Wien Bridge Oscillator

The Wien Bridge Oscillator

In the previous RC Oscillator  tutorial we saw that a number of resistors and capacitors can be connected together with an inverting amplifier to produce an oscillating circuit. One of the simplest sine wave oscillators which uses a RC network in place of the conventional LC tuned tank circuit to produce a sinusoidal output waveform, is the Wien Bridge Oscillator.

The Wien Bridge Oscillator is so called because the circuit is based on a frequency-selective form of the Whetstone bridge circuit. The Wien Bridge oscillator is a two-stage RC coupled amplifier circuit that has good stability at its resonant frequency, low distortion and is very easy to tune making it a popular circuit as an audio frequency oscillator but the phase shift of the output signal is considerably different from the previous phase shift RC 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 0^o. Consider the circuit below.

RC Phase Shift Network

The above RC network consists of a series RC circuit connected to a parallel RC forming basically a High Pass Filter connected to a Low Pass Filter producing a very selective second-order frequency dependant Band Pass Filter with a high Q factor at the selected frequency, ƒr.

At low frequencies the reactance of the series capacitor (C1) is very high so acts like an open circuit and blocks any input signal at Vin. Therefore there is no output signal, Vout. At high frequencies, the reactance of the parallel capacitor, (C2) is very low so this parallel connected capacitor acts like a short circuit on the output so again there is no output signal. However, between these two extremes the output voltage reaches a maximum value with the frequency at which this happens being called the Resonant Frequency, (ƒr).

At this resonant frequency, the circuits reactance equals its resistance as Xc = R so the phase shift between the input and output equals zero degrees. The magnitude of the output voltage is therefore at its maximum and is equal to one third (1/3) of the input voltage as shown.

Output Gain and Phase Shift

It can be seen that at very low frequencies the phase angle between the input and output signals is "Positive" (Phase Advanced), while at very high frequencies the phase angle becomes "Negative" (Phase Delay). In the middle of these two points the circuit is at its resonant frequency, (ƒr) with the two signals being "in-phase" or 0^o. We can therefore define this resonant frequency point with the following expression.

Resonant Frequency

• Where:
• ƒr  is the Resonant Frequency in Hertz
• R  is the Resistance in Ohms
• C  is the Capacitance in Farads

Then this frequency selective RC network forms the basis of the Wien Bridge Oscillator circuit. If we now place this RC network across a non-inverting amplifier which has a gain of 1+R1/R2 the following oscillator circuit is produced.

Wien Bridge Oscillator

The output of the operational amplifier is fed back to both the inputs of the amplifier. One part of the feedback signal is connected to the inverting input terminal (negative feedback) via the resistor divider network of R1 and R2 which allows the amplifiers voltage gain to be adjusted within narrow limits. The other part is fed back to the non-inverting input terminal (positive feedback) via the RC Wien Bridge network.

The RC network is connected in the positive feedback path of the amplifier and has zero phase shift a just one frequency. Then at the selected resonant frequency, ( ƒr ) the voltages applied to the inverting and non-inverting inputs will be equal and "in-phase" so the positive feedback will cancel out the negative feedback signal causing the circuit to oscillate.

Also the voltage gain of the amplifier circuit MUST be equal to three "Gain = 3" for oscillations to start. This value is set by the feedback resistor network, R1 and R2 for an inverting amplifier and is given as the ratio -R1/R2. Also, due to the open-loop gain limitations of operational amplifiers, frequencies above 1MHz are unachievable without the use of special high frequency op-amps.

Wien Bridge Oscillator Summary

Then for oscillations to occur in a Wien Bridge Oscillator circuit the following conditions must apply.

• 1. With no input signal the Wien Bridge Oscillator produces output oscillations.
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• 2. The Wien Bridge Oscillator can produce a large range of frequencies.
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• 3. The Voltage gain of the amplifier must be at least 3.
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• 4. The network can be used with a Non-inverting amplifier.
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• 5. The input resistance of the amplifier must be high compared to R so that the RC network is not overloaded and alter the required conditions.
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• 6. The output resistance of the amplifier must be low so that the effect of external loading is minimised.
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• 7. Some method of stabilizing the amplitude of the oscillations must be provided because if the voltage gain of the amplifier is too small the desired oscillation will decay and stop and if it is too large the output amplitude rises to the value of the supply rails, which saturates the op-amp and causes the output waveform to become distorted.
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• 8. With amplitude stabilisation in the form of feedback diodes, oscillations from the oscillator can go on indefinitely.

Example No1

Determine the maximum and minimum frequency of oscillations of a Wien Bridge Oscillator circuit having a resistor of 10kΩ and a variable capacitor of 1nF to 1000nF.

The frequency of oscillations for a Wien Bridge Oscillator is given as:

Lowest Frequency

Highest Frequency

In our final look at Oscillators, we will examine the Crystal Oscillator which uses a quartz crystal as its tank circuit to produce a high frequency and very stable sinusoidal waveform.