Oscillator Theory Question

[geozog86]

Hello!

I was reading a book about classifying all oscillators, and i have the following question: What signal form does the output of a relaxation oscillator and of a harmonic oscillator have? Is relaxation a square-wave like output and harmonic a sinus-like output or is it something more general?

Thx very much

 

[Chipmunk]

I think you are right about the harmonic oscillator having a sinus output. If you define a harmonic oscillator as "a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x" (from wikipedia), then the sinus output follows from the differential equation of the system.

It's more complicated for the relaxation oscillator, I guess it can be pretty much any periodic waveform, because of the non-linear elements in the system.

 

[LvW]

Yes, it is the task and the goal that a harmonic oscillator produces a sinusoidal output.
However, because of the (small) non-linearity that is absolutely necessary for proper operation the output can be only "quasi-sinusoidal" (sinus with distortions).

The classical relaxation generator produces an exponential shaped signal across a capacitor that drives an amplifier (with positive feedback) into saturation - thus producing a squarewave signal.

 

[geozog86]

Sorry LvW but integrating a constant current on a capacitor gives a linear ramp, not an exponential signal (unless you consider the ramp as a slewed exponential signal???) and the rest you say i understand and agree And thx to both of you

 

[LvW]

Sorry LvW but integrating a constant current on a capacitor gives a linear ramp, not an exponential signal (unless you consider the ramp as a slewed exponential signal???) and the rest you say i understand and agree And thx to both of you

Yes - I agree in case of integrating the output of a current source.
However, I spoke about the "classical" opamp relaxation circuit (with a voltage source) driving an RC combination.

---------- Post added at 20:49 ---------- Previous post was at 20:38 ----------

By the way - perhaps I can challenge some forum members with the following claim:
A linear oscillator, which has the task to deliver a sinusoidal signal must contain a certain degree of non-linearity for proper operation. Sounds a bit contradictory, does it not?
(There are even some authors who claim that a harmonic oscillator is a "strong non-linear system"; I don't agree to that statement.)

 

[geozog86]

Guess: Suppose a one pole simple oscillator (which only builds relaxation oscillators, but still) : An oscillator transfers time information to amplitude information when excited.... So we have an amplitude changing, but in order to make it "periodical" then the slope is not enough. The system surrounding the time reference (RC? for example) needs to contribute. But it should not contribute with another timing reference (cause then we go to 2-pole oscillator). So it needs to have a non-linear behavior.

And this holds to a larger extent for a harmonic oscillator? Hmmmm but then again we have 2 poles, so the surrounding circuitry could be linear.

There's a gap in my newbie's way of thinking.....waiting with interest