Oscillators

22

OscillatorsOscillators It converts dc power supply to the ac power in the load ( just It converts dc power supply to the ac power in the load ( just

opposite to rectifier )opposite to rectifier )

It incorporates active and passive componentsIt incorporates active and passive components

It delivers an output voltage of given waveform without the It delivers an output voltage of given waveform without the application of an external input signalapplication of an external input signal

Classification of OscillatorsClassification of Oscillators

S. Kal, IIT-Kharagpur

33

OscillatorsOscillators


44

Let switch SLet switch S11 be closed and S be closed and S22 be opened initially. be opened initially. ((ff=0)=0)

ii = = ss and and ff = B( = B() ) 00 = B( = B() . A() . A() . ) . ii

or f /I = B() . A() = open – loop gain

Principle of Sinusoidal OscillationPrinciple of Sinusoidal Oscillation


55

Both A and B are functions of frequency. If for a particular Both A and B are functions of frequency. If for a particular frequency, frequency, = = 00 , B( , B(00 ) . A( ) . A(00 ) = 1 then ) = 1 then f f = = ii = = ss

Now if SNow if S11 is open and S is open and S22 is closed to close the loop, then since is closed to close the loop, then since ff

= = ii at at = = 00 , the feed back signal will be in phase with the input , the feed back signal will be in phase with the input

signal and has the same magnitude. Hence the system will signal and has the same magnitude. Hence the system will sustain oscillation at the particular frequency sustain oscillation at the particular frequency 00 ( = 2 ( = 2f ), even if f ), even if

ss is withdrawn. is withdrawn.

The condition of oscillation, also called Barkhausen criterion, is

B (B (00) . A () . A (00) = 1) = 1



66

Since A and B are complex quantities, it gives two Since A and B are complex quantities, it gives two alternative sets of conditionsalternative sets of conditions

1) 1) Re [B(Re [B(00 ) . A( ) . A(00 )] = 1 )] = 1 B( B(00 ) . A( ) . A(00 ) ) = 1 = 1

2) 2) Im [B(Im [B(00 ) . A( ) . A(00 )] = 0 )] = 0 B( B(00 ) . A( ) . A(00 ) = 0 ) = 0

The first condition means that the signal fed back to the The first condition means that the signal fed back to the input should be of the same magnitude as the input signal, input should be of the same magnitude as the input signal, while the second condition dictates that the feedback while the second condition dictates that the feedback should be positive with zero phase shift.should be positive with zero phase shift.

The second condition determines the frequency of The second condition determines the frequency of oscillation.oscillation.



77

If the first condition is satisfied, but not the second condition, If the first condition is satisfied, but not the second condition, oscillation will die out ( or decay ) because the input signal will oscillation will die out ( or decay ) because the input signal will gradually decay due to phase cancellation of signals fed back gradually decay due to phase cancellation of signals fed back to the input after successive trips round the loop.to the input after successive trips round the loop.

The practical oscillators do not require an input signal, The practical oscillators do not require an input signal, ss to to

trigger oscillation. trigger oscillation.

Then how does oscillation grow ? And, from what ?Then how does oscillation grow ? And, from what ?



88

The random movement of electrons in conductors and The random movement of electrons in conductors and resistors, random emission of carriers in a transistor and resistors, random emission of carriers in a transistor and diode, random electron-hole recombination phenomena etc. diode, random electron-hole recombination phenomena etc. produce random fluctuation of voltage of very small produce random fluctuation of voltage of very small magnitude ( nV - magnitude ( nV - V range ) called electrical noise.V range ) called electrical noise.

Noise has a broad spectrum consisting of all frequencies. Noise has a broad spectrum consisting of all frequencies. The noise voltage at The noise voltage at = = 00 is the starting or triggering signal is the starting or triggering signal from which oscillation grows.from which oscillation grows.

Other frequency components cannot grow because they do Other frequency components cannot grow because they do not satisfy the phase reinforcement condition, viz., net phase not satisfy the phase reinforcement condition, viz., net phase shift = 0.shift = 0.

For the starting of oscillation, in fact, For the starting of oscillation, in fact, ABAB should be slightly should be slightly greater than unity. But in the steady state, greater than unity. But in the steady state, ABAB = 1 and = 1 and AB AB = 0.= 0.



99

Thus the condition of oscillations are : (i) the magnitude of the loop gain must be equal to unity and (ii) the feed back must be of regenerative type ( positive feed back , phase of AB is either 0 or integer multiples of 3600 )



1010

The basic amplifier ( CE ) provides a phase shift of 180The basic amplifier ( CE ) provides a phase shift of 18000 , and the , and the feed back network provides another 180feed back network provides another 18000 of phase shift, so that of phase shift, so that the total phase shift is 360the total phase shift is 36000 or 0 or 000 ( Note that any integral multiple ( Note that any integral multiple of 2of 2 or 360 or 36000 is equivalent to 0 is equivalent to 000 phase shift). phase shift).

Some Oscillator CircuitsSome Oscillator Circuits

1. RC Phase Shift Oscillator ( using BJT )


1111

The maximum phase shift provided by each CR section of the The maximum phase shift provided by each CR section of the feedback network is limited to 90feedback network is limited to 9000 for which RC for which RC 0 ( 0 ( = tan-1 = tan-1 1/1/CR for each RC section). R and C are adjusted such that CR for each RC section). R and C are adjusted such that each section provides a phase shift of 60each section provides a phase shift of 6000 at the oscillation at the oscillation frequency. So, at least three CR sections will be required to frequency. So, at least three CR sections will be required to produce a phase shift of 180produce a phase shift of 18000..

In this connection, feedback signal is coupled through the In this connection, feedback signal is coupled through the feed back resistor R` in series with the amplifier stage input feed back resistor R` in series with the amplifier stage input resistance ( Rresistance ( Rii ) such that (R`+R ) such that (R`+Rii = R). = R).

The frequency of oscillation is given byThe frequency of oscillation is given by

ffoo = 1/ [2 = 1/ [2RC RC ( 6 + 4R ( 6 + 4Rcc / R)] / R)]

The condition of oscillation is given byThe condition of oscillation is given by

hhfefe(min) = 4R(min) = 4Rc c / R + 23 + 29.R / R/ R + 23 + 29.R / Rcc S. Kal, IIT-Kharagpur

1212

The output of the Op Amp is fed to a three stage RC network The output of the Op Amp is fed to a three stage RC network which provides the needed 180which provides the needed 18000 of phase shift (at an attenua- of phase shift (at an attenua-tion factor of 1/29) . If the Op Amp provides gain ( set by tion factor of 1/29) . If the Op Amp provides gain ( set by resistors Rresistors R11 and R and Rff , A = - R , A = - R11/ R/ Rf f ) of greater than 29, a loop gain ) of greater than 29, a loop gain greater than unity results and the circuit acts as an oscillator.greater than unity results and the circuit acts as an oscillator.

The frequency of oscillation is given by, The frequency of oscillation is given by,

ff00 = 1 / [ 2 = 1 / [ 2RCRC6 ]6 ]

2. RC Phase Shift Oscillator using Op Amp


1313

A balanced bridge is used as a feed back network, which is Wien bridge

The active element is an op Amp which has a very large positive voltage gain (non-inverting mode) Av, negligible output resistance, very high input resistance. It is further assumed that Av is constant over the range of frequency of operation of this circuit.

3. Wien Bridge Oscillator


1414

Analysis of the bridge results, Analysis of the bridge results,

RR33/R/R44 = R = R11/R/R22 + C + C11/C/C22 Frequency of oscillation is given by :Frequency of oscillation is given by :

ff00 = 1 / (2 = 1 / (2 R R11RR22CC11CC22 ) ) In practical circuit,In practical circuit,

RR1 1 = R= R22 = R ( say) and C = R ( say) and C11 = C = C22 = C (say) = C (say)

ff00 = 1 / 2 = 1 / 2RC RC and R and R33 /R /R44 = 2 or R = 2 or R33 = 2 R = 2 R44

Thus a ratio of RThus a ratio of R33/R/R44 greater than 2 will provide greater than 2 will provide sufficient loop gain for circuits to oscillate at the sufficient loop gain for circuits to oscillate at the frequency, ffrequency, f00 = 1 / 2 = 1 / 2RC.RC.

3. Wien Bridge Oscillator


1515

4. High Frequency Tuned Oscillators4. High Frequency Tuned Oscillators

Hartley Oscillator Colpitts Oscillator

f0 = 1/ (2 LC)LC) f0 = 1/ [2 (LC(LC11CC22/(C/(C11+C+C22)))) S. Kal, IIT-Kharagpur

1616

5. Non – Sinusoidal Oscillators (Astable Multivibrator)5. Non – Sinusoidal Oscillators (Astable Multivibrator)

Circuit diagram Waveform S. Kal, IIT-Kharagpur

Oscillators

Documents

feed back network

wien bridge oscillator

input signal

phase shift

op amp

sinusoidal oscillation

input

phase