# Wien Bridge Oscillator: Circuit, Op-amp & variable frequency Explained

Hey, friends welcome to the kohiki. In the previous article, we understood the basic working principle of the oscillator. And then we have also seen, how to design the RC phase shift oscillator.

## Introduction to Wein Bridge Oscillator

Wein Bridge Oscillator So, in this article, we will see one more type of RC oscillator which is known as the Wien bridge oscillator. So, this Wien bridge oscillator is the harmonic oscillator.

Meaning that the output of the oscillator is the sinusoidal signal. And it is used for the generation of a sinewave typically in the range of audio frequency.

So, if you see the circuit the RC oscillator then it will look like this. So, as you can see over here it involves the bridge circuit.

Now, let me just redraw the same circuit in a different way. So, as you can see over here it involves the bridge circuit. Now, let me just redraw the same circuit in a different way.

So as you can see over here, these resistorsR3 and R4 are part of the amplifier. And these two branches of the bridge circuit form the RC feedback network.

So, here the op-amp is used in the non-inverting configuration and the positive feedback is provided to this op-amp through this RC feedback circuit.

So, now if you see this RC circuit, it consists of two RC networks. One is the series RC network and the other one is the parallel RC network.

So, here this series RC circuit acts as a high pass filter. While this parallel RC circuit acts like a low pass filter.

So, at low frequencies, this capacitor acts like an open circuit. So, it does not pass the low-frequency signals. On the other end at high frequencies, this capacitor provides a very low impedance.

So, it easily allows the high frequencies components. So, in a way, it acts as a high pass filter. On the other end, if you see this parallel RC circuit, at low frequencies, this capacitor will act as an open circuit.

So, the output voltage at this node will directly appear across this resistor R2. And at very high frequencies, the impedance of this capacitor will be very low.

So, the output will get short-circuited to the ground terminal. So, in a way, this parallel RC network will act as a low pass filter.

### What is meant by Wein bridge oscillator?

A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies.

What is the working principle of Wein bridge oscillator?

The Wien Bridge Oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance circuit depending upon the frequency. At the resonant frequency ƒr the phase shift is 0o.

What is the use of Wein bridge oscillator?

The Wien bridge oscillator is used to find unknown values of components. In most cases, this oscillator is used in the audios. The oscillators are designed simply, size is compressed and it has stable frequency output.

## What is the frequency of Wein bridge oscillator?

So, this RC network does not allow low frequencies as well as high frequencies. But at one particular frequency, the output of the circuit will be maximum. And that frequency is known as the resonant frequency.

So, in a way, this Rc feedback network will act as a notch filter. And if you see the response, then the response of this Rc feedback network will look like this Wien Bridge Oscillator.

So, only at one particular resonant frequency, the output of the circuit will be maximum and at the rest of the frequencies, the output will be minimum Wien Bridge Oscillator.

So, at this resonant frequency, the phaseshift of the circuit will be equal to zero and the ratio of output by input will be equal to 1/3.

And if we consider this R1= R2 and C1=C2, in that case, this resonant frequency fr can be given by the expression 1/(2*Pi*R*C)And if this condition is not true, in that case, resonant frequency fr can be given as1/(2*Pi *√(R1*R2*C1*C2)).

So, this is the expression of a resonant frequency in a case when R1, R2, and C1, C2 are different.

And here, the ratio of output by the input is also known as the feedback fraction. So, here we have feedback fraction beta is equal to 1/3 Wien Bridge Oscillator.

And to get a sustained oscillations A-Beta of this oscillator should be equal to 1. So, in a way, we can say that the gain of this amplifier should be equal to 3 Wien Bridge Oscillators.

Now, as we know this op-amp is configured in a non-inverting configuration, so the gain of the op-amp will be equal to 1+(R4/R3). Or we can say that 1+(R4/R3) = 3.

That means R4/R3= 2So, in this way, at the resonant frequency, the feedback fraction of this feedback network will be equal to 1/3, and that frequency.

if we want to get the sustained oscillations then the ratio of R4/R3, should be equal to 2.

So, whenever these conditions are satisfied at that time, at the resonant frequency we will get the sustained oscillations.

### What is the frequency of oscillation of Wein bridge oscillator?

the frequency of oscillation of Wein bridge oscillator is 2πRC.

### How frequency is measured using Wien’s bridge?

The Wien’s bridge use in AC circuits for determining the value of unknown frequency. The bridge measures the frequencies from 100Hz to 100kHz. The accuracy of the bridges lies between 0.1 to 0.5 percent.

### What frequency does bridge measure?

The Wien bridge is one of many common bridges. Wien’s bridge is used for precision measurement of capacitance in terms of resistance and frequency. It was also used to measure audio frequencies.

## What Is Design of Wein Bridge Oscillator

So, now considering R1=R2 and C1=C2, let’s design a Wien bridge oscillator of frequency 10 kHz. So, here we are assuming that R1=R2 and C1=C2. And the frequency of this oscillator is equal to 10 kHz.

So, under this condition, the resonant frequency can be given by the expression, 1/(2*Pi*R*C) Now, here let’s assume that C= 0.01 uF.

So, let’s find out the value of R for the given values. So, R will be equal to 1/(2*Pi*f*C)That means 1/(2*Pi*10^4 *10^(-8)) Or Wien Bridge Oscillator if you calculate the value of R then it will roughly come around 1.59 kilo-ohm.

And in this design, the gain of this amplifier should be equal to 2. So, let’s assume that R4= 20 kilo-ohm andR3 = 10 kilo-ohms. And here C1 and C2 0.01 uF and R1 and R2 are1.59 kilo-ohm.

Now, what we can do, we can use a potentiometer of 5 kilo-ohms for these two resistors and we can tune these two resistors to the value of 1.59 kilo-ohm.

So, in this way, by using this expression we can select the values of R1, R2 and C1, C2, and we can design a Wien bridge oscillator of the desired frequency.

### What is the application of Wien bridge oscillator?

Temperature bridge oscillator circuit. The Wien bridge oscillator is used to find unknown component values. In most cases, this oscillator is used for audio. The oscillator is simple in design, compact in size, and stable in frequency output.

• It is used to measure the audio frequency.
• Wien bridge oscillator designs the long-range of frequencies
• It produces a sine wave.

### What is the working principle of Wein bridge oscillator?

The Wein bridge oscillator uses a feedback circuit in which is connected to a series RC circuit that produces a phase delay or phase advance circuit parallel to the same component RC depending on the frequency. The shift of phase at the resonant frequency is 0o.

### How do you make a Wien bridge oscillator?

The Wien bridge oscillator includes an op-amp, four resistors, and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. At the resonant frequency, the reaction shunt of the series R2-C2 arm will be an exact multiple of the R1-1-1 arm. If the two R3 and R4 arms are adjusted in the same ratio, the bridge is balanced.

## Derivation of frequency for the Wein Bridge Oscillator

Now, so far we have directly used this expression for this Wien bridge oscillator. so, let’s derive this expression for the Wien bridge oscillator.

And let’s also see at this resonant frequency, why the feedback fraction of this RC network is equal to 1/3.

So, for the derivation let’s assume that the impedance of this series RC circuit is equal to Z1 and the impedance of the parallel RC circuit is equal to Z2.

Now, for this Rc network, the output voltage V out can be given as Z2*Vin/(Z2+Z1). Or we can say that Vo/Vin is equal to Z2/(Z1+Z2)Now here Z2 is equal to R2 in parallel with (1/jwC2)Or we can say that that is equal to R2/(1+ jwR2*C2)Similarly, this Z1 is equal to R1 +1/(jwC1) So, let’s put the value of Z1 and Z2 in this expression.

So, we can write, Vo/Vin = R2/(1+ jwR2*C2)/ [(R1 +1 /jwC1) + R2/(1 + jwC2*R2) ] So, if we simplify this expression then we can write this expression as Vo/Vin = R2*(jwC1)/ [ {R1* ( jwC1) (1 +jwC2*R2)} + (1+ jwC2*R2)+ jW*R2*C1)] and further if we simplify it then we can write this expression as Vo/Vin = jwR2*C1/ [1- w^2R1*R2*C1*C2 +jw { R1C1 +R2C2 +R2C1} ]

So, after simplification, we will get this expression. Now, as we have discussed, at the resonant frequency the phase shift that is offered by this feedback network will be equal to zero Wien Bridge Oscillator.

That means this term should be equal to zero so that this j w will get canceled out at the numerator and the denominator.

And the overall phase shift that is provided by the circuit will be equal to zero. So, from this, we can say that at the resonant frequency, this w^2*R1*R2*C1*C2 = 1 Or we can say that w = 1/√(R1*R2*C1*C2)That means f will be equal to 1/( 2*Pi*√(R1*R2*C1*C2)).

Now, if we consider R1 = R2 and C1= C2, in that case, this expression will get simplified to 1/(2*Pi* R*C)But for a moment let’s assume that R1, R2, and C1, C2 are different Wien Bridge Oscillator.

So, now if we consider this condition then/Vin = R2C1/ (R1C1 +R2C2 +R2C1) Now, if R1, R2, and C1, C2 are equal in that case, this Vo/Vin or the feedback fraction beta will become 1/3 Wien Bridge Oscillator.

But if they are different then this will be the feedback fraction for this RC network. Now, as we have discussed for the sustained oscillations, the A-beta of this oscillator should be equal to 1.

Or we can say that the loop gain should be equal to 1. Now, this is the value of Beta for this feedback network. So, we can say that A should be equal to 1divided by Beta Wien Bridge Oscillator.

Or we can say that the gain of the amplifier should be equal to[ (R1*C1 +R2*C2 +R2*C1)/ R2*C1]And if we simplify it then we can say that the amplifier gain A will be equal to (R1/R2)+(C2/C1 )+1 .

Now, here the gain of the op-amp is equal to 1 +R4/R3. Because it is configured in the non-inverting configuration Wien Bridge Oscillator.

So, we can say that A is equal to 1+ R4/R3should be equal to (R1/R2)+(C2/C1)+1 Or we can say that R4/R3 = (R1/R2) + (C2/C1)So, this is the condition which should get satisfied for the sustained oscillations.

Now, if we consider R1 = R2 and C1= C2 then we will get the condition which we have discussed earlier. That is R4/R3 = 2 Wien Bridge Oscillator.

So, in this way, we have derived the expression of the resonant frequency and we have also seen, at the resonant frequency the feedback fraction Beta will be equal to 1/3, provided R1 = R2 and C1= C2. And to get sustained oscillations the ratio of R4/R3 should be equal to 2 Wien Bridge Oscillators.

So here I add a youtube video based on Wein Bridge Oscillator, Which was uploaded by PhysiCrux Tutorial

## FAQ’s

### What is a Wien bridge oscillator used for?

Wien bridge oscillator is a simple circuit that can be set to continuous oscillation, which outputs a sine wave. The Wien bridge oscillator acts as a useful reference oscillator for analog circuits, and the output signal can then be manipulated with other analog circuits.

### How does a Wien bridge oscillator work?

The Wien Bridge Oscillator. … The Wien Bridge Oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance circuit depending upon the frequency. At the resonant frequency ƒr the phase shift is 0o.

### What is the frequency of Wein bridge oscillator?

Wien-Bridge networks are low frequency oscillators which are used to generate audio and sub-audio frequencies ranging between 20 Hz to 20 KHz. Further, they provide stabilized, low distorted sinusoidal output over a wide range of frequency which can be selected using decade resistance boxes.

### What are the advantages of Wein bridge oscillator?

Due to the advantages like good frequency stability, very low distortion and ease of tuning, a Wien bridge oscillator becomes the most popular audio frequency range signal generator circuit. This type of oscillator uses RC feedback network so it can also be considered as RC oscillator.

### Why do we use Wein Bridge?

The Wien bridge is one of many common bridges. Wien’s bridge is used for precision measurement of capacitance in terms of resistance and frequency. It was also used to measure audio frequencies.

So, I hope in this article you understood how we can design a Wien bridge oscillator using the op-amp.

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