# Sinusoidal Oscillators

An oscillator is an electronic circuit that produces a periodic signal. If the oscillator produces sinusoidal oscillations, it is called as a **sinusoidal oscillator**. It converts the input energy from a DC source into an AC output energy of a periodic signal. This periodic signal will be having a specific frequency and amplitude.

The **block diagram** of a sinusoidal oscillator is shown in the following figure −

The above figure mainly consists of **two blocks**: an amplifier and a feedback network.The feedback network takes a part of the output of amplifier as an input to it and produces a voltage signal. This voltage signal is applied as an input to the amplifier.

The block diagram of a sinusoidal oscillator shown above produces sinusoidal oscillations, when the following **two conditions** are satisfied −

The

**loop gain**$A_{v}\beta$ of the above block diagram of sinusoidal oscillator must be greater than or equal to**unity**. Here, $A_{v}$ and $\beta$ are the gain of amplifier and gain of the feedback network, respectively.The total

**phase shift**around the loop of the above block diagram of a sinusoidal oscillator must be either**0**or^{0}**360**.^{0}

The above two conditions together are called as **Barkhausen criteria**.

## Op-Amp Based Oscillators

There are **two** types of op-amp based oscillators.

- RC phase shift oscillator
- Wien bridge oscillator

This section discusses each of them in detail.

### RC Phase Shift Oscillator

The op-amp based oscillator, which produces a sinusoidal voltage signal at the output with the help of an inverting amplifier and a feedback network is known as a **RC phase shift oscillator**. This feedback network consists of three cascaded RC sections.

The **circuit diagram** of a RC phase shift oscillator is shown in the following figure −

In the above circuit, the op-amp is operating in **inverting mode**. Hence, it provides a phase shift of 180^{0}. The feedback network present in the above circuit also provides a phase shift of 180^{0}, since each RC section provides a phase shift of 60^{0}. Therefore, the above circuit provides a total phase shift of 360^{0} at some frequency.

The

**output frequency**of a RC phase shift oscillator is −

$$f=\frac{1}{2\Pi RC\sqrt[]{6}}$$

The

**gain $A_{v}$**of an inverting amplifier should be greater than or equal to -29,

$$i.e.,-\frac{R_f}{R_1}\geq-29$$

$$=>\frac{R_f}{R_1}\geq-29$$

$$=>R_{f}\geq29R_{1}$$

So, we should consider the value of feedback resistor $R_{f}$, as minimum of 29 times the value of resistor $R_{1}$, in order to produce sustained oscillations at the output of a RC phase shift oscillator.

### Wien Bridge Oscillator

The op-amp based oscillator, which produces a sinusoidal voltage signal at the output with the help of a non-inverting amplifier and a feedback network is known as **Wien bridge oscillator**.

The **circuit diagram** of a Wien bridge oscillator is shown in the following figure −

In the circuit shown above for Wein bridge oscillator, the op-amp is operating in **non inverting mode**. Hence, it provides a phase shift of 00. So, the feedback network present in the above circuit should not provide any phase shift.

If the feedback network provides some phase shift, then we have to **balance the bridge** in such a way that there should not be any phase shift. So, the above circuit provides a total phase shift of 0^{0} at some frequency.

The

**output frequency**of Wien bridge oscillator is

$$f=\frac{1}{2\Pi RC}$$

The

**gain $A_{v}$**of the non-inverting amplifier should be greater than or equal to 3

$$i.e.,1+\frac{R_f}{R_1}\geq3$$

$$=>\frac{R_f}{R_1}\geq2$$

$$=>R_{f}\geq2R_{1}$$

So, we should consider the value of feedback resistor $R_{f}$ at least twice the value of resistor, $R_{1}$ in order to produce sustained oscillations at the output of Wien bridge oscillator.