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The Wien Bridge Oscillator

One of the main problems with any phase shift oscillator is that the R and C values must be precisely matched in order to produce the desired output frequency. Since this is not an easy or inexpensive task, such oscillators are used where the exact frequency of oscillation is not critical. Another problem is that such circuits do not lend themselves to an easily-variable output frequency. Therefore we would like a feedback circuit that is more stable and yet can more easily be made variable.

The circuit shown to the right is one approach to solving this problem. It is based on a variation of the Wheatstone bridge, where one side of the bridge contains a series RC circuit above a parallel RC circuit, where R and C are the same in both legs of the bridge. This type of bridge circuit is known as a Wien (pronounced "Veen") bridge.

The Wien bridge will balance only at the frequency at which XC = R. At this frequency, the series leg has an impedance ZS = 1.414 R, and the parallel leg has an impedance ZP = 0.707 R. Therefore, the gain of the amplifier must be 3 to compensate. We do this by setting RF = 2RG. The same resistance ratio is required to balance the bridge without an amplifier.

Because this circuit uses only two matched resistors and two matched capacitors to set the frequency, it is practical and not too expensive to accomplish the match. In addition, if the two resistors are made variable but on a common control so they both change the same amount at the same time, it is quite practical to vary the output frequency over a 10:1 range or more.

Regardless of the value of R, this circuit will oscillate at a frequency of ω = 2πf = 1/RC, which once again is the frequency at which the bridge is balanced.

While the Wien bridge oscillator is quite stable as to its frequency of operation, it is very sensitive to the values of RF and RG. These resistors set the gain of the amplifier, and even very small changes will affect the performance of the circuit. If the gain is too low, the circuit will not oscillate. If it is too high, the output waveform becomes distorted. A number of methods have been devised to stabilize the gain of the circuit.

The classical method is to replace RG with a small incandescent light bulb. This works because the tungsten filament has a resistance that increases about tenfold as the temperature increases from completely cold to normal operating brightness. Thus, as VOUT increases, the voltage applied to the bulb increases, and the current through the bulb increases. This warms up the filament a bit, increasing its resistance and thus reducing the gain of the circuit. The result is that VOUT is held at a nearly constant amplitude. With the proper choice of RF to go with the light bulb, we can maintain a very clean, low-distortion sine wave at the output.

Where VOUT must be controlled even more closely, we can augment RG with an AGC (Automatic Gain Control) circuit, such as the one shown to the left.

In this circuit, Q is an N-channel field-effect transistor (FET), whose channel resistance changes according to the voltage applied to the gate. The more negative the applied voltage, the higher the channel resistance. The channel resistance is added to RG to form the total resistance in this leg of the bridge circuit.

The negative voltage comes from VOUT, which is sampled by diode D so that capacitor C1 charges to the negative peak of VOUT. Resistors R1 and R2 work with C1 to form a low-pass filter. This prevents the output amplitude from shifting too rapidly, and thus helps to limit distortion in the output waveform.

The output signal from this circuit is very clean and stable, making it an excellent choice as a source for audio test signals.

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