# Frequency of square wave generated by Wien bridge oscillator

I have designed the wien bridge oscillator circuit for 20Hz square wave generation. It gives a 20Hz sinusoid as output when I keep the non-inverting amplifier gain 3V/V. But when the non-inverting amplifier gain is very large, the circuit gives a 7.5Hz square wave as output instead of 20Hz. Why is the frequency 7.5Hz? How can I make it 20? Is there any general solution to this problem?

Here's the output:

The frequency response of the wien bridge:

• Reduce the gain to 3 and add a comparator.
– user16324
Feb 14, 2022 at 14:12

I don't think that the circuit can be seen as a relaxation oscillator. For a relaxation mode, the active device switches abruptly between charging and discharging a capacitor.

It is still a Wien-type circuit which, however, is operated in the non-linear part of the op-amp's transfer characteristic.

I am pretty sure that the reduction of the repetition rate (the term "frequency" should be reserved for sinusoidal waveforms) is caused by the very bad slew rate (large signal behaviour) of the amlifier (µA 741). It is well known that slewing effects will cause certain phase delays. Moreover, saturation (overdrive) delays within the amplifier may exist (depending on the 741-model used for simulation).

When you analyze the rise time of the square wave (increased time resolution) you will see that the slope will be app. 0.5V/µs.

Added: When the gain of the op-amp is larger than "3" (and without any other method for amplitude control) we will observe a certain clipping of the "quasi-sinusoidal" waveform.

And the clipping effect will increase when the gain is further rising - until the waveform looks like a squarewave. This is a continuous effect - but the circuit will not abruptly change its working principle from a "quasi-linear" Wien oscillator (no oscillator is really linear !) to a relaxation type.

• When the gain is more than 3 the circuit does switch suddenly between states because of the positive feedback through C2. It would still oscillate without C1. It is not a limiting sine wave oscillator. Feb 14, 2022 at 17:01
• No Sir - thats wrong. Measurements as well as simulations show that we get a sinus like waveform with limiting (clipping) effects. By the way: Each working WIEN oscillator has a small-signal gain which is (slightly) larger than 3. Remember that in relaxation circuits - which show such a switching effect - the positive feedback loop consists of resistors (without any delay) only.
– LvW
Feb 14, 2022 at 17:55

Its not a Wien bridge oscillator anymore when you increase the gain - its a relaxation oscillator.

The frequency will still be determined by R3, R4, C1 and C2 but in a different manner to that in the Wien bridge.

To create a square wave using a Wien bridge oscillator is usually done by feeding the sine wave from the oscillator into a squaring circuit such as a comparator.

• Is there any formula for the frequency? Feb 14, 2022 at 2:50
• I think it is stil a WIEN type circuit which is operated under heavy overdrive conditions. That means: Not a "relaxation type". The typical behaviour of relaxation circuits cannot be observed,
– LvW
Feb 14, 2022 at 9:37

Because when you have gain higher than 3V/V, you get faster transitions.

With faster transistion, you get a square wave rather than a sine wave.

With a square wave, the capacitors in the relaxation oscillator charge or discharge at maximum (saturated) voltage as soon as the transition occurs instead of gradually building a voltage differential (sine wave) to charge or discharge the caps.

Faster charge or discharge cycles means higher frequency of oscillation.

• But I get a square wave of lower frequency,7.5Hz. The wien bridge is designed for 20Hz sinusoid if non-inverting amplifier gain is 3V/V. Feb 14, 2022 at 8:30