# Wien Bridge Sine Wave Oscillator / Generator

### The Op amp Wien Bridge sine wave oscillator or generator is an excellent circuit for generating a sine wave signal at audio frequencies and above.

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One of the popular methods of generating a sine wave with an operational amplifier is to use the Wien bridge configuration.

As the name implies, the op amp Wien bridge oscillator or generator is based around the Wien bridge. This is a form of bridge circuit that was developed by Max Wien in 1891 and it comprises four resistors and two capacitors.

## What is a Wien bridge

The basic Wien Bridge circuit is shown below and as it can be seen from this.

The basic bridge circuit was used in many applications including measuring the value of capacitors where variable resistors and a known capacitor could be used to determine the value of a capacitor, typically C1.

The Wien bridge is particularly flexible and does not require equal values of R or C. At some frequency, the reactance of the series R2–C2 arm will be an exact multiple of the R1–C1 arm. If the two R3 and R4 arms are adjusted to the same ratio, then the bridge will balance.

In terms of determining the balance frequency some simple equations can be used.

$\frac{{C}_{1}}{{C}_{2}}=\frac{{R}_{4}}{{R}_{3}}-\frac{{R}_{2}}{{R}_{1}}$

The equations simplify if one chooses R1 = R2 and C1 = C1; the result is R4 = 2 R3.

In practice, the values of R1 / R2 and C1 / C2 will never be exactly equal, but the equations above show that for fixed values in these arms, the bridge will balance at some ω and some ratio of R4/R3.

## Op amp Wien bridge oscillator

This fact can be used within an oscillator circuit, as the bridge can be used within the feedback loop and the circuit is able to oscillate at the balance point. Also the very high input impedance levels and very low output impedance levels of the operational amplifier mean that there is minimal loading on the bridge elements.

The basic Wien bridge oscillator or generator circuit is shown below and contains the elements of the bridge circuit wrapped around the operational amplifier itself. The oscillator can also be viewed as a positive gain amplifier combined with a band-pass filter that provides positive feedback.

The elements of the bridge containing the capacitors are associated with the non-inverting input and the purely resistive elements are associated with the inverting input. For the circuit to oscillate analysis of the circuit reveals there must be a 180° phase shift and this requires that the C1 = C2 and R1 = R2. Additionally Rf is typically set to be 2 Rg. The frequency of oscillation can be determined from the simple equation:

One of the issues with this form of Wien bridge oscillator / generator circuit is the level of distortion created. If the value of Rf is increased (increasing the gain of the circuit), then it is found that the level of distortion also increases as the operational amplifier runs into saturation more. One easy way of overcoming this that has been used in many instances is to replace the resistor Rg with a small incandescent lamp or a thermistor. The ratio of resistances Rf is set to remain at around 2Rg. This idea operates because when the oscillator is first powered, the lamp is cool and the resistance is small. The current flowing through it is larger and the lamp or thermistor heats up, thereby increasing its resistance which in turn causes the gain to fall and the current to fall. After a while an equilibrium point is reached and the oscillator will self-regulate the gain and hence the distortion level.

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