# Differentiator/Integrator circuits: Op-amp vs RLC circuits

It is possible to use a capacitor/inductor in an op-amp to allow it to perform the mathematical function of differentiating or integrating an input signal. It is also possible to do this without an op-amp, using simply resistors, inductors and/or capacitors.

So what are the advantages of using an op-amp for this purpose? It seems op-amps are the prime choice but I've searched online and haven't been able to find anything useful. Why are op-amps better for use as integrator/differentiator circuits?

Thanks!

BiP

Let´s discuss integration (more relevant):
1.) A simple passive R-C (or L-R) first order lowpss can be used as a (very poor) integator for frequencies very far beyond the 3dB cutoff frequency only.
This is because an ideal integrator must produce a phase shift of -90 deg between input and output.
Such a passive first-order lowpass produces this phase shift for infinite frequencies only! That means: For very large frequencies we can have phase shifts lower than 90deg only. An "good" integration is not possible - even if very large capacitors are used (large time constant - equivalent to a very low cutoff frequency).
As another consequence, the output voltage across this large capacitor is very low.

2.)This situation is much better for active integrating circuits. The corresponding circuit is the "Miller integrator", which exploits the Miller effect.
Here we have a capacitor C in the feedback path - which acts as an enlarged capacitor due to the Miller effect: C*Aol (Aol: open-loop gain of the opamp).
As a consequence, we have a rather large frequency range with a phase shift of app. 90 deg (89.5....90.5 deg) which can be used for integrating purposes.
As another advantage - the amplified output voltage now is available at the opamp output with reasonable amplitudes.
However, one should know that it`s an inverting integrator with +90deg phase shift.
However, non-inverting integrators are also available (BTC and Deboo integrators).

Svein
As long as you can live with the characteristics of passive circuit, by all means do so.Bear in mind, though, that they have different characteristics. An integrating RC combination has an exponential response, an op-amp integrator a linear response. As for filters, you have much more freedom when designing with an op-amp.

An integrating RC combination has an exponential response, an op-amp integrator a linear response.
Hopefully I am not too "sophistic" - however, if the step response has an exponential shape we cannot speak about an "integrating" circuit, do we?
(Instead, it is the classical first-order lowpass response).

Svein
Hopefully I am not too "sophistic" - however, if the step response has an exponential shape we cannot speak about an "integrating" circuit, do we?
Well, here is the standard step response of the passive RC circuit:

I think we can agree that this is not the integral of a step input. On the other hand, an integrator with an op-amp has this step response:

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jim hardy
Gold Member
Dearly Missed
As svein points out, with RC you can only approximately integrate and your time constant must be looonnnnggg with respect to the signal of interest..

More succinctly,
your RC is by nature a voltage divider
so your output signal will be smaller than your input signal. Considerably smaller.

An opamp relieves that restraint.
Try an RC integrator with a ten second time constant .. The attenuation is so great one's signal gets lost in the surrounding electrical noise of the room. Unless he has elaborate shielding.