# 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. The electronic circuit design is quite easy and it provides good overall performance.

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

The Wien bridge oscillator is one that has been around for many years, and it finds applications in many areas as an audio oscillator, either using discrete electronic components, or using operational amplifiers.

As op amps are such easy electronic components to use, providing near perfect operation, they are widely used in circuits like these.

## 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 the measuring the value of capacitors where variable resistors and a known capacitor could be used to determine the value of a capacitor, typically C1.

First let's take a look at the circuit from a qualitative viewpoint. This helps explain the actual operation of the circuit and gives an understanding of how it works.

From the diagram, it can be seen that the circuit can be split into two: a series element of the Wien bridge, i.e. the series resistor and capacitor form a high pass filter; and parallel capacitor resistor element form ing a low pass filter from the line to ground.

In other words there is a series high pass filter and a parallel low pass filter. The overall effect is that the combination of the two forms a selective second order band pass filter which has quite a high Q factor and with a resonant frequency of f_{0}.

Looking at the network very simply, at zero frequency, the series low pass filter consisting of the electronic components R1 and C1 will have an infinite impedance because DC cannot pass through the capacitor.

Similarly at very high frequencies, the parallel circuit effect is dominated by the virtually zero impedance of the capacitor - it virtually short circuits the output.

Between these frequencies there is is a point where the output reaches a maximum - its "resonant frequency", F_{0}.

At this resonant frequency, the reactance of the overall circuit equals its resistance, that is: Xc = R, and the phase difference between the input and output is zeros. The magnitude of the output voltage at this maximum pint is equal to a third of the input voltage.

It is also found that the phase shift in the network varies with frequency, cutting though the axis at the resonant frequency, f_{0}.

Looking at the circuit from a more mathematical viewpoint for electronic circuit design. The Wien bridge is particularly flexible and does not require equal values of the electronic component 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 electronic circuit design equations simplify if R1 = R2 and C1 = C1; the result is R4 = 2 R3.

In practice, the values of the electronic components 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.

By making these assumptions and simplifications, the electronic circuit design is made very much easier.

## Op amp Wien bridge oscillator

For the eelctronic circuit design of a sine wave oscillator, the bridge can be used within the feedback loop and the circuit oscillates at the balance point, i.e. the "resonant point" of the network. 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, and this simplifies the electronic circuit design.

The Wien bridge oscillator can be considered as a positive gain amplifier combined with a bandpass filter through which the positive feedback is applied. As positive feedback is used, it is necessary to be able to limit the gain to avoid undue distortion levels. This is achieved in a number of ways by using automatic gain control, intentional non-linearity and incidental non-linearity limit the output amplitude and they can be used in different circuits in different ways.

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 positive gain amplifier and band-pass filter that provides positive feedback can be seen within the circuit.

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.

## Diode amplitude limiter for Wien bridge oscillator

Another method of limiting the amplitude swing of the oscillator and hence reducing the distortion is to use a pair of back to back diodes in the oscillator feedback loop. The diodes can be placed across part of the resistance R_{f}. As the amplitude increases, so the resistance effectively decreases and the amplitude is decreased.

This circuit is able to provide a lower level of distortion that the circuit without any amplitude limitation.

The Wien bridge oscillator is used in many applications to provide a sine wave signal. Although distortion levels can be higher than some other forms of audio oscillator, it nevertheless provides a very convenient and reliable form of audio sine wave oscillator.

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