How does positive feedback generates ac waveforms in an opamp?

Question

How can an ac oscillation be obtained by using an opamp and some components and what is the working principle behind?

Answer 1

The principle is that it takes SO LONG for the signal to go through the circuit, that by the time it comes out and is looped around to the start again, it is exactly in-phase, exactly one-cycle-behind, exactly the input signal required to make an identical output signal.

Of course if the output is any bigger than the input was last time around, the signal will grow. If the output is any smaller than the input was last time around, the signal will drop.

So either the circuit has to be EXACTLY balanced just right so that the signal doesn't grow or shrink (almost impossible), or the circuit has to be more-or-less non-linear: if flattens out signals which are too big, it amplifies signals which are too small.

If the circuit is MORE linear, you get an almost-sine-wave going through the circuit. (Sinasoids are the eigenfunctions of linear systems). If the circuit is LESS linear, you get a square wave going through the system.

Since periodic signals are repetitive, the same delay can match any harmonic frequency. So oscillator circuits are also designed to block/diminish signals at other frequencies. Sometimes this happens more-or-less automatically, because the frequency response of the amplifier rolls-off at higher frequencies. Often the reason the frequency reponse of the amplifer rolls-off at higher frequencies is to prevent unwanted oscillation.

Either way, you can then feed the signal into another filter or another non-linear system, to get a sine wave from a square wave, or a square wave from a sine wave.

To get different frequencies, you adjust the delay, the time it takes a signal to go through and around the circuit. Any random noise at the input will start oscillation, and the oscillation will be at the delay frequency (because that's how long it takes to go around and through the circuit).

It's common to think of electronics as being immediate - you turn the switch on, the light comes on - but that's simply not true, as shown by circuits like this.

Answer 2

An op-amp oscillator can be two types usually: -

• A squarewave relaxation oscillator when the op-amp is used as a schmitt trigger
• A sinewave oscillator where the op-amp is used as a linear amplifier

I'm assuming that the question relates to the 2nd type of oscillator.

To generate a sinewave you need positive feedback to the input. Positive feedback means feeding back a signal that is exactly in phase i.e. op-amp output and op-amp input are in phase exactly. If they are not in phase exactly a sustained oscillation frequency is not achieved.

There are then two more criteria to be met for a sustained sinewave oscillation: -

• The feedback has to produce a non-zero degrees phase change for all frequencies except one.
• The feedback has to control the sinewave amplitude to prevent the op-amp from clipping i.e. it has to produce the coherent sinwave at just the right amplitude.

It's easy with a squarewave oscillator - you don't mind the op-amp saturating because it won't affect the shape of the squarewave but for a sinewave it can be a little tricky. The circuitry that produces only one coherent frequency is usually a phase shifting network made from resistors and capacitors i.e. it is a filter. Another type of phase shifting network has a specific name - a wein bridge oscillator. This also uses resistors and capacitors.

What ever method is chosen, the result is the same - the signal that gets fed back exactly (and coherently) reinforces the signal at the input to the op-amp amplifier.

Amplitude control is usually based around a circuit element that behaves like a voltage dependent resistor (VDR); the output signal is converted to a dc level representing the amplitude and this is used to reduce the op-amp amplifier's gain via the VDR - if the signal gets too big the gain is reduced thus, the amplitude is kept reasonably constant and free from distortion.