# The theory behind oscillator circuit

#### anhnhamoi

Joined Apr 24, 2012
11
Hi,
I am learning about oscillator circuit, in my text book draw out a basic configuration of oscillator circuit and from it they introduce the configuration of colpitts and Hartley oscillator and so on.I want to understand deeply about it but I can find where to give me detail about it.Would you help me explain why the oscillator have to configuation like that? Or can you show me where i can find the answers.

#### #12

Joined Nov 30, 2010
18,223
Just for starters, an oscillator must continue oscillating by itself or it isn't an oscillator. The output must get back to the input some way, and the closed loop gain must be more than 1 after considering all the losses and all the amplification. The path from the output back to the input determines the frequency of oscillation.

These things are true of every oscillator from a crystal oscillator to a guitar and a microphone.

That's all I have. Maybe you could google, "oscillator theory".

#### erik.lindberg

Joined Jan 11, 2014
3
Hi,
I am learning about oscillator circuit, in my text book draw out a basic configuration of oscillator circuit and from it they introduce the configuration of colpitts and Hartley oscillator and so on.I want to understand deeply about it but I can find where to give me detail about it.Would you help me explain why the oscillator have to configuation like that? Or can you show me where i can find the answers.
Oscillator basics

Oscillators are systems for which the variables of the mathematical models (differential equations and algebraic equations) vary with time with some steady state average amplitude and average frequency.
The variation may be limit cycle behavior or chaotic behavior.

Linear oscillators must be damped oscillators. You can't balance the poles on the imaginary axis in the complex frequency plane.

Steady state oscillators must be nonlinear circuits which means that it is very difficult to derive analytical conditions concerning oscillation (frequency and amplitude). Barkhausens criterion (observation) is just a starting point.

The kernel in our SPICE simulation programs is the iterative solution of a linear circuit at each integration step. If you investigate your oscillator as a time-varying linear circuit i.e. if you study the linearized Jacobian of the differential equation model for your circuit - the instant small signal model at the instant bias point - you may study poles and zeros.

The imaginary part of the complex pole-pair defines the instant frequency of the circuit. If it is as constant as possible as function of time during the period you may minimize phase noise and harmonics as Hewlett did in his master-thesis from 1939 when he invented the Wien Bridge Oscillator.

The real part of the complex pole-pair moves between the half planes of the complex frequency plane (RHP and LHP) so we have an energy balance determining the amplitude.

#### MikeML

Joined Oct 2, 2009
5,444