Wien Bridge Oscillator

Wien Bridge Oscillator:

The Wien Bridge oscillator is a standard oscillator circuit for low to moderate frequencies, in the range 5Hz to about 1MHz. It is mainly used in audio frequency generators.

The Wien Bridge oscillator uses a feedback circuit called a lead lag network as shown in fig. 1. At very low frequencies, the series capacitor looks open to the input signal and there is no output signal. At very high frequencies the shunt capacitor looks shorted, and there is no output. In between these extremes, the output voltage reaches a maximum value. The frequency at which the output is maximized is called the resonant frequency. At this frequency, the feedback fraction reaches a maximum value of 1/3. At very low frequencies, the phase angle is positive, and the circuit acts like a lead network. On the other hand, at very high frequencies, the phase angle is negative, and the circuit acts like a lag network. In between, there is a resonant frequency fr at which the phase angle equals 0°. The output of the lag lead network is

Fig. 1

The gain of the feedback circuit is given by

The phase angle between V_out and V_inis given by

These equations shows that maximum value of gain occurs at X_C = R, and phase angle also becomes 0°. This represents the resonant frequency of load lag network. Fig. 2, shows the gain and phase vs frequency.

Fig. 2

How Wien Bridge Oscillator Works:

Fig. 3, shows a Wien Bridge oscillator. The operational amplifier is used in a non-inverting configuration, and the lead-lag network provides the feedback. Resistors R_f and R₁ determine the amplifier gain and are selected to make the loop gain equal to 1. If the feedback circuit parameters are chosen properly, there will be some frequency at which there is zero phase shift in the signal fed back to non inverting terminal. Because the amplifier is non inverting, it also contributes zero phase shift, so the total phase shift around the loop is 0 at that frequency, as required for oscillation.

The oscillator uses positive and negative feedback. The positive feedback helps the oscillations to build up when the power is turn on. After the output signal reaches the desired level the negative feedback reduces the loop gain is 1. The positive feedback is through the lead lag network to the non-inverting input. Negative feedback is through the voltage divider to the inverting input.

Fig. 3

At power up, the tungsten lamp has a low resistance, and therefore, negative feedback is less. For this, reason, the loop gain AB is greater than 1, and oscillations can build up at the resonant frequency f_r. As the oscillations build up, the tungsten lamp heats up slightly and its resistance increases. At the desired output level the tungsten lamp has a resistance R'. At this point

Since the lead lag network has a gain (=B) of 1/3, the loop gain AB equals unity and than the output amplitude levels off and becomes constant. The frequency of oscillation can be adjusted by selecting R and C as

The amplifier must have a closed loop cut off frequency well above the resonant frequency, f_r.

Fig. 4

Fig. 4, shows another way to represent Wein Bridge oscillator. The lead lag network is the left side of the bridge and the voltage divider is the right side. This ac bridge is called a Wein Bridge. The error voltage is the output of the Wein Bridge. When the bridge approaches balance, the error voltage approaches zero.

Example -1:

Design a Wien-bridge oscillator that oscillates at 25 kHz.

Solution:

Let C₁ = C₂ = 0.001 µF. Then, the frequency of oscillation is given by,

or, 

Let R₁ = 10 KΩ. Then,

or, R_f = 20KΩ