# Sinusoidal Oscillators

**Sinusoidal oscillators** play an important role in electronic systems that use harmonic signals. Despite that, in many instances are known as linear oscillators, it is necessary to use some non-linear feature to generate a sine wave output.

In fact, the sinusoidal oscillators are essentially non-linear which complicates the technical design and analysis of such circuits.

The design of oscillators is done in two phases: a linear method based in the frequency domain using the analysis of feedbacked circuits, and a non-linear method, using nonlinear mechanisms for the control of the amplitude.

An oscillator is basically an autonomous circuit. In other words, this circuit is capable of generating a periodic sinusoidal signal with no need for any input.

A fundamental difference with multivibrator circuits is that these are not linear circuits (based on comparators, Schmitt triggers, …) as opposed to the quasi-linear circuits of the oscillators

The quality of the sine wave is expressed through the total harmonic distortion coefficient or THD, defined as:

Where Dk represents the relationship between the amplitude of the harmonic k and the fundamental harmonic described in Fourier series.

For example, the Fourier transform of a triangular wave has only odd harmonics, whose amplitude on the fundamental harmonic is 1/k. In this case, the TDH takes the value:

In other words, a triangular wave is a rough approximation of a sine wave with a THD of 12%. It is clear that the purpose of the sinusoidal oscillators is to generate signals with THD = 0.