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RC PHASE SHIFT OSCILLATOR USING OPAMP | CIRCUIT, FREQUENCY, AND ANALYSIS

2Apr 201726 May 2021

--------------------------------------------------------------------------------

1 Comment

RC Phase Shift Oscillator basically consists of an amplifier and a feedback
network consisting of resistors and capacitors arranged in ladder fashion. Hence
such an oscillator is also called ladder-type RC Phase Shift Oscillator.

To understand the operation of this oscillator let us study RC circuit first,
which is used in the feedback network of this oscillator. The Fig. 2.90 shows
the basic RC circuit.



The capacitor and resistance are in series. Now is the capacitive reactance in
ohms given by,



The total impedance of the circuit is,



The r.m.s. value of the input voltage applied is say volts. Hence the current is
given by,









From the expression of current, it can be seen that current I leads input
voltage by angle

The output voltage is the drop in resistance R given by,



The voltage across the capacitor is,



The drop is in phase with current while the drop lags current by i.e. leads by .
The phasor diagram is shown in the Fig. 2.90 (b).

By using proper values of and , the angle is adjusted in practice equal to .


RC FEEDBACK NETWORK

As stated earlier, the RC network is used in the feedback path. In the
oscillator, the feedback network must introduce a phase shift of 180° to obtain
a total phase shift around a loop as 360°. Thus if one RC network produces a
phase shift of 4) = 60° then to produce a phase shift of 180° such three RC
networks must be connected in cascade.

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Hence in RC phase shift oscillator, the feedback network consists of three RC
sections each producing a phase shift of 60°, thus total phase shift due to
feedback is 180° (3x 60°). Such a feedback network is shown in Fig. 2.91.

The network is also called the ladder network. All the resistance values and all
the capacitance values are the same so that for a particular frequency, each
section of R and C produces a phase shift of 60°.


RC PHASE SHIFT OSCILLATOR USING OP-AMP

R-C phase shift oscillator using op-amp uses an op-amp in inverting amplifier
mode. Thus it introduces the phase shift of 180° between input and output. The
feedback network consists of 3 RC sections each producing 60° phase shift. Such
an RC phase shift oscillator using op-amp is shown in Fig. 2.92.

The output of the amplifier is given to the feedback network. The output of the
feedback network drives the amplifier. The total phase shift around a loop is
180° of the amplifier and 180° due to 3 RC section, thus 360°. This satisfies
the required condition for positive feedback and circuit works as an oscillator.



Let us find the transfer function of the RC feedback network :



Applying KVL to various loops we get,



Replacing jω by s and writing the equations in the matrix form,



Using the Crammer’s rule to obtain I3










This is the frequency with which circuit oscillates,

At this frequency,



The negative sign indicates a phase shift of 180°



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Now to have the oscillations,





Thus circuit will work as an oscillator which will produce a sinusoidal waveform
if the gain is 29 and total phase shift around a loop is 360°. This satisfies
the Barkhausen criterion for the oscillator. These oscillators are used over the
audio frequency range i.e. about 20 Hz up to 100 kHz.


ADVANTAGES

The advantages of R-C phase shift oscillator are,

 1. The circuit is simple to design.
 2. Can produce output over the audio frequency range.
 3. Produces sinusoidal output waveform. –
 4. It is a fixed-frequency oscillator.


DISADVANTAGES

By changing the values of R and C, the frequency of the oscillator can be
changed. But the values of R and C of all three sections must be changed
simultaneously to satisfy the oscillating conditions. But this is practically
impossible. Hence the phase shift oscillator is considered as a fixed frequency
oscillator, for all practical purposes.

And the frequency stability is poor due to the changes in the values of various
components, due to the effect of temperature, ageing etc.


Categories:
 * Analog Electronics
 * Linear integrated circuits & applications
 * Oscillator


PUBLISHED BY ASHOK SAINI

MTech in Power Electronics & Machine Drives at IIT Delhi (2021-23) || BTech in
Electrical Engineering (EE) from NIT Jaipur (2015-19) View all posts by Ashok
Saini

Tags: frequency, How does RC phase shift oscillator work?, Op-amp Phase-lead RC
Oscillator Circuit, phase shift oscillator, rc phase shift oscillator, RC Phase
Shift Oscillator : Circuit using BJT, rc phase shift oscillator derivation, rc
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phase shift oscillator online calculator, rc phase shift oscillator ppt, rc
phase shift oscillator theory, rc phase shift oscillator theory for record, rc
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using transistor, rc phase shift oscillator viva questions, What are the
applications of RC phase shift oscillator?, What is RC phase shift oscillator?,
What is the frequency of RC phase shift oscillator?, What is the gain of RC
phase shift oscillator?, Why RC oscillator is called phase shift oscillator?


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1 COMMENT

 1. Rob says:
    25 Apr 2022 at 12:49 PM
    
    Hello there,
    
    thanks for your comprehensive analysis. I think there’s a typo in equation
    22 … shouldn’t R be to the third power in the denominator? It’s right in
    equation 23.
    
    Cheers
    
    LikeLike
    
    Reply
    


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