Wien Bridge Oscillator

Wien Bridge Oscillators

In the previous RC Oscillators  tutorial we saw that a resistor and capacitor can be connected together to produce an oscillating circuit. Another type of oscillator which uses a RC network in place of the conventional LC tuned circuit to produce a sinusoidal output waveform, is the Wien Bridge Oscillator.

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 RC Oscillators.

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-advance circuit depending upon the frequency. 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 2nd order frequency dependant Band Pass Filter with a high Q factor at the selected frequency. At low frequencies the reactance, Xc of the series capacitor is very high so the series capacitor acts like an open circuit and blocks any input signal, Vin and therefore there is no output signal, Vout. At high frequencies, the reactance of the parallel capacitor is very low so the parallel 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 and the frequency at which this happens is called the Resonant Frequency, (ƒr) as the circuits reactance equals its resistance, Xc = R. At this resonant frequency the output voltage is one third (1/3) of the input voltage.

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 signals being "in-phase" or 0^o and we can define this resonant frequency point with the following expression.

Resonant Frequency

• Where:
• fr  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 the following oscillator circuit is produced.

Wien Bridge Oscillator

The output of the operational amplifier is fed back to the inputs "in-phase" with part of the feedback signal is connected to the inverting input terminal via the resistor divider network of R1 and R2, while the other part is fed back to the non-inverting input terminal via the RC network. 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 the negative feedback signal causing the circuit to oscillate. Also the voltage gain of the amplifier circuit MUST be 3 as set by the resistor network, R1 and R2.

Wien Bridge Oscillator Summary

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

• 1. The Voltage gain of the amplifier must be at least 3.
•  
• 2. The network can be used with a Non-inverting amplifier.
•  
• 3. 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.
•  
• 4. The output resistance of the amplifier must be low so that the effect of external loading is minimised.
•  
• 5. 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 if it is too large the waveform becomes distorted.

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