ref:06103104hknee3110 oscillator1 lecture 3 oscillator introduction of oscillator linear oscillator...

Ref:06103104HKN EE3110 Oscillator 1

Lecture 3 Oscillator

• Introduction of Oscillator

• Linear Oscillator– Wien Bridge Oscillator– RC Phase-Shift Oscillator– LC Oscillator

• Stability


Oscillators

Oscillation: an effect that repeatedly and regularly fluctuates about the mean value

Oscillator: circuit that produces oscillation

Characteristics: wave-shape, frequency, amplitude, distortion, stability


Application of Oscillators

• Oscillators are used to generate signals, e.g.– Used as a local oscillator to transform the RF

signals to IF signals in a receiver;– Used to generate RF carrier in a transmitter– Used to generate clocks in digital systems;– Used as sweep circuits in TV sets and CRO.


Linear Oscillators

1. Wien Bridge Oscillators

2. RC Phase-Shift Oscillators

3. LC Oscillators

4. Stability


Integrant of Linear Oscillators

For sinusoidal input is connected “Linear” because the output is approximately sinusoidal

A linear oscillator contains:- a frequency selection feedback network- an amplifier to maintain the loop gain at unity

+

+Amplifier (A)

Frequency-SelectiveFeedback Network ()

Vf

Vs VoV

PositiveFeedback


Basic Linear Oscillator

+

+

SelectiveNetwork(f)

Vf

Vs VoV

A(f)

)( fso VVAAVV and of VV

A

A

V

V

s

o

1

If Vs = 0, the only way that Vo can be nonzero is that loop gain A=1 which implies that

0

1||

A

A (Barkhausen Criterion)


Wien Bridge OscillatorFrequency Selection NetworkLet

11

1

CX C

and

111 CjXRZ 2

2

1

CX C

22

22

1

222

11

C

C

C jXR

XjR

jXRZ

Therefore, the feedback factor,

)/()(

)/(

222211

2222

21

2

CCC

CC

i

o

jXRXjRjXR

jXRXjR

ZZ

Z

V

V

222211

22

))(( CCC

C

XjRjXRjXR

XjR

Vi Vo

R1 C1

R2C2

Z1

Z2


can be rewritten as:

)( 2121221221

22

CCCCC

C

XXRRjXRXRXR

XR

For Barkhausen Criterion, imaginary part = 0, i.e.,

02121 CC XXRR

Supposing,

R1=R2=R and XC1= XC2=XC,

2121

2121

/1

11or

CCRR

CCRR

)(3 22CC

C

XRjRX

RX

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

Fee

dbac

k fa

ctor

-1

-0.5

0

0.5

1

Phas

e

Frequency

=1/3

Phase=0

f(R=Xc)


Example

Rf

+

R

R

C

CZ1

Z2

R1

Vo

By setting , we get

Imaginary part = 0 and

RC

1

3

1

Due to Barkhausen Criterion,

Loop gain Av=1

where

Av : Gain of the amplifier

1

131R

RAA f

vv

21

R

R fTherefore, Wien Bridge Oscillator


RC Phase-Shift Oscillator

+

Rf

R1

R R R

C C C

Using an inverting amplifier The additional 180o phase shift is provided by an RC

phase-shift network


Applying KVL to the phase-shift network, we have

R R R

C C CV1 Vo

I1 I2 I3Solve for I3, we get

)2(0

)2( 0

)(

32

321

211

C

C

C

jXRIRI

RIjXRIRI

RIjXRIV

C

C

C

C

C

jXRR

RjXRR

RjXRR

jXRR

VRjXR

I

20

2

000

02

3

1

)2(])2)[(( 222

21

3CCC jXRRRjXRjXR

RVI

Or


The output voltage,

)2(])2)[(( 222

31

3CCC

o jXRRRjXRjXR

RVRIV

Hence the transfer function of the phase-shift network is given by,

)6()5( 2323

3

1 CCC

o

XRXjRXR

R

V

V

For 180o phase shift, the imaginary part = 0, i.e.,

RC

R

XXRX CCC

6

1

6X

(Rejected) 0or 0622

C

23

and,

29

1

Note: The –ve sign mean the phase inversion from the voltage


LC Oscillators

+

~

Av Ro

Z1 Z2

Z3

12

Zp

The frequency selection network (Z1, Z2 and Z3) provides a phase shift of 180o

The amplifier provides an addition shift of 180o

Two well-known Oscillators:• Colpitts Oscillator• Harley Oscillator


+

~Av Ro

Z1 Z2

Z3

Zp

Vf Vo

321

312

312

)(

)//(

ZZZ

ZZZ

ZZZZ p

For the equivalent circuit from the output

po

pv

i

o

p

o

po

iv

ZR

ZA

V

V

Z

V

ZR

VA

or

Therefore, the amplifier gain is obtained,

)()(

)(

312321

312

ZZZZZZR

ZZZA

V

VA

o

v

i

o

oof VZZ

ZVV

31

1

Zp AvVi

Ro

+

+

Vo

Io


The loop gain,

)()( 312321

21

ZZZZZZR

ZZAA

o

v

If the impedance are all pure reactances, i.e.,

332211 and , jXZjXZjXZ

The loop gain becomes,)()( 312321

21

XXXXXXjR

XXAA

o

v

The imaginary part = 0 only when X1+ X2+ X3=0 It indicates that at least one reactance must be –ve (capacitor) X1 and X2 must be of same type and X3 must be of opposite type

2

1

31

1

X

XA

XX

XAA vv

With imaginary part = 0,

For Unit Gain & 180o Phase-shift,1

2 1X

XAA v


R L1

L2

C

RC1

C2

L

Hartley Oscillator Colpitts Oscillator

T

oLC

1

1

2

RC

Cgm

21

21

CC

CCCT

CLLo

)(

1

21

2

1

RL

Lgm


Colpitts Oscillator

RC1

C2

L

Equivalent circuit

In the equivalent circuit, it is assumed that: Linear small signal model of transistor is used The transistor capacitances are neglected Input resistance of the transistor is large enough

+

V

gmVR C1C2

L


)(11 LjiVV At node 1,

where,

VCji 21

)1( 22

1 LCVV

Apply KCL at node 1, we have

0111

2 VCjR

VVgVCj m

01

)1( 122

2

Cj

RLCVVgVCj m

0)(1

213

212

2

CLCCCj

R

LC

Rgm

For Oscillator V must not be zero, therefore it enforces,

+

V

gmVR C1C2

Lnode 1

I1

I2I3

I4

V


Imaginary part = 0, we have

0)(1

213

212

2

CLCCCj

R

LC

Rgm

T

oLC

1

1

2

RC

Cgm

21

21

CC

CCCT

Real part = 0, yields


Frequency Stability

• The frequency stability of an oscillator is defined as

• Use high stability capacitors, e.g. silver mica, polystyrene, or teflon capacitors and low temperature coefficient inductors for high stable oscillators.

Cppm/ T

o

oo d

d

1


Amplitude Stability

• In order to start the oscillation, the loop gain is usually slightly greater than unity.

• LC oscillators in general do not require amplitude stabilization circuits because of the selectivity of the LC circuits.

• In RC oscillators, some non-linear devices, e.g. NTC/PTC resistors, FET or zener diodes can be used to stabilized the amplitude


Wien-bridge oscillator with bulb stabilization

Vrms

irms

Operating point

+

R

R

C

C

R2

Blub


Wien-bridge oscillator with diode stabilization

Rf

+

R

R

C

C

R1

Vo


Twin-T Oscillator

+

low pass filter

high pass filter

low pass region high pass region

fr f

Filter output


Bistable Circuit

+

vo

v1

v+

Vth

+Vcc

-Vcc

vo

v1

-Vth

+Vcc

-Vcc

vo

v1Vth

+Vcc

-Vcc

vo

v1-Vth


A Square-wave Oscillator

+

vo

vc

vf

vc

vo

+vf

¡Ðvf

+vmax

¡Ðvmax

ref:06103104hknee3110 oscillator1 lecture 3 oscillator introduction of oscillator linear oscillator...

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