In Wikipedia's positive feedback article it is stated that given the closed loop gain $$A=\frac{a}{1-af}$$ the system is unstable if \$af>1\$.
I don't really get this. If \$a=10\$ and \$f=0.5\$ (just to give a very simple example), I just see that \$af>1\$ but \$A=-2.5\$, which is not infinite. So what is really happening here?
I know that a system is unstable if the transfer function (i.e. the gain in Laplace domain) has poles in the right-half complex plane. But here, \$A\$ would be a constant so I don't see why unstability would occur.
This question arised when I was trying to analyze a Schmitt trigger using feedback. Quantitavely, I see why the output will go to saturation voltages. I just don't see it mathematically. Suppose that the Op-Amp was ideal (so it has infinite gain and it doesn't depend on frequency). Then why would, mathematically, anything diverge in this circuit, if \$A=\frac{-1}{f}\$ which is a finite value? That's the question that led me to thinking about positive feedback and unstability in general.
To sum up:
- Why is positive feedback often related to unstability?
- Why does \$af>1\$ imply that a system is unstable if using positive feedback?
