positive feedback amplifiers (oscillators) lc and crystal ...rhabash/elg4139ln3oscillators.pdf ·...

ELG4139: Oscillator Circuits

Positive Feedback Amplifiers (Oscillators)

LC and Crystal Oscillators

JBT; FET; and IC Based Oscillators

The Active-Filter-Tuned Oscillator

Multivibrators

1

Introduction

• There are two different approaches for the generation of sinusoids, most commonly used for the standard waveforms:

– Employing a positive-feedback loop that consists an amplifier and an RC or LC frequency-selective network. It generates sine waves utilizing resonance phenomena, are known as linear oscillators (circuits that generate square, triangular, pulse waveforms are called non-linear oscillators or function generators.)

– A sine wave is obtained by appropriate shaping a triangular waveform.

2

The Oscillator Feedback Loop A basic structure of a sinusoidal oscillator consists of an amplifier and a frequency-

selective network connected in a positive-feedback loop.

The condition for the feedback loop to provide sinusoidal oscillations of

frequency w0 is

Barkhausen Criterion:

At w0 the phase of the loop gain should be zero.

At w0 the magnitude of the loop gain should be unity.

(a) Colpitts and (b) Hartley.

LC and Crystal Oscillators For higher frequencies (> 1MHz)

CLLwo

)21(

1

)21

21(

1

CC

CCL

wo

Hartley Oscillator Used in radio receivers and transmitters More stable than Armstrong

oscillators Radio frequency choke (RFC)

21

210

&

22

1

LLbetweencouplingMutualM

MLLLwhereCL

feq

eq

L1 L2

C

Colpitts Oscillators BJT; FET; and IC Based

-

Rf

Ri

21

21

02

1

CC

CCCwhere

LCf

eq

eq

LC network LC network

C1 C1 C2 C2

RFC is an impedance which is high (open) at high RF frequencies and low (short) to dc voltages

Equivalent Circuit of the Colpitts Oscillator

)21

21(

1

CC

CCL

wo

Complete Circuit for a Colpitts Oscillator

Crystal Oscillators

8

Radio communications, broadcasting stations

Piezoelectric effect

Why are crystal oscillators used in many commercial

transmitters?

Crystal is a piezo-electric device which converts mechanical pressure to electrical voltage or vice-vasa

LCffrequencySeries

S

S

2

1

LCC

CCffrequencyParallel

PS

PS

P

2

1

An Application of Crystal Oscillator

9

Two crystals producing two different frequencies for measuring

temperature Timing devices

Crystals are fabricated by cutting the crude quartz in a very exacting

fashion. The type of cut determines the crystal’s natural resonant frequency

as well as it’s temperature coefficient.

Crystal are available at frequencies about 15kHz and up providing the

best frequency stability. However above 100MHz, they become so small

that handling becomes a problem.

10

Op-amp

-

+

R2 Cs

Vz

Rf

R1

Op-Amp Crystal Oscillator

Op-amp voltage gain is controlled by the negative feedback circuit formed by Rf and

R1. More NFB will damp the oscillation, critical NFB will have a sine wave output and

less NFB will have a square wave output.

The two Zener diodes connected face to

face is to limit the peak to peak output

voltage equal to twice of Zener voltage.

It is very flexible to construct the Op. Amp.

crystal oscillator due to high amplifier gain

and differential input facility of the Op.

Amp.

The crystal is fed in series to the positive feedback which is required for oscillation.

Therefore the oscillation frequency will be crystal series resonant frequency fs.

Example

11

Crystal used instead of inductor in the tank

circuit of Colpitts oscillator

The Phase Shifter Oscillator

The phase-shifter consists of a negative gain amplifier (-K) with a third

order RC ladder network in the feedback.

The circuit will oscillate at the frequency for which the phase shift of the

RC network is 180o. Only at the frequency will the total phase shift around

the loop be 0o or 360o.

The minimum number of RC sections is 3 because it is capable of

producing a 180o phase shift at a finite frequency.

bAVi = Vi (or) Ab =1

A Vi

AVi bAVi

b R

C

R R

C C

Phase-shift Oscillator

C

RD= ?

VDD

R

R

C R

C= ?

-

kkk

kkRkkRrRRBut

kSg

RRgAALetA

DDdDL

m

LLm

10840

408840////

85000

40404029401

b

nFkkRf

CRC

f 5.661102

1

62

1

62

1

f = 1kHz

rd= 40k gm= 5000mS R=10k

FET Phase-shift Oscillator

Example:

Determine the value of capacitance C and the

value of RD of the Phase-shift oscillator

shown, if the output frequency is 1 kHz. Take

rd = 40k and

gm=5000mS, for the FET and R = 10kW.

A

b

62

1

RCf

Frequency of oscillation

29

1b

29

1

A

Ab

Condition of oscillation

14

BJT Phase-Shift Oscillator

C

VDD

R2

R

C R

C= ? RC

R1

R’

R Example: Determine the value of capacitance C and

the value of hfe of the Phase-shift oscillator

shown, if the output frequency is 1kHz.

Take R=10 k. RC =1 k.

nFFkkkk

C

kkkCkHz

RRRCf

C

6006.010/1461102

1

10/146102

11

/462

1

4.3134.02902310

14

1

102923

42923

k

k

k

k

R

R

R

RhBJTfor C

C

fe

RRRCf

C/462

1


R

R

R

RhBJTfor

AA

C

C

fe42923

291

b 29

1bCondition of oscillation

15

IC Phase-shift Oscillator

R

C

+

-

R

C

R

C

Rf

Ri

Example:

Determine the value of capacitance C and the value of Rf of the IC Phase-shift oscillator

shown, if the output frequency is 1kHz. Take R =10kW. Ri =1kW.

nFkkRf

CRC

f 5.661102

1

62

1

62

1

k292929

,

if

i

fRR

R

RA

amplifierinvertingICfor

A b

62

1

RCf


29

,

291

i

f

R

RA

amplifierinvertingICfor

AAb

29

1b


Wien Bridge Oscillator

+

-

R1 C1

R3 R4

R2 C2

22112

1

CRCRf

CCC

RRRif

RCf

21

21

2

1


1

2

2

1

4

3

C

C

R

R

R

R

CCC

RRRif

R

R

21

21

4

3 2


Example: Determine the value of capacitance C1 and R1 if R2 =10kW C2 = 0.1mF R3 =10k R4

=1kW in the Wien bridge oscillator shown has an output frequency of 1kHz.

1

122

22

2211

2211

2

2

2211

025.0025.0

1.01014

1

4

1

4

1

2

1

R

msCms

kkCRfCR

CRCRf

CRCRf


pFk

msC

kkkR

k

R

ms

F

k

R

k

k

C

C

R

R

R

R

25000025.0100

025.0

10096.9910996.9

996.925

1.010

10025.0

1.0

101

10

1

1

11

1

2

2

1

4

3

-


Tuned Oscillators (Radio Frequency Oscillators)

17

Tuned oscillator is a circuit that generates a radio frequency output by using LC

tuned (resonant) circuit. Because of high frequencies, small inductance can be used for the radio frequency of oscillation.

Tuned-input and tuned-output Oscillator

tuned-output

tuned-input

feedback coupling RF output

C2

C1 L1

Cco

Cci

L2

2211

0

2

1

2

1

CLCLf

The Active-Filter-Tuned Oscillator

Assume the oscillations have already started. The output of the band-pass filter will be

a sine wave whose frequency is equal to the center frequency of the filter.

The sine-wave signal is fed to the limiter and then produces a square wave.

Practical implementation of the active-filter-tuned oscillator

Bistable Multivibrators

Another type of waveform generating circuits is the nonlinear oscillators

or function generators which uses multivibrators.

A bistable multivibrator has 2 stable states. The circuit can remain in

either state indefinitely and changes to the other one only when triggered.

Metastable state: v+=0 and vO=0. The circuit cannot exist in the mestastable state for any length of time since any disturbance causes it to switch to either stable state.

Bistable Circuit with Inverting Transfer Characteristics

Assume that vO is at one of its two possible levels, say L+, and thus v+ = βL+.

As vI increases from 0 and then exceeds βL+, a negative voltage developes between

input terminals of the op amp.

This voltage is amplified and vO goes negative.

The voltage divider causes v+ to go negative, increasing the net negative input and

keeping the regenerative process going.

This process culminates in the op amp saturating, that is, vO = L-.

The circuit is said to be inverting Trigger signal

Bistable Circuit with Noninverting Transfer Characteristics

Application of the Bistable Circuit as a Comparator

To design a circuit that detects and counts the zero crossings of an arbitrary

waveform, a comparator whose threshold is set to 0 can be used. The comparator

provides a step change at its output every time zero crossing occurs.

Bistable Circuit with More Precise Output Level

Limiter circuits are used to obtain more precise output levels for the bistable circuit.

L+ = VZ + VD1 + VD2 and L– = –(VZ +

VD3 + VD4).

L+ = VZ1 + VD and L– = –(VZ2 + VD),

where VD is the forward diode drop.

Operation of the Astable Multivibrator Connecting a bistable multivibrator with inverting transfer characteristics in a

feedback loop with an RC circuit results in a square-wave generator.

Operation of the Astable Multivibrator

Generation of Triangular Waveforms

Triangular waveforms can be obtained by replacing the low-pass RC circuit

with an integrator. Since the integrator is inverting, the inverting characteristics

of the bistable circuit is required.

Generation of a Standard Pulse

In the stable state, VA=L+ (why?), VB=VD1, VC=βL+ (D2: ON and R4>>R1).

When a negative-going step applies at the trigger input:

D2 conducts heavily and pulls node C down (lower than VB).

The output of the op amp switch to L- and cause VC to go toward βL-.

D2 OFF and isolates the circuit from changes at the trigger input.

D1 OFF and C1 begins to discharge toward L-.

When VB < VC, the output of the op amp switch to L+.

Generation of a Standard Pulse

The 555 Circuit

Commercially available integrated-circuit package such as 555 timer exists that

contain the bulk of the circuitry needed to implement monostable and astable

multivibrator.

2/3 VCC

1/3 VCC

positive feedback amplifiers (oscillators) lc and crystal ...rhabash/elg4139ln3oscillators.pdf ·...

Documents