# RC Phase Shift Oscillators Using Op-Amps

### Key Takeaways

• Oscillators are amplifiers with feedback.

• The two main requirements of an oscillator are that the magnitude of the gain must be at least 1, and the total phase shift of the gain must be either 0° or 360°.

• Each RC network provides a 60° phase shift, thereby making the total phase shift equal to 360° or 0°.

In an RC phase shift oscillator, the three RC networks provide a 180° phase shift to the output voltage waveform

Oscillators are wave generators and can be designed using transistors or op-amps. When wired as amplifiers with infinite gain, op-amps can produce output signals without input signals – these are called oscillators. Variants such as Wien bridge oscillators, quadrature oscillators, and RC phase shift oscillators using op-amps are used for different applications in analog electronics.

Diagram of an oscillator

The circuits that generate alternating voltage and current waveforms are called oscillators. Even in the absence of an external input signal, the oscillator circuit generates repetitive voltage or current waveforms of constant amplitude and frequency.

Oscillators are used in:

• Television
• Computers
• Communication systems

## Oscillators and Feedback

Oscillators are amplifiers with feedback. Feedback is the process in which the output signal of the circuit is fed back to the input section. When the amplifier is fed back with its output signal, the characteristics of the circuit change and begin to behave like an oscillator. The signal fed back can be voltage or current, and feedback can be either in series or parallel with the input signal.

## Types of Feedback

The feedback signal can be directly proportional to the output signal. There are four types of feedback possible:

1. Series - Voltage
2. Series - Current
3. Shunt - Voltage
4. Shunt - Current

The figure below shows the block diagram of an oscillator. The represents the gain of the feedback block and the feedback voltage Vf.

The load connected to the amplifier is presented by the feedback network or network. The voltage gain of the oscillator circuit GV = A is dependent on the load connected to the amplifier.

The equations governing the oscillator circuit are:

Voltage gain with feedback,

## Positive Feedback

In the above equation (7), what if the magnitude of (1-A) was less than unity. Such feedback networks are called positive or regenerative feedback.

One of the practical application cases of positive feedback is where A=1. If A=1, then the equation (7) reduces to the following and corresponds to an oscillator circuit.

In the oscillator, the circuit is arranged to give A=1 at a predetermined frequency, which is the frequency of the output signal.

## Requirements of an Oscillator

The two main requirements of an oscillator are:

1. The magnitude of the gain A must be at least 1.
2. The total phase shift of the gain A must be either 0° or 360°.

## Op-Amp Oscillators

As mentioned above, the oscillator circuit can be realized using op-amps. Using op-amps, oscillators of different types can be wired. The types of oscillators using op-amps are:

1. RC-phase shift oscillators
2. Wien Bridge oscillators

## RC-Phase Shift Oscillators Using Op-Amps

The figure below shows an RC phase oscillator using an op-amp. It consists of the amplifier stage and the feedback circuit. The amplifier stage consists of an op-amp and associated components. The op-amp in the amplifier stage is used in its inverting mode. In inverting mode, the signal given to the inverting terminal is shifted by 180° at the output.

RC phase shift oscillator using an op-amp

In the RC phase shift oscillator illustrated in the figure, RC cascaded networks are used as feedback circuits. The feedback network gives the feedback voltage from the output to the input of the amplifier. The additional 180° phase shift, as mentioned in the oscillator requirements, is provided by RC cascaded networks. Each RC network provides a 60° phase shift, thereby making the total phase shift equal to 360° or 0°.

When the phase shift provided by the cascaded RC network is exactly 180°, the amplifier gain becomes sufficiently large. At this condition, the circuit starts oscillating at that frequency. This frequency is the frequency of the oscillator output and can be given by the following equation.

At fo, the gain A must be at least 29.

When the gain of the oscillator is 29 and the total phase shift is around 360°, the oscillator produces a sinusoidal waveform of frequency f0 .

## Designing RC Phase Shift Oscillators Using Op-Amps

In an RC phase shift oscillator using an op-amp, both the magnitude and frequency of the output signal are predetermined. The oscillator circuit is designed to produce this desired magnitude and frequency.

The desired magnitude can be obtained by using Zeners connected in a back-to-back fashion at the output terminals. Firstly, capacitor C is chosen. Using the relationship given in equation (9), the values are calculated. When designing the RC phase shift oscillator using an op-amp, the op-amp selection should be made based on the frequency. For lower frequencies, 741 op-amps are preferred. For higher frequencies, use an LM318.

Implementing RC phase shift oscillators using op-amps and transistors is easier when you use PCB design and analysis software. The layout and simulation tools in OrCAD and the full suite of analysis tools from Cadence allow you to build and analyze the behavior of your oscillator circuits and help you identify signal problems that can arise in complex layouts.

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