If you plot the gain vs frequency of a cmos amplifier for example, the poles are the places the the gain starts to fall -20db/dec and the zeroes are the places it start to rise 20db/dec.

But according to the transfer function H(s), the poles are the places where the gain approaches infinity and zeroes are where it approaches zero. So why are the these not represented as spikes or dips in the plot?

 

I figured this out. Forgot it was the magnitude of H(s). So a pole for example would look like this: \(sqrt{\omega^2 - p^2}\)

As omega approaches p, the p value is still much bigger so it dominates and leaves the magnitued largely unchanged. When omega reaches p, that is -3db point (halved), then the omega term dominates.