Harmonic Oscillator Design - controls approach

[DragonPetter]

I have a question regarding an oscillator design from a controls perspective.

An ideal harmonic oscillator has just 2 poles, both on the imaginary axis, and their location along the axis determines the frequency of oscillation as well as the amplitude.

Now, please correct me if this is wrong, but there will never be a true physical circuit that can have this root-locus plot, right?

That leads me to think I should design the oscillator with the 2nd order oscillator equation, which is basically a bandpass filter. I can do this with two RC networks, a LPF and a HPF in series, but then I get a zero.

If I increase the gain enough and have a high enough Q factor, and apply positive feedback to push the 2nd order equations poles towards the imaginary axis, will I get the desired harmonic oscillation of just the peak frequency? Will it be distorted since other frequencies won't be entirely attenuated?

My main question is: is the 2nd order equation the way to go in designing a harmonic oscillator? I am using just 2 discrete transistors for gain and one to invert the phase again to get positive feedback, so it looks much like an astable multivibrator except with a different RC network.

 

[anorlunda]

You are partially right, a harmonic oscillator requires a 2nd order equation. I don't see why you think HPF and LPF.

The simplest harmonic oscillator is just two integrators in series with a negative feedback around the two.

$G=1/s^2$
$H=1$
$G/(1+GH)$ is the transfer function.