How does the transfer function of a filter change if I change it form active to passive keeping the order and cutoff frequencies unchanged?
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If you keep all the poles and zeros the same, and use ideal components, the transfer function will not be changed.
If you use real components instead of ideal components, then the parasitics will likely change the transfer function somewhat. This could happen, though, even if you just changed from one active realization to another. If the components are well chosen, the parasitic effects should not have a large effect on the transfer function in the frequency bands you care about. It's unlikely you'll be able to avoid parasitics having some effect at very high frequencies (relative to your operating band), though.
answered Sep 6, 2015 at 2:20
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\$\begingroup\$ Yes - agreed, However, I would explicitely mention the influence of the limited and frequency-dependent gain of the opamps. I think this "deficiency" is not a "parasitic" property but an unavoidable deviation from the assumed amplifier characteristics. \$\endgroup\$– LvWCommented Sep 6, 2015 at 6:40
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\$\begingroup\$ Also note that "well chosen" passive components may not be physically or economically feasible - absurdly large capacitors, or large inductors with no parasitic capacitance and near-zero resistance - if the active filter has high Q sections. \$\endgroup\$– user16324Commented Sep 6, 2015 at 11:34