RC Phase Shift Oscillator using Op-Amp

When an RC phase shift oscillator employs an op-amp in its circuit, it becomes an electronic oscillator with a stable sine wave output. It functions by developing two groups of 180-degree phase shifts, one via the RC network and the other via an op-amp in an inverting circuit. Due to this phase shift arrangement, it produces nearly pure sinusoidal signals with extreme frequency stability and finds a good application in audio processes, signal generation, as well as other electronic systems requiring precise AC signals.

Using an RC phase shift oscillator and op-amp offers better control than transistor-based designs as it has improved accuracy of frequency, amplitude stability, and less loading effects. The following explains the complete circuit diagram with working principles, mathematical derivations, and application details

Apart from generating the sine wave output, they are also used to provide significant control over the phase-shifting process. Other usages of phase shift oscillators are:

1. In audio oscillators
2. Sine Wave Inverter
3. Voice Synthesis
4. GPS units
5. Musical Instruments.

Before we start designing the RC phase shift oscillator, let's learn more about its phase and phase shift.

What is Phase Shift in RC Oscillator Circuits?

A phase is a full cycle period of a sinusoidal wave in a 360-degree reference. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. Phase is denoted as a pointed position on this waveform cycle. If we see the sinusoidal wave, we can easily identify the phase.

In the above image, a complete wave cycle is shown. The initial starting point of the sinusoidal wave is 0 degrees in phase, and if we identify each positive and negative peak and 0 points, we will get 90, 180, 270, and 360-degree phases. So, when a sinusoidal signal starts its journey other than the 0-degree reference, we call it a phase shift differentiating from the 0-degree reference.

For sinusoidal signals, 360° means one complete wave cycle. While working with RC circuits, we observe:

At 0° phase: The waveform starts from zero and moves to positive amplitude
At 90° phase: The waveform is at its maximum positive amplitude
At 180° phase: The waveform goes back to zero while moving negatively
At 270° phase: The waveform reaches the greatest negative amplitude
At 360° phase: The waveform finishes one complete cycle

If we see the next image, we will identify what a phase-shifted sinusoidal wave looks like…

In this image, there are two AC sinusoidal signal waves presented, the first Green Sinusoidal wave, is 360 degrees in phase, but the red one is 90 degrees phase shifted out of the green signal.

This phase shifting can be done using a simple RC network.

RC phase shift oscillator using op amp

A simple RC phase shift oscillator provides a minimum phase shift of 60 degrees.

The above image shows a single-pole phase shift RC network or ladder circuit, which shifts the phase of the input signal equal to or less than 60 degrees.

Phase Shift in RC Networks

Ideally, the phase shift of the output wave of an RC circuit should be 90 degrees, but in practice it is approximately. 60 degrees, as the capacitor is not ideal. The formula for calculating the phase angle of the RC network is mentioned below:

φ = tan-1(Xc / R)

Where Xc is the reactance of the capacitor and R is the resistor connected in the RC network.

If we cascade there RC network, we will get a 180-degree phase shift.

Now to create oscillation and sine wave output, we need an active component, either a Transistor or an Op-amp in inverting configuration.

If you want to learn more about the RC Phase Shift Oscillator, then follow the link

Why use an Op-amp for an RC Phase Shift Oscillator instead of a Transistor?

There are some limitations in using a Transistor for building an RC Phase Shift Oscillator:

1. It is stable for low frequencies only.
2. RC phase shift oscillator requires additional circuitry to stabilise the amplitude of the waveform.
3. Frequency accuracy is not perfect, and it is not immune to noisy interference.
4. Adverse Loading Effect. Due to cascade formation, the second pole’s input impedance changes the resistance properties of the first pole filter. The more filters cascaded, the worse the situation worsens, as it will affect the accuracy of the calculated phase shift oscillator frequency.

Due to the attenuation across the resistor and the capacitor, the loss across each stage is increased, and the total loss is approximately 1/29th of the input signal.

As the circuit attenuates at 1/29th, we need to recover the loss. Learn more about them in our previous tutorial.

Working of RC Phase Shift Oscillator Using Op-Amp

When we use an op-amp for an RC phase shift oscillator, it functions as an inverting amplifier. Initially, the input wave is introduced into the RC network, due to which we get a 180-degree phase shift. And, this output of RC is fed into the inverting terminal of the op-amp.

Now, as we know that the op-amp will produce a 180-degree phase shift when it functions as an inverting amplifier. So, we get a 360-degree phase shift in the output sine wave. This RC phase shift oscillator, using an op-amp provides a constant frequency even under varying load conditions.

Oscilloscope Analysis of Phase Shifts

Measurement Point	Phase Shift	Signal Characteristics
After the 1st RC Stage	60°	Sine wave with slight attenuation
After the 2nd RC Stage	120°	Further attenuated sine wave
After the 3rd RC Stage	180°	Significantly attenuated, phase-shifted sine wave
Op-Amp Output	360° (0°)	Amplified sine wave, original phase restored

Key Circuit Components for RC Phase Shift Oscillator Circuit

• Op-Amp IC – LM741
• Resistor – (100k – 3nos, 10k – 2nos, 4.7k)
• Capacitor – (100pF – 3nos)
• Oscilloscope

RC Phase Shift Oscillator Using Op-amp Circuit Diagram

Simulation of RC Phase Shift Oscillator using Op-Amp

RC phase shift oscillator provides an accurate sine wave output. As you can see in the simulation video, in the end, we have set the probe of the oscilloscope to four stages of the circuit.

Oscilloscope Probe	Wave Type
First – A	Input Wave
Second – B	Sine wave with 90 degree Phase Shift
Third – C	Sine wave with 180 degree Phase Shift
Fourth – D	Output Wave (Sine wave) with 360 degree Phase Shift

Here, the feedback network is offering a phase shift of 180 degrees. We are getting 60 degrees from each of the RC networks. And, the remaining 180-degree phase shift is generated by the op-amp in the inverting configuration.

Frequency of Oscillation Derivation

For calculating the frequency of oscillation, use the following formula:

F = 1 / 2πRC√2N

Advantages of the RC Phase Shift Oscillator Using OP AMP

The RC Phase Shift Oscillator was said to have a mighty few advantages while using the op-amp in comparison with the one with the conventional transistor:

• High input impedance: Does not load the RC network.
• Low output impedance: Delivers a stable output voltage regardless of the load change.
• Good frequency stability: The Frequency of oscillation is constant.
• Low harmonic distortion: Sinusoidal output free from harmonics.
• Temperature stability - Less variation with temperature.

Practical Applications

• Audio signalling: Musical instruments and audio testing
• Function Generators: Lab and test uses
• Clock Generation: To generate timing for digital systems accurately
• Commercial Setups: Local oscillator and carrier generator
• Medical Units: Therapeutic and diagnostic

Troubleshooting Common Issues

Problem	Possible Cause	Solution
No oscillation	Insufficient gain	Increase the feedback resistor value
Frequency deviation	Component tolerance	Use precision components
Distorted output	Excessive gain	Reduce the feedback resistor value
Unstable oscillation	Poor power supply	Add decoupling capacitors

Frequently Asked Questions

⇥ Why does the RC phase shift oscillator must provide a 360-degree phase shift? 
RC phase shift oscillator must provide a 360-degree phase shift to secure the satisfaction of the Barkhausen criterion required for oscillation. The 360 degrees of shift is equivalent to zero degrees of shift-the feedback signal is therefore in phase with the input signal. This positive feedback thereby satisfies the conditions for sustained oscillations if coupled with sufficient gain, without requiring an external input signal
 

⇥ What is the minimum gain needed for an RC phase shift oscillator?
The minimum gain needed for the RC phase shift oscillator is 29. This is because the three-stage RC network of feedback reduces the signal by a factor of 1/29. The op-amp should deliver at least such gain to counteract the attenuation and achieve sustained oscillation as per the Barkhausen criterion.

⇥ What are the uses of an RC phase shift oscillator using an op-amp?
Applications of the RC phase shift oscillator with an op-amp are:

• Audio signal generators and musical instruments
• Function generators for equipment testing
• Sine wave inverters for power supply
• Voice synthesis equipment
• GPS devices and communication equipment
• Clock generation for digital circuitry
• Medical and therapy equipment

⇥ How does an RC phase shift oscillator using an op-amp operate?
RC phase shift oscillator using an op-amp operates by:

• Three RC networks achieve 180° phase shift (60° each)
• An op-amp in inverting mode introduces an additional 180° phase shift
• Total 360° phase shift meets oscillation requirements
• An op-amp amplifies a reduced signal from an RC network
• Positive feedback ensures sustained oscillation
   

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