Why does an Oscillator produce sine waves?

Question

By the definition of Oscillator: 'An Electronic circuit that produces a repetitive, oscillating electronic signal, often a sine wave or a square wave'
I'm familiar with RC Phase Shift Oscillator and Wien Bridge Oscillator. Both satisfy the Barkhausen criteria,so should produce an output, But why is the output Sine ?
If someone could elaborate using either of the two oscillators, or maybe some proof/result that give a better idea on the shape of the output wave.

I also know the principle of a square wave generator using op-amp, but that isn't an oscillator and works on the principle of saturation of op-amp. Am I correct in stating that oscillator and sq. wave generator are different ?

Answer 1

If the gain of a system at every particular delay is constant, the system will produce oscillations with those periods which have a gain of one. At periods where the gain exceeds one, the strength of the oscillations will grow unless or until something causes the gain falls to below one. If there were one frequency where the gain stabilized at exactly one, and it were less than one at all other frequencies, the circuit would produce a sine wave at the frequency in question. The wave would be a sine wave because any other type of wave would have content at frequencies where the gain is less than one.

Note that in practice, many types of oscillating circuits have gains which vary widely during the course of each "cycle". Such variations make it very difficult to predict analytically the frequency content of their output. Because there is a very fine line between having oscillations die down to nothing, and having oscillations grow without bound, even circuits which are intended to produce sine waves generally end up having a gain which is sometimes greater than 1 and sometimes less than one, though ideally there's a gain control mechanism that will try to settle on the right value.

Incidentally, some circuits use incandescent light bulbs for that purpose, since their resistance varies with temperature. If the power fed to a light bulb is proportional to the strength of an oscillator's signal, and if an increase in resistance will cause a reduction in gain, then the light bulb's temperature will tend to reach an equilibrium where the gain is 1. If the frequency in question is fast enough, the light bulb will only heat up or cool down a little bit during each cycle, allowing reasonably-clean sine waves to be generated.

Addendum

Rather than using the term "constant gain", it may be more helpful to use the term "linear circuit". To borrow an analogy from a magazine I read some years back, comparing "linear circuits" to "non-linear circuits" is like comparing "kangaroo biology" to "non-kangaroo biology"; linear circuits are a particular subcategory of circuits, and non-linear circuits are everything else.

A one-input one-output linear black box is one which takes an input signal and produces an output signal, with the characteristic that if F(x) represents the signal produced by the box when it is fed signal x, and if A and B are two input signals, then F(A+B) will equal F(A)+F(B). There are many kinds of things a linear black box can do to a signal, but all must obey the above criterion. The output produced by a linear black box when given a combination of many different frequency signals will be the sum of the outputs that would be produced for each frequency in isolation.

The behavior of many practical circuits is close to that of a one-input one-output linear black box. Since any wave other than a sine wave is a combination of sine waves at multiple frequencies, for a circuit to oscillate with anything other than a sine wave, there must be multiple frequencies which, if fed in individually, would cause the output to precisely match the input in phase and amplitude. While it is certainly possible to construct such circuits, most practical circuits will only have one frequency where such behavior will occur.

Answer 2

Why does an oscillator produce sine waves?

Often, sine waves are the desired output, for example in a radio system where we want to only transmit on a specified frequency band. We actually have to work hard to design an oscillator that produces a pure sine wave output.

Generally, by fourier analysis, any repetitive signal can be seen as a sum of harmonically related sine waves. If what we want is a sine wave, then all the harmonic content is considered harmonic distortion, and you need to use careful design and/or output filters to remove it.

I also know the principle of a square wave generator using op-amp, but that isn't an oscillator and works on the principle of saturation of op-amp. Am I correct in stating that oscillator and sq. wave generator are different ?

If it oscillates, I would still consider it an oscillator. Specifically, the op-amp circuit you're probably thinking of is a form of relaxation oscillator. Wikipedia even uses a diagram of an op-amp oscillator as the first illustration on their page on Electronic Oscillators.

Edit In reply to your comment, harmonic content is the content at frequencies that are harmonics (multiples) of the fundamental operating frequency. For example, from a 1 kHz oscillator you will get output at 1 kHz, 2 kHz, 3 kHz, etc.

The oscillator doesn't filter it out, but you can add a filter at the output of your oscillator to try to filter it out.

If you want a sine wave output, you design the oscillator carefully to generate as little harmonic content as possible. But in general, no matter how careful you are, there will be some harmonics in the output. They don't die out over time, they are part of the output as long as the oscillator runs. Supercat's answer explains some of the reasons why harmonic distortion in the output is unavoidable.

Harmonic content is often undesirable, so you try to design your oscillator to not produce it, but there are no perfect components, so you are always stuck with some harmonic distortion in the output.

Answer 3

Theoretically, RC and Wien bridge oscillators generate a single output frequency at a determinable precise point in the spectrum. This precise point in the spectrum will yield a feedback signal that is either:

• a 180º phase shift (plus an amplifer inversion = 360º) or,
• a 360º phase shift with a non-inverting amplifier

At other frequencies the phase shift will be different and will not sustain oscillation. A sinewave is a single point in the spectrum therefore a sinewave is produced by these types of oscillator.