: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

37

Max, Min inductor current

( )

RCfD

VV

r

NN

fRDV

L

fLDV

LDTV

NN

RD

DV

I

LDTV

NN

RD

DV

iII

LDTV

NN

RD

DV

iII

dm

m

d

m

dd

L

m

dd

LLL

m

dd

LLL

m

mmm

mmm

=∆=

���

����

�−=�

==���

����

=

−���

����

−=

∆−=

+���

����

−=

∆+=

0

0

2

2

12

min

2

1

22

min

2

1

22

min,

2

1

22

max,

boost, similar to isn calculatio Ripple

2)1(

22)1(

0, CCM,For

2)1(

2

2)1(

2

Page 38: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

38

ExampleThe Flyback converter has these specifications:DC input voltage: 40VOutput voltage: 25VDuty cycle: 0.5Rated load: 62.5WMax peak-peak inductor current ripple:25% of the average inductor current.Maximum peak-peak output voltage: 0.1VSwitching frequency: 75kHz

Based on the abovementioned specifications, determinea) Transformer turns ratiob) Value of magnetizing inductor Lm. c) Maximum and minimum inductor current.d) Value of capacitor C.

Page 39: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

39

Full-bridge converter

SW2SW4

SW3

VS

NS

NS

+

−vx C

Lx

R+

−Vo

+

vp

SW1

SW1,SW2

SW3,SW4 DT T

2T DT

T +2VP

VS

-VS

Vx

���

����

P

SS N

NV

DT2T

DTT +2

T

Page 40: Chopper

Power Electronics and Drives (Version 3-2003)

Dr. Zainal Salam, UTM-JB

40

Full bridge: basic operation

• Switch “pair”: [S1 & S2];[S3 & S4].

• Each switch pair turn on at a time as shown. The other pair is off.

• “AC voltage” is developed across the primary. Then transferred to secondary via high frequency transformers.

• On secondary side, diode pair is “high frequency full wave rectification”.

• The choke (L) and (C ) acts like the “buck converter” circuit.

• Output Voltage

DNN

VVp

sso ⋅

��

��

�= 2


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