# Stability and resonance

1. Nov 4, 2005

### EvLer

Can a circuit that has transfer function with poles in right-hand side part of the imaginary-real plane (unstable system) have resonant frequency?

2. Nov 6, 2005

### Staff: Mentor

Sure. Several of my circuit designs had a resonant frequency that they kept wanting to find.... :-)

3. Nov 7, 2005

### SGT

No passive circuit can have poles in the RHP. An active circuit can have them and the output (assuming second order behavior) will be:
$$ke^{\alpha t}cos(\omega_g t + \phi)$$, where [tex] \omega_g[\tex] is the resonant frequency.
Theoretically this circuit will produce oscillations in the frequency [tex] \omega_g[\tex] with amplitude growing to infinity.
In a real circuit, when the amplitude grows, non linearities arise and the circuit will oscillate with fixed amplitude. Only we would not have a sinusoid anymore, but a distorted waveform, whose fundamental frequency is [tex] \omega_g[\tex] .

I don´t understand why LaTex has not generated the correct image.

Last edited by a moderator: Nov 7, 2005