# Op-amp - Slew-Rate vs Exponential Output

I'm having some difficulty understanding why an op-amp has an exponential response even if its slew-rate is infinite?

Isn't the exponential response of the op-amp output caused by the parasitic capacitances of the internal op-amp structure (CGS, CGD, etc.). And the slew-rate is caused by output capacitance?

I'm having some trouble distinguishing the two. I always thought that the exponential response of an op-amp to a step input was due to capacitances.

## 1 Answer

Consider, when the output is slew-rate limited, the response isn't exponential, it's linear. So if there is an exponential response behavior, it has nothing to do with slew rate limiting and removing the slew rate limitation won't remove it.

Now if you study linear systems in general (such as simple RC circuits) you will see that single-pole linear systems have exponential responses (if I understand what you mean by "exponential response"). That is, the response to a step input has the form $$\y(t) = A\left(1-\exp(t/\tau)\right)\$$

So if you model your op-amp as a single-pole linear system it will have an exponential response. Of course the real op-amp's behavior is only approximately exponential, with the approximation being more accurate the more the op-amp acts like a single-pole linear system.

• Ah, I think I understand now. Let's say we have a large capacitor at the output of the op-amp. If the op-amp has infinite slew-rate, the output voltage will follow the exponential nature of the capacitor and it is able to supply tons of current as the capacitor needs it. However, if our op-amp is slew-rate limited, then we will see a linear output voltage as the current the capacitor is receiving is fixed at a certain value by the slew-rate. Would that be a correct way of thinking about it? – AlfroJang80 Jul 12 '20 at 15:41
• The capacitor doesn't have an "exponential nature". The combination of a capacitor with a resistive charging circuit (and no other energy-storage elements) does. – The Photon Jul 12 '20 at 15:44
• I see. I believe I need to review some of my basics. Thanks very much. – AlfroJang80 Jul 12 '20 at 15:54
• RC response due to linear compensation cap is exponential with no load. Slew rate is current limit controlled by some fixed R and current sense to cutoff and excess CdV/dt load current. Infinite slew rate implies 0 Ohm Rce or RdsOn drivers – Tony Stewart EE75 Jul 12 '20 at 17:16