Transcript
Page 1: Basic Principles of Sinusoidal Oscillators

12 - 1 Electronics(3), 2012Prof. Tai-Haur Kuo

Basic Principles of Sinusoidal OscillatorsLinear oscillatorLinear region of circuit : linear oscillationNonlinear region of circuit : amplitudes stabilization

Barkhausen criterion

loop gain L(s) = β (s)A(s)characteristic equation 1-L(s) = 0oscillation criterion L(j0= A(j0) β(j0) = 1

Amplifier ASXOX

fX

Frequency-selectivenetwork

Page 2: Basic Principles of Sinusoidal Oscillators

12 - 2 Electronics(3), 2012Prof. Tai-Haur Kuo

Basic Principles of Sinusoidal Oscillators (Cont.)at 0, the phase of the loop should be zero and themagnitude of the loop gain should be unity.Oscillation frequency 0 is determined solely by

A steep phase response results in a small for agiven change in phase

0

dωdφ∆φ∆ω0

∆φ

0

φ

0ω ω

Page 3: Basic Principles of Sinusoidal Oscillators

12 - 3 Electronics(3), 2012Prof. Tai-Haur Kuo

Nonlinear Amplitude ControlTo sustain oscillation : βA>1a.overdesign for βA variationsb.oscillation will grow in amplitudepoles are in the right half of the s-planec.Nonlinear network reduces βA to 1 when the desired

amplitude is reachedpoles will be pulled to j-axis

Page 4: Basic Principles of Sinusoidal Oscillators

12 - 4 Electronics(3), 2012Prof. Tai-Haur Kuo

Nonlinear Amplitude Control (Cont.)Limiter circuit for amplitude control linear region

54

5O

54

4B

32

2O

32

3A

i1

fO

RRRV

RRRVV

RRRV

RRRVV

)VRR(V

2D

1D

R1

OVIVRf

R2

R3

R4

R5

A

B

V

-V

Page 5: Basic Principles of Sinusoidal Oscillators

12 - 5 Electronics(3), 2012Prof. Tai-Haur Kuo

Nonlinear Amplitude Control (Cont.)nonlinear region

)RR(1V

RRVL similarly,

)RR(1V

RRV

)VRR

RV(R

RRL V

5

4D

5

4

2

3D

2

3

D32

3

2

32-VVO DA

1

3f

R)R(RSlope

L

L

01

4f

R)R(RSlope

OV

IV

1

f

RRSlope

Page 6: Basic Principles of Sinusoidal Oscillators

12 - 6 Electronics(3), 2012Prof. Tai-Haur Kuo

OPAMP-RC Oscillator CircuitsWien-bridge oscillator

_

C R

C R

1R

2R

SZ

PZ

OV

dV

2RR1sL

RC1ω

RCω1RCω 0. phase For

ωRC1ωRCj3

RR1

jωL

SCR1SCR3

RR1

ZZZ

RR1sL

1

2

0

00

1

2

1

2

sp

p

1

2

Page 7: Basic Principles of Sinusoidal Oscillators

12 - 7 Electronics(3), 2012Prof. Tai-Haur Kuo

OPAMP-RC Oscillator Circuits (Cont.)Wien-bridge oscillator with a limiter

15V

_

16nF 10k

20.3k

1V

16nF10k

2D

1D 3kR3

1kR4

1kR5

3kR6

10k

b

a

15V

OV

Page 8: Basic Principles of Sinusoidal Oscillators

12 - 8 Electronics(3), 2012Prof. Tai-Haur Kuo

OPAMP-RC Oscillator Circuits (Cont.)

10k

-

16nF 10k

10k

16nF

50k b ap

Ov

Page 9: Basic Principles of Sinusoidal Oscillators

12 - 9 Electronics(3), 2012Prof. Tai-Haur Kuo

Phase-Shift OscillatorWithout amplitude stabilization

------- phase shift of the RC network is 180 degrees.Total phase shift around the loop is 0 or 360 degrees.

C

RRR

CCK-

Page 10: Basic Principles of Sinusoidal Oscillators

12 - 10 Electronics(3), 2012Prof. Tai-Haur Kuo

Phase-Shift Oscillator (Cont.)With amplitude stabilization

16nF

RRC C C

16nF16nF

10k 10k

100k

1R

2R

3R

4R

V

V

2D

1D

tR1P

50k

_x Ov

Page 11: Basic Principles of Sinusoidal Oscillators

12 - 11 Electronics(3), 2012Prof. Tai-Haur Kuo

Quadrature Oscillator

O1V

_

_

X R 2R

2R

2R

1R

2R

3R

4R

C

-V

V

1OP

2OPO2V

fR2R) (NominallyC

Page 12: Basic Principles of Sinusoidal Oscillators

12 - 12 Electronics(3), 2012Prof. Tai-Haur Kuo

Quadrature Oscillator (Cont.)-------Break the loop at X, loop gain

oscillation frequency

-------Vo2 is the integral of Vo1

90° phase difference between Vo1 and Vo2

“quadrature” oscillator

222X

02

RCS1

=VV

=L(s)

RC1

0

Page 13: Basic Principles of Sinusoidal Oscillators

12 - 13 Electronics(3), 2012Prof. Tai-Haur Kuo

Active-Filter Tuned OscillatorBlock diagram

High-distortion v2

High-Q bandpass low-distortion v1

V-

2V 1V

t

1V

V 2V

0f

t

V

V-

Page 14: Basic Principles of Sinusoidal Oscillators

12 - 14 Electronics(3), 2012Prof. Tai-Haur Kuo

Active-Filter Tuned Oscillator (Cont.)Practical implementation

-

CRQRR R

R

1V2V 1R

C

Page 15: Basic Principles of Sinusoidal Oscillators

12 - 15 Electronics(3), 2012Prof. Tai-Haur Kuo

A General Form of LC-Tuned Oscillator Configuration

Many oscillator circuits fall into a general form shown below

Z1,Z2,Z3 :capacitive or inductive

-

OR 2

3Z

2Z

1Z

3Z

2Z

1Z

1

3

OV

LZLZ

1

32

OV

OR

A

0I

13V 13V

13V13vVA- ˆ

13V

Page 16: Basic Principles of Sinusoidal Oscillators

12 - 16 Electronics(3), 2012Prof. Tai-Haur Kuo

A General Form of LC-Tuned Oscillator Configuration (Cont.)

2

1

31

1

312

21

321

312321

21

332211

312321

21

13

13

31

113

13

)(

0

)()(

1

)()(ˆ

ˆ

XXAT

XXXA

XXXXXAT

XXX

XXXXXXjRXXAT

CXLX

jXZjXZjXZZZZZZZR

ZZAVVTV

ZZZV

RZZVAV

v

vv

O

v

O

vO

OL

LvO

01T n,oscillatio for

ecapacitanc for inductance for

, , if

Page 17: Basic Principles of Sinusoidal Oscillators

12 - 17 Electronics(3), 2012Prof. Tai-Haur Kuo

A General Form of LC-Tuned Oscillator Configuration (Cont.)

With oscillation|T| = 1 and T = 0, 360, 720, … degree.

X1 & X2 must have the same sign if Av is positiveX1 & X2 are L, X3 = -(X1 + X2) is C

or X1 & X2 are C, X3 = -(X1 + X2) is LTransistor oscillators1.Collpitts oscillator

-- X1 & X2 are Cs, X3 is L2.Hartley oscillator

-- X1 & X2 are Ls, X3 is C

)ωC1

-=X or ωL=(X 1=T i.e.

Page 18: Basic Principles of Sinusoidal Oscillators

12 - 18 Electronics(3), 2012Prof. Tai-Haur Kuo

LC Tuned OscillatorsTwo commonly used configurations1.Collpitts (feedback is achieved by using a capacitive

divider)2.Harley (feedback is achieved by using an inductive

divider)Configuration

1.Collpitts 2.Hartley

1C

L

2L

1L

C

R

2C

R

)V(da.c. groun DD )V(da.c. groun DD

Page 19: Basic Principles of Sinusoidal Oscillators

12 - 19 Electronics(3), 2012Prof. Tai-Haur Kuo

LC Tuned Oscillators (Cont.)Collpitts oscillatorEquivalent circuit

R = loss of inductor + load resistance of oscillator + output resistance of transistor

πV

2 πsC V 2O π 2V V (1 s LC )L

R 1CπGmV2C

2 πsC VC

Page 20: Basic Principles of Sinusoidal Oscillators

12 - 20 Electronics(3), 2012Prof. Tai-Haur Kuo

LC Tuned Oscillators (Cont.)

For oscillations to start, both the real and imaginary parts must be zero

Oscillation frequency

)c+ccc

L(

1=ω

21

210

22 m 1 2

3 2 21 2 1 2 m

232

m 1 2 1 2

1SC V+g v+( +SC )(1+S LC )V=0RLC 1S LC C +S ( )+S(C +C )+(g + )=0R R

1 w LC(g + )+j W(C +C ) W LC C =0R R

S=jw

Page 21: Basic Principles of Sinusoidal Oscillators

12 - 21 Electronics(3), 2012Prof. Tai-Haur Kuo

LC Tuned Oscillators (Cont.)Gain

Oscillation amplitude1.LC tuned oscillators are known as self – limiting

oscillators. (As oscillations grown in amplitude, transistor gain is reduced below its small – signal value)

2.Output voltage signal will be a sinusoid of high purity because of the filtering action of the LC tuned circuit

Hartley oscillator can be similarity analyzed

)ccRg (Actually,

ccRg

1

2m

1

2m

Page 22: Basic Principles of Sinusoidal Oscillators

12 - 22 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillatorsSymbol of crystal

Circuit model of crystal

r

SCPC

L

Page 23: Basic Principles of Sinusoidal Oscillators

12 - 23 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillators (Cont.)Reactance of a crystal assuming r = 0

(Crystal is high – Q device)

Sω ω0

inductive

capacitive

reactanceCrystal

SPSP

2P

2

2S

2

P

PS

2P

S

2S

PS

SP2

S

2

P

S

P

ωω then ,CC Ifωωωω

ωC1jjωZ

C1

C1

L1ω

LC1ω

Let

CLCCCs

LC1s

sC1

sC1sL

1sC

1Z(s)

Page 24: Basic Principles of Sinusoidal Oscillators

12 - 24 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillators (Cont.)The crystal reactance is inductive over the narrow frequency band between ws and wp

Collpitts crystal oscillatorConfiguration

R 1C

2C

crystal

)V(da.c. groun DD

Page 25: Basic Principles of Sinusoidal Oscillators

12 - 25 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillators (Cont.)Equivalent circuit

S P 1 2

0 SS

C <<C , C , C1ω =ω

LC

LPC

SC

-

2C πv 1CR

Page 26: Basic Principles of Sinusoidal Oscillators

12 - 26 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillators (Cont.)

2.2kΩ

-22V

C=300pF

gd strayC +C

1MHzXTAL

10M0.02μF

2N2608S

D

C -22V

CL

Bias circuit

(For AC,-22V and ground are the same=0)

uH~

L12261

Page 27: Basic Principles of Sinusoidal Oscillators

12 - 27 Electronics(3), 2012Prof. Tai-Haur Kuo

Crystal oscillators (Cont.)

Since return ratio then X1 must be large for the loop gain to be greater than one.

X1 is very large when

PS

p

ωωωand ω to closes ω

1 2 3 3 1 2

2

2

1X +X +X =0 & X = X &X are inductiveωC

1 jZ =L//C= =1 1jω C+ ω C+jω L ω L

1 1 1X = >0 ωL> ω>1 ωC LCωC+ωL

v 1

2

A XT=X

For 1MHz crystal,

C=300pFL 84.4μH

1 1 1MHz2π LC

Page 28: Basic Principles of Sinusoidal Oscillators

12 - 28 Electronics(3), 2012Prof. Tai-Haur Kuo

Bistable MultivibratorsMultivibrators bistable:two stable states

(3 types) monostable:one stable stateastable:no stable state

BistableHas two stable statesCan be obtained by connecting an amplifier in a

amplifier in a positive-feedback loop having a loop gain greater than unity. I.e. βA>1 where β=R1/(R1+R2)

Page 29: Basic Principles of Sinusoidal Oscillators

12 - 29 Electronics(3), 2012Prof. Tai-Haur Kuo

Bistable Multivibrators (Cont.)Bistable circuit with clockwise hysteresis

Clockwise hysteresis (or inverting hysteresis)L+:positive saturation voltage of OPAMPL- :negative saturation voltage of OPAMP

-

-

1R 2R

Ov

Iv

THVTLV

-L

Lov

Iv0

+v

Page 30: Basic Principles of Sinusoidal Oscillators

12 - 30 Electronics(3), 2012Prof. Tai-Haur Kuo

Bistable Multivibrators (Cont.)

– Hysteresis width = VTH - VTL

LRR

RβLV

LRR

RβLV

21

1TL

21

1TH

Page 31: Basic Principles of Sinusoidal Oscillators

12 - 31 Electronics(3), 2012Prof. Tai-Haur Kuo

Noninverting Bistable CircuitCounterclockwise hysteresisConfiguration

2 1+ I 0

1 2 1 2

10 + + I TL TL +

2

10 - + I TH TH

2

R Rv =v +vR +R R +R

RFor v =L , v =0,v =v v = L ( )RRFor v =L , v =0,v =v v = L ( )R

-

-

1R 2R

Ov

Iv

THVTLV

-L

L

ov

Iv0

+v

Page 32: Basic Principles of Sinusoidal Oscillators

12 - 32 Electronics(3), 2012Prof. Tai-Haur Kuo

Noninverting Bistable Circuit (Cont.)Comparator characteristics with hysteresisCan reject interference

t

THV

TLV0RV

ceinterferenwithcorruptedSignal

crossings zeroMultiple

Page 33: Basic Principles of Sinusoidal Oscillators

12 - 33 Electronics(3), 2012Prof. Tai-Haur Kuo

Generation of Square and Triangular Waveforms using Astable Multivibrators

Can be done by connecting a bistable multivibrator with a RC circuit in a feedback loop.

THVTLV

-L

L2v

1v0

βLVTH

βLVTL

t

C R

-L

L

1v2v

t

Page 34: Basic Principles of Sinusoidal Oscillators

12 - 34 Electronics(3), 2012Prof. Tai-Haur Kuo

Generation of Square and Triangular Waveforms using Astable Multivibrators (Cont.)

-

-

1R 2R

Ov-v R

- 0

0

-L To

L To

-L

L tOv 1T 2T

Time constant = RC

0 t

t

t

+v

βLVTH

βLVTL

βLVTH

βLVTL

t-v

tv

Page 35: Basic Principles of Sinusoidal Oscillators

12 - 35 Electronics(3), 2012Prof. Tai-Haur Kuo

Generation of Square and Triangular Waveforms using Astable Multivibrators (Cont.)

During T1

During T2

βLLβ

TTt at βL Vif

RRRβ RC, whereeβLLLV

11

21

1t

1

1lnτ

ττ

assumed is LL ;ββTTT

βLLβ

TTt at βL Vif

eβLLLV

21

22

t

11lnτ2

1

1lnτ

τ

Page 36: Basic Principles of Sinusoidal Oscillators

12 - 36 Electronics(3), 2012Prof. Tai-Haur Kuo

Generation of Triangular Waveforms

THVTLV

-L

L

2v

1v0

_

tC

R

Bistable

t

1V

2V1V 2V

2V

2T1T

TL

L

0

1V

2T1T-LSlopeRC

THV

TLV0

RCLSlope

tt

Page 37: Basic Principles of Sinusoidal Oscillators

12 - 37 Electronics(3), 2012Prof. Tai-Haur Kuo

Generation of Triangular Waveforms (Cont.)During T1

During T2

To obtain symmetrical waveforms

;

1T

1TL TH C C0

TH TL1

1 L T LV V i dt where iC RC R

V VT RCL

TH TL

2

SimilarilyV VT RC

L

LLTT 21

L

Page 38: Basic Principles of Sinusoidal Oscillators

12 - 38 Electronics(3), 2012Prof. Tai-Haur Kuo

Monostable MultivibratorsIts alternative name is “ one shot “Has one stable stateCan be triggered to a quasi-state

_

2C 2D

2R

3R1D 1C

B

1RA

-βL

-βL

βL

-L

L

)t(Bv

)t(v

)t(Av

T

+ D2(βL V )

D1V L To

L To

4R

E

)t(Ev

Page 39: Basic Principles of Sinusoidal Oscillators

12 - 39 Electronics(3), 2012Prof. Tai-Haur Kuo

Monostable Multivibrators (Cont.)During T1

βL+ is greater then VD1

Stable state is maintained

)β1

1(CRT|L|ForV

)LβLLVln( CRT

)eV(LLβLβL(T)V

)eV(LL(t)V

13D1

D113

CRT

D1B

CRt

D1B

13

13

Page 40: Basic Principles of Sinusoidal Oscillators

12 - 40 Electronics(3), 2012Prof. Tai-Haur Kuo

Monostable Multivibrators(Cont.)Monostable multivibrator using NOR gates

C

RDDV

NOR NOR

O2VinV Xv

1T

O1v

1T

DDV

O2v

TVV

0 1T Tt

inv

t t0 0

XV

t1T0

DDVDD

TDD

V 23VV

2VV DDT

o1V

DDV

Page 41: Basic Principles of Sinusoidal Oscillators

12 - 41 Electronics(3), 2012Prof. Tai-Haur Kuo

Mono-stable Multivibrator (Cont.)

;

1

tRC

x DDT

RCx 1 T DD

DD1

DD T

DDT T

v V (1 e )

v (T ) V V (1 e )VT RCln RCln2 0.693RC

V VVwhere V V is NOR gate threshold voltage2

RCt

TDDx eVVv

0(0)vC

-

-O1V 0

DDV

R

C

-

XvcV

DDV

T1C V)(Tv

-

-O1 DDV V

R

C

-

XvcV

Page 42: Basic Principles of Sinusoidal Oscillators

12 - 42 Electronics(3), 2012Prof. Tai-Haur Kuo

Mono-stable Multivibrator (Cont.)Monostable multivibrator with catching diode

DDV

RCconstant Time

C

R D

NOR NOR

O2VinV o1V

xV

XV

t1T0

5.6V

5VDV CRconstant Time f

forward resistance of diode

Page 43: Basic Principles of Sinusoidal Oscillators

12 - 43 Electronics(3), 2012Prof. Tai-Haur Kuo

Astable Multivibrator Using NOR(or Inverter) Gates

Transient behavior(1)0<t<T1

:

o 1 D D

o 2 D D- t

R Cx D D T

- tR C

c x O 2 D D D D T

( i ) v :V 0 w h e n t= 0( i i ) v 0 V w h e n t= 0

( i i i ) v = ( V + V ) e

( iv ) v = v - V = - V + ( V + V ) e

C

Cv _

O2VO1VXV

R

o 1v

T 10 t

o 2v

2 T 1

D DV

2 T 1

T 10 t2 T 1

D DV

TV

TV

T 1

0 t

XvDD TV V

2D D

TVV

TVCv

T 10 t2 T 1

D DV

Page 44: Basic Principles of Sinusoidal Oscillators

12 - 44 Electronics(3), 2012Prof. Tai-Haur Kuo

Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)

(2)T1<t<(T1+T2)

1

1

o 1 D D 1

o 2 D D 1

( t-T )R C

x D D D D T

( t-T )R C

c x O 2 x D D D D T

( i) v :0 V w h e n t= T( ii) v :V 0 w h e n t= T

( ii i) v = V - (V + V )e

( iv )v = v -V = v = V - (V + V )e

Page 45: Basic Principles of Sinusoidal Oscillators

12 - 45 Electronics(3), 2012Prof. Tai-Haur Kuo

Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)

Oscillation frequency

x 1 Tt

RCDD T T

DD T1

T

DDT 1 2

0

v (T )=V

(V +V )e =VV +VT =RCln

VVIf V = , then T =RCln3 and T =RCln32

1 0.455oscillation frequency f = 2RCln3 RC

Page 46: Basic Principles of Sinusoidal Oscillators

12 - 46 Electronics(3), 2012Prof. Tai-Haur Kuo

Astable Multivibrator Using NOR(or Inverter) Gates (Cont.)

With catching diode at

Asymmetrical square wave

RC0.721

2RCln21f

RCln2TT

0

21

21

DDT

R(ii)R2

V(i)V

C

Cv _

O2VO1VXV

R

0 DDV

C

Cv _

O2VO1VXV

2R1R

1D 2D

XV

Page 47: Basic Principles of Sinusoidal Oscillators

12 - 47 Electronics(3), 2012Prof. Tai-Haur Kuo

The 555 IC TimerWidely used as both a monostable and astable multivibratorUsed as monostable multivibrator

)t(tv

TLt Vv

0

v(t)

1T0

)t(Ov

nS0011

nR0101

n+1QnQ

10

N/A

nQ 1

2

32

32 1

3

cc

cc

ccc n

VV

VV

VV R

CCV

_

_

R

S

Q

Q

1R

1R

1R

transistor Discharge

ComparatorThreshold

Trigger

1Q

OVTHV

Comparator

1

2

Totem-poleoutput stage

TLV

C cV

tV

)t(cv

0 1T

)e(1V RCtCC

32V V

CC

TH

Page 48: Basic Principles of Sinusoidal Oscillators

12 - 48 Electronics(3), 2012Prof. Tai-Haur Kuo

The 555 IC Timer (Cont.)For 0 t T1

For t = T1,

0)V(V(0) eV(0)VVv CE(sat)RC

t

CCCCx

32VV)(Tv CC

TH1C

0)(V(0) RCln3

3V

V(0)VRClnTCC

CC1

Page 49: Basic Principles of Sinusoidal Oscillators

12 - 49 Electronics(3), 2012Prof. Tai-Haur Kuo

The 555 IC Timer (Cont.)Used as an astable multivibrator

Oscillation frequency1 B 2 1 A BT R Cln2 ,T T (R R )Cln2

)Cln22R(R1

T1f

BA2

OV

Comparator

( )A BR R C

2 0, 13

1, 03

2 03 3

ccc

ccc

cc ccc

VV S R

VV S R

V VV S R

_

_

R

S

Q

Q

1R

1R

1R

transistor Discharge

ComparatorThreshold

Trigger

1Q

THV

1

2

Totem-poleoutput stage

TLV

C

cV

tV

R A

R B

555 timer chip

0 1T

CCVcc

T H2VV =

3

2Tt

ccTL

VV =3

VCC

Page 50: Basic Principles of Sinusoidal Oscillators

12 - 50 Electronics(3), 2012Prof. Tai-Haur Kuo

Sine-Wave ShaperShape a triangular waveform into a sinusoidExtensively used in function generatorsNote:linear oscillators are not cost-effective for low

frequency application not easy to time over wide frequency ranges

0

Ov

fv tT2

T0

0

2T

Tt

Page 51: Basic Principles of Sinusoidal Oscillators

12 - 51 Electronics(3), 2012Prof. Tai-Haur Kuo

Sine-Wave Shaper (Cont.)Nonlinear-amplification methodFor various input values, their corresponding output

values can be calculatedTransfer curve can be obtained and is similar to

CRCR

1Q 2Q

R

II

CCV

EEV-

Ov _

wave)(Sine

wave)r(Triangula

iv

Page 52: Basic Principles of Sinusoidal Oscillators

12 - 52 Electronics(3), 2012Prof. Tai-Haur Kuo

Sine-Wave Shaper (Cont.)Breakpoint methodPiecewise linear transfercurveLow-valued R is assumed V1 and V2 are constant

D2 01in2

45

51DinD10

D22in1

inout1in1

V Vto Vlimit on is DV VRR

R)VV(VVVV

) Vdrop (voltage on is DVVVVVVVV

Page 53: Basic Principles of Sinusoidal Oscillators

12 - 53 Electronics(3), 2012Prof. Tai-Haur Kuo

Sine-Wave Shaper (Cont.)

1R

V

3R

2R

3R

3R

1R

V

3D

1D

2D

4D

4RIn

2V

1V

1V

2V

5R

5R

Inout

2V

1V1V

2V0

1

2

3

4

5

out

Page 54: Basic Principles of Sinusoidal Oscillators

12 - 54 Electronics(3), 2012Prof. Tai-Haur Kuo

Precision Rectifier CircuitsPrecision half-wave rectifier --- “superdiode”

An alternate circuit

_

R

OV

AV

"Superdiode"

iV

OV

iV

11

_OV1D

2D 2R

1R

iV1

1

OV

0

0 iV

Page 55: Basic Principles of Sinusoidal Oscillators

12 - 55 Electronics(3), 2012Prof. Tai-Haur Kuo

Precision Rectifier Circuits (Cont.)Application:Measure AC voltages

Average ;where Vp is the peak amplitude of an input sinusoid

1

2P1 R

RπVV

_

OV

1D

2D

2R

1R

iV

1V

_3R

4R

C

1A2A

Page 56: Basic Principles of Sinusoidal Oscillators

12 - 56 Electronics(3), 2012Prof. Tai-Haur Kuo

Precision Rectifier Circuits (Cont.)

If ;ωmin is the lowest expected frequency of the input sine wave

min4

ωCR

1

3

4

1

2P2 R

RRR

πVV

Page 57: Basic Principles of Sinusoidal Oscillators

12 - 57 Electronics(3), 2012Prof. Tai-Haur Kuo

Precision Full-Wave Rectifiers

1

LR

AD

BD

A

B

C

or

A

B

Page 58: Basic Principles of Sinusoidal Oscillators

12 - 58 Electronics(3), 2012Prof. Tai-Haur Kuo

Precision Full-Wave Rectifiers (Cont.)

1A

_

2A

_

2R

AiV

1D

2D

LR

OV

OV

iVP

1R

E

F

C

Page 59: Basic Principles of Sinusoidal Oscillators

12 - 59 Electronics(3), 2012Prof. Tai-Haur Kuo

Peak RectifierWith load

buffered

1D1A

2A

2D

Civ

Ov

R

-

-

__

iv

-

_

Ov

-LRC

diode Super


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