# A two-pole system can never be unstable?

I was reading in some textbooks and places online that a single pole introduces a -90 degree phase shift and that in the phase plot, it never actually reaches -90, it goes asymtotic to it.

Similarly, for a two-pole system, it never reaches -180 degrees, just reaches very close to it.

Does that mean that single-pole and two-pole systems can never be unstable since there is no phase crossover frequency?

• If you build what you think is a 2 pole system, you will often have additonal poles at high frequency due to finite opamp GBW products, strays etc, which at some frequency will tip you over into instability. Have you ever seen the humble emitter follower become an oscillator due to strays! – Neil_UK Jan 19 '20 at 7:34
• What do you mean by system? – Andy aka Jan 19 '20 at 10:27

• There are plenty two pole systems that are unstable, such as, $$H(s) = \frac{1}{(s-1)(s+1)}, ~~ H(j\omega) = \frac{1}{(-1+j\omega)(1+j\omega)}.$$