1. If pole and zero are exact the same, of course they are "transparent" to the signal path.
2. The pole-zero doublet effect requires pole and zero in the same s-plane(left s-plane). If zero in right plane while pole in left plane, even they have same value, it would not be a doublet.
3. Since pole-zero are very close, normally AC simulation can show its effects in the Amplitude-frequency/phase-frequency plot, however it does impact on transient response(linear part) as follows,
V(t)=Vo(1-k1*exp(-omegabw*t)+k2*exp(-omegaz*t)
where k2=(omegaz-omegap)/omegabw,
omegabw is the unity gain-bandwidth.
When omegaz=omegap, the linear step time constant depends on GBW only
4. You will never pay attention if the pole-zero doublet is at high frequency. E.g. like ahjua compensation, there is instrinsic pole-zero doublet and most of case regarded as fully cancelled and show very minor effects on transient response of the OPA with Ahjua compensation.
Hopefully you understand. |