RAMA ARORA, PHYSICS DEPARTMENT PGGCG-11, CHANDIGARH OSCILLATORS.

RAMA ARORA,PHYSICS DEPARTMENT

PGGCG-11 , CHANDIGARH

OSCILLATORS

Oscillators

An oscillator is an electronic device which converts DC power from the supply into AC power in the load without the application of an external input signal. The essential components of the oscillator are: Tank circuit, Transistor amplifier, and Feedback circuit

Tank circuit

Amplifier and Feedback diagram

Classification of Oscillators

Depending upon the method of producing oscillations. (a) Feedback oscillators (b) Negative resistance oscillatorsDepending upon nature of generated waveform (a) Sinusoidal or harmonic oscillators (b) Non-sinusoidal or relaxation oscillators Both sinusoidal and relaxation oscillators may be negative

resistance and feedback type.Depending upon the frequency of generated voltage. (a) Audio frequency (AF) oscillator (b) Radio frequency (RF) oscillator (c) very high frequency (VHF) oscillators (d) ultrahigh frequency (UHF) oscillators (e)Microwave oscillators

Fundamental Principle of Oscillators

In oscillator, a negative resistance is provided to compensate for the losses in the circuit.

In a feedback oscillator, external positive feedback sufficient to make the overall gain infinity, provides the negative resistance required to overcome the natural damping of the oscillations.

In a negative resistance oscillator internal positive feedback is present and serves to provide the required negative resistance.

In an oscillator no external signal is applied. The initial signal to trigger the oscillations is ordinarily supplied by the noise voltage. This noise voltage originates when the power supply is switched on. Since the frequency spectrum of noise is very wide, it always possesses a component voltage at a frequency that is correct for the oscillator operation.

Feedback oscillators

The basic requirements of a feedback oscillator are:

An amplifier with positive feedback to provide negative resistance in the circuit.

Some circuit non-linearity to define amplitude of oscillators.

A frequency determining network to produce oscillations at a desired frequency.

Dc power supply to act as energy source.

Tuned collector oscillator

The basic circuit of a tuned collector oscillator is shown in figure. It is called the tuned-collector oscillator, because the tuned circuit is connected to the collector. The tuned circuit, constituted by the capacitor C and transformer primary coiL, forms the load impedance and determines the frequency of oscillation. 

Hartley oscillator

Hartley oscillator is an electronic oscillator circuit that uses an inductor and a capacitor in parallel to determine the frequency.

It is used in radio receiver as a local oscillator because

(i) It is easy to tune

(ii) It’s adaptability to a wide range of frequencies

Hartley Oscillator is generally of two types:

1. Series fed oscillator2. Parallel or shunt fed Hartley oscillator

Series Fed Hartley oscillator

In series fed Hartley oscillator, the junction of two inductors of the tuned circuit is

directly connected to Vcc and one end of the LC circuit is connected to the

collector of the transistor. The lower portion of the tank coil is inductively coupled

to the upper portion.

Shunt fed Hartley oscillator

Shunt fed Hartley oscillator uses a transistor in CE configuration, in which

the collector current is divided into two parallel paths.

One branch connects the collector

to the Vcc through RFC and

provides the path for DC keeping

the AC out. The other branch

connects the collector to LC tank

through a capacitor and provides

the path for AC keeping the DC

out.

AC equivalent circuit of Hartley oscillator

The frequency of oscillation is given by,

(a) (b)

oe

fe

oe h

Ih

h

IV 12

2

Let the currents I1, I2 and I3 be non-zero. Applying Kirchhoff’s voltage law to loop (1), we get

0)( 3121 1 IIjXVhIh Lreie

Similarly, applying Kirchhoff’s voltage law to loop (2) and (3), we get

0)( 3212

2 IIjX

h

Ih

h

IL

oe

fe

oe

and 0)()( 32313 21 IjXIIjXIIjX cLL

From fig. (b), we have

Rearranging the above eqns. We get

011 321

L

oe

reL

oe

refeie XjII

h

hIjX

h

hhh

01

12 221

LL

oeoe

fe XjIIjXh

Ih

h

0)( 321 2121 IjXjXjXIjXIjX cLLLL

For non-zero I1, I2, I3, the determinant of above three eqns. must be zero.

At frequency of oscillation,CLL )(

1

21

2

021

cLL jXjXjX

Taking real part of the equation equal to zero, we get

0)()( 22

1212 LLLfereLrefeoeie XXXhhXhhhh

Since hre < < 1and putting hie hoe – hfe hre = ∆he, the above equation becomes,

022

1212 LLLfeLe XXXhXh

12 2

42

Le

efefeL X

h

hhhX

In general, > > 4 ∆ he feh2

12 Lh

hL

e

fe

Therefore,

This is the equation for sustained oscillations.

2

1

2121 )(

1

LLCLLh

h

fe

oe

Taking imaginary part of the equation equal to zero, we get

CLL )(

1

21

CLLf

)(2

1

221

LCf

2

1

This is the frequency of oscillations of Hartley oscillator.

15

Colpitts LC-Tuned Oscillator Feedback amplifier with inductor L

and capacitors C1 and C2 in feedback network. Feedback is frequency dependent. Aim to adjust components to get

positive feedback and oscillation. Output taken at collector Vo. No input needed, noise at

oscillation frequency o is picked up and amplified.

RB1 and RB2 are biasing resistors. RFC is RF Choke (inductor) to allow

dc current flow for transistor biasing, but to block ac current flow to ac ground.

Simplified circuit shown at midband frequencies where large emitter bypass capacitor CE and base capacitor CB are shorts and transistor capacitances (C and C) are opens.

CB

CE

V0

Vi

V0

Vi

Colpitts LC-Tuned Oscillator Voltage across C2 is just V

Neglecting input current to transistor (I 0),

Then, output voltage Vo is

KCL at output node (C)

Setting s = j

AC equivalent circuit

VsC

Z

VI

CC 2

22

VsC

Z

VII

CCL 2

22

22

2 1))(( LCsVsLVsCVZIVV LLo

01

011

01

2122

213

22

12

12

RgCCs

R

LCsCLCs

LCsVsCR

VgVsC

VsCR

VgVsC

m

m

om

01

213

212

2

CLCCCj

R

LC

Rgm

Iπ ≈ 0

sC2V

sC2V

V0

Assuming oscillations have started, then V ≠ 0 and Vo ≠ 0, so

Colpitts LC-Tuned Oscillator To get oscillations, both the real and

imaginary parts of this equation must be set equal to zero.

From the imaginary part we get the expression for the oscillation frequency

From the real part, we get the condition on the ratio of C2/C1

01

213

212

2

CLCCCj

R

LC

Rgm

21

2121

21

213

21

1

0

CC

CCL

CLC

CC

CLCCC

o

oo

RgC

C

C

C

CLC

CCLCLCRg

R

LC

Rg

m

om

om

1

2

1

2

21

2122

2

22

11

01

Colpitts LC-Tuned Oscillator Given:

Design oscillator at 150 MHz

Transistor gm = 100 mA/V, R = 0.5 K Design:

Select L= 50 nH, then calculate C2, and

then C1

sradxxfo /104.91015022 86

50)5.0)(/100(1

2 KVmARgC

Cm

pFpFC

C

pFFxxnHC

C

LC

C

C

LCCLC

CC

o

o

2350

130,1

50

130,11013.1)501()104.9(50

11

1

11

21

928

1

222

1

2

221

21

Example

Phase Shift Oscillator

Based on op amp using inverting input

Combination of R’s and C’s in feedback loop so get additional phase shift. Target 180o to get oscillation.

Analysis assumes op amp is ideal.

V0

VX

R

IC1

R

IC2IC3

IR1IR2

If Rf

2

23

2

2

223

22

212

112

)(

143

)(

131

12

Finally

)(

131

12

111

11

12

12

12

111

11

sCRsCRsCR

V

sCRsCRsCR

V

sCRsCR

V

sC

IVV

sCRsCRR

V

sCRsCRsCRR

V

sCRR

V

sCRsCRR

VIII

sCRsCRR

V

R

VI

sCRsCR

V

sCsCRR

V

sCR

VZIVV

sCRR

V

R

V

sCRR

VIII

f

o

f

o

f

oCX

f

o

f

o

f

o

f

oCRC

f

oR

f

o

f

o

f

oCC

f

o

f

o

f

oCRC

V1V2

f

o

f

oR

f

oCC

Cf

of

sCRR

V

sCR

V

RR

VI

sCR

VZIVV

IR

VIsoVV

1

0

11

11

1

CC C

Phase Shift Oscillator

RR

soR

R

CR

RRCRRC

ωRRC

)L(ω

so)L(ω

RCso

CRCR

CRCRj

RRC

CRCRj

CRj

sCRsCR

sCR

V

VAL

sCRsCRsCR

V

f

fff

of

o

o

ff

f

X

f

oX

12

1123

1

44

get wefor ngsubstituti and14

1 need also wens,oscillatioget To

3

113

so frequency oneat thisachievecan We

zero. togo to termimaginary theneed wens,oscillatioget To

134

)(14

3

1

)(14

3

)()()(

gain loop for theget we

)(

143V

gRearrangin

22

2220

220

0

o

22

2

2

0

2

V0

VX

R

IC1

R

IC2IC3

IR1IR2

If Rf

V1V2

ExampleOscillator specifications: o=1x106 rad/s

KR

sradxnFCR

RC

nFC

f

o

o

67.0)58(12

Then

58)/101(103

1

3

13

1 fromthen

,10 econveniencfor Selecting

6

Note: We get 180o phase shift from op amp since input is to inverting terminal and another 180o from the RC ladder.

CC C

WIEN BRIDGE OSCILLATOR

Wien bridge oscillator is a two stage amplifier. The first stage is CE amplifier and the second

stage is CC amplifier. The output of the second stage is fed back to the first stage through feed

back network consisting of R1C1 in series and R2C2 in parallel. It is advantageous over phase

shift oscillator as its frequency can be varied over a frequency range of 10:1.

The ratio of output voltage of the network to the input voltage is given by

impedancetotal

ncombinatioparallelofimpedance

V

V

i

o

c

cc

c

c

jXR

RjXjXR

jXR

jXR

.

cc

c

i

o

jRXXR

jRX

V

V

322

If the imaginary term vanishes, the phase shift will be zero i.e.

022 cXR

RX c

RC

1

Therefore, frequency of oscillation is,

RC

1

LCf

2

1

2

3

1

3

c

c

i

o

jRX

jRX

V

VAlso, we have

Hence the oscillations will be sustained if the amplifier has a gain just exceeding 3.

The End