Wien Bridge Oscillator

Introduction

The Wien Bridge Oscillator is a circuit which can be used to produce a stable amplitude and low distortion sine-wave output.

A non-linear element must be employed in the feedback loop to ensure the signal amplitude does not continue building until the amplifier reaches saturation, nor decrease until the circuit ceases oscillation. Back-to-back diodes are often used however they introduce non-linear distortion on the order of 1-5% THD. An incandescent bulb/lamp can be used instead to stabilise the output amplitude - if the output starts to increase in amplitude, the filament of the bulb heats up, increasing in resistance and lowering the closed-loop gain. Accordingly if the output decreases the filament cools, resistance drops and closed-loop gain is increased. The time constant of filament heating and therefore change in filament resistance is on the order of many wavelengths of the sine-wave signal therefore negligible non-linear distortion is imparted by the bulb.

R1,R2,C1,C2 form a bandpass filter where R1=R2=r, C1=C2=c, and Fo=1/(2*pi*r*c). For continuous oscillation Rf and Rb are configured so that the closed-loop gain =-3.

Characterising bulbs

To characterise a bulb, it is hooked up to a bench powersupply with multimeters to measure the voltage across the bulb and the current draw at various points across the bulb's operating range. The resistance at a given voltage can then be calculated as the measured V/I. By graphing the data, the non-linearity of bulbs can be observed:

An ideal resistor would plot a linear line between (0,0) and (100,100) for current, and a constant resistance at any voltage.

The point of interest is where the gradient of the resistance curve is steepest, and happens to be at about 1.5~3% of the rated voltage for both of the bulbs tested. The voltage around this point will determine the optimal voltage of the output signal.

If we take the CML bulb, (1.5%~3%)*48V = 0.72v~1.44v. Since Rf and Rb form a voltage divider, and Rf=2*Rb, the output will be 3 times the voltage across the bulb. Therefore the optimal output voltage range for the CML bulb will be 2.16~4.32VrmsAC or 6.11~12.22Vp-p.

A general rule of thumb would be to choose a bulb rated at 10-20x the desired output voltage (VrmsAC), and as low power as you can find. Opamps generally increase in distortion as output current increases, so the smaller the current requirement for the bulb the better.

Real world testing

I decided to use the CML bulb and a target of 4Vrms output for the oscillator. Looking up 4/3=1.33V in the measured data gives a hot resistance of around 410ohms, so i used Rf=820ohms.

R1,R2=160Kohm and C1,C2=1nF gives Fo=995Hz. An LM4562 opamp was used with a +/-10v supply. The circuit measured 4.3Vrms output, with lower harmonic distortion than the FFT function on my oscilloscope could measure. The discrepency in oscillation frequency is due to the tolerance of the capacitors used.

I hooked up the output to my PC soundcard and recorded a 15 second clip of the waveform. This was then processed with an FFT in MATLAB and the output spectrum plotted. Total Harmonic Distortion can also be calculated.

2nd 3rd, 5th and 7th order harmonics can be seen clearly above the noise floor. The frequency stability of this circuit was not very good - it varied a couple of Hz every minute or so.

Improvements

I changed the capacitors to 100pF C0G Ceramic (previous 1nF were an unknown ceramic dielectric, likely Class 2 or 3), and changed R1 and R2 to 1MegOhm.

Frequency stability increased considerably and harmonic distortion was lower too with only 2nd and 3rd order clearly visible above the noise floor.

Microphonics

One disadvantage of using a lightbulb is that they are microphonic - that is, they convert vibration into an electrical signal.

Tapping on the bulb or even the breadboard causes serious fluctuations in the amplitude of the signal. I played a 4Khz tone through a nearby speaker and the tone appeared on the spectrum of the output: