# Does op-amp open loop gain change with DC input voltages versus small-signal AC input

I was wondering whether or not DC voltages can be amplified by op-amps. I thought about a typical Miller op-amp structure (differential pair input) and I suppose it could amplify a DC voltage.

I am slightly confused though, does the open-loop gain of the op-amp as a whole not change when faced with DC input voltages compared to small-signal AC voltages? We always derive our op-amps small-signal gain, DC large-signal gain will be different right?

From the Analog IC Design concepts I have learned, we always used to talk about the small-signal gain of different amplifier stages (common-source, gate, etc.) The DC voltages was just for bias. For example, lets say my amplifier was a MOS common-source stage with a drain resistance, the open loop small-signal gain would be -gmRd. But that's only small-signal, not a DC voltage.

• You seem to have a basic terminology confusion. On amplifier design, “DC” can sometimes be used to denote “Bias conditions” and “AC” to denote “small-signal conditions.” This is just the first two terms of a Taylor approximation to the circuit operation, and has nothing to do with the signals being actually DC or AC. Commented Apr 6, 2021 at 23:49

Let's first get this out of the way: the inputs have to be very close to each other in voltage for the op-amp to do anything besides be a comparator. This is because op-amp open loop DC gain is large, in the thousands to tens of thousands, and can vary by an order of magnitude in some cases. More about that here: https://www.analog.com/media/ru/training-seminars/tutorials/MT-044.pdf

That said, an op-amp can be configured with feedback to amplify DC as well as AC, small signals or large. It will nearly perfectly give the gain you're seeking so long as you understand the limits of what the particular op-amp you're using can do.

I think maybe what you're asking is, "is the gain affected by the DC offset of the signal pair?" The answer is yes, somewhat. The specification for this is expressed as the Common Mode Rejection Ratio, or CMRR. More about that here: https://www.elprocus.com/common-mode-rejection-ratio-cmrr-operational-amplifier/

Op-amps also have input offset error which affects DC gain fidelity.

• Thanks for the answer. Sorry, I wasn't clear in my original question. I'm coming at this from an Analog IC design course perspective. We have learned about common-source stage, common-drain, differential pairs and we told that these are the building blocks inside op-amps. When analysing these amplifier stages, we always looked at the small-signal AC gain, never the DC gain. The DC was only for biasing. So that's why I am slightly confused how the open-loop gain of the op-amp does not change for DC voltages compared to small-signal AC voltages. Commented Apr 6, 2021 at 23:04

Op amps are used all the time to amplify DC, or really slow DC coupled signals, or AC signals with DC bias.

As long as the op-amp input voltages and output voltages and currents are within the operating limits, they will just work.

If you look at the open-loop gain plot, or gain-bandwidth product, it simply shows that it is possible to amplify slow signals (DC) more that fast signals (AC). So by itself, signal being DC or AC does not change the open-loop gain plot in any way, you just have an open-loop gain that varies with frequency to begin with, and the signal frequency determines how much open-loop gain there is at the given frequency.

• Thank you for the answer. I understand that but my confusion is more at the transistor level. From the Analog IC Design concepts I have learned, we always used to talk about the small-signal gain of different amplifier stages (common-source, gate, etc.) The DC voltages was just for bias. For example, lets say my amplifier was a MOS common-source stage with a drain resistance, the open loop small-signal gain would be -gmRd. But that's only small-signal. Commented Apr 6, 2021 at 23:00