Differences between Active/passive integrator/differentiators

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Active integrator circuits, utilizing op-amps, do not face the same frequency limitations as passive integrators due to their ability to provide gain, which enhances performance across a wider frequency range. This advantage also applies to active differentiators, which can respond more effectively to higher frequencies compared to passive differentiators. Additionally, active integrators and differentiators can function as low-pass and high-pass filters, respectively, similar to passive circuits, but with improved performance and flexibility. The output behavior of passive integrators is constrained by the relationship between output and input voltages, necessitating specific resistance and capacitance conditions. Overall, active circuits offer significant advantages in terms of frequency response and filtering capabilities.
mathman44
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Homework Statement



Hi,

I have a few questions about some differences between the two.

Why does an active integrator circuit, using an op-amp, not have the frequency restrictions found in a passive integrator circuit? Why does this also apply for two type of differentiator circuits?

Lastly, can active integrators/differentiators be used as low-pass and high-pass filters, respectively, in the same way as their passive circuit counterparts?
 
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The first one has to do with the fact that the output of a passive integrator circuit only integrates the signal if Vo<<Vi, so R>>1/wc.
 

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