Wien Bridge Oscillator

Introduction

Oscillators are circuits that produce periodic waveforms without any input signal. They generally use some form of active devices like transistors or OPAMPs as amplifiers with feedback network consisting of passive devices such as resistors, capacitors, or inductors.

The Wien bridge oscillator is one of the simplest oscillators. It is widely used in the laboratories as a variable frequency signal generator covering the entire audio-frequency range. Excellent frequency stability together with relative ease in changing the frequency, almost no distortion and low attenuation of the output voltage make the Wien bridge oscillator most popular. Here OPAMP is used as the amplifying device and the Wien bridge is used as the feedback element.

The main difference between the general oscillator and Wien bridge oscillator is that in an oscillator in general, the amplifier stage introduces 180 degrees phase shift and additional 180 degrees phase shift is introduced by feedback network so as to obtain the 360 degrees or zero phase shift around the loop to satisfy the Barkhausen criterion.

But, in case of the Wien bridge oscillator, a non-inverting amplifier used in amplifier stage does not introduce any phase shift. Hence there is no need of an additional phase shift through feedback network is required in order to satisfy the Barkhausen criterion. Let us discuss in brief about Wien bridge oscillator.

Circuit operation

The basic circuit of Wien bridge oscillator using an OPAMP as the active device is shown in figure 1. The name of the oscillator originates from the name of the bridge network (Wien bridge) shown in figure 2.

Figure 1

Figure 2

(a) One arm of the bridge consisting of a series combination of resistances R₁ and R₂ is used to build a non-inverting amplifier around the OPAMP (figure 3). The gain of the amplifier, controlled by R₁ and R₂, is given by

A = 1 + R₂/ R₁ .

If one choses R₂ = 2R₁, then A = 3. Thus the basic amplifier has a gain of 3 and is of non-inverting type.

(b) The other two arms of the Wien bridge consists of the “lead-lag network” (figure 4) which provides feedback in proper phase to the input of the non-inverting amplifier. Thus the output voltage of the amplifier becomes input voltage of the lead-lag network whilst the output of the lead-lag network becomes the input voltage of the amplifier.

Figure 3

Figure 4

Analysis of the lead-lag network

The lead-lag network consists of a series RC branch connected to a parallel RC branch, 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, f₀.

At low frequencies the reactance of the series capacitor is very high so acts a bit like an open circuit, blocking any input signal at v_i resulting in virtually no output signal, v₀. Likewise, at high frequencies, the reactance of the parallel capacitor becomes very low, so this parallel connected capacitor acts a bit like a short circuit across the output, so again there is no output signal.

So there must be a frequency point between these two extremes, where v₀ reaches its maximum value (figure 5). The frequency value of the input waveform at which this happens is called the oscillators resonant frequency (f₀).

At frequencies lower than f₀, the phase angle of v₀ with respect to v_i is positive and the circuit acts as a lead-network. At frequencies higher than fo, The circuit acts as a lag network. However, at the resonant frequency, the circuit’s reactance equals its resistance, that is: X_C = R, and the phase difference between the input and output equals zero degree. The magnitude of the output voltage is therefore at its maximum and is equal to one third of the input voltage as shown in figure 5.

Figure 5

It can be seen from figure 5 that at very low frequencies the phase angle between the input and output signals is “Positive” (leading), while at very high frequencies the phase angle becomes “Negative” (lagging). In the middle of these two points the circuit is at its resonant frequency, (f₀) with the two signals being “in-phase” or 0^o. We can therefore define this resonant frequency by using the following mathematical analysis.