# Which op-amp parameter indicates the minimum amplificable voltage?

I'm a newbie trying to measure μV-range voltages using cheap op-amps, with some software calibrations or error corrections, for education and practice.

At first, I looked at some op-amp datasheets and looked for parameters with their unit defined as "mV" or "V", because I thought it should be indicated as volts, but didn't find anything which I could relate except Vio. I think that aforementioned parameter which I call "sensitivity" should be Vio (input offset voltage), because it's the minimum differential voltage that can make the output non-zero, and hence, amplify it.

According to this document from TI it is defined as:

The input offset voltage is defined as the voltage that must be applied between the two input terminals of the op amp to obtain zero volts at the output.

## So, is this unknown parameter, the Vio?

If the answer is yes, the LM358 datasheet mentions a Vio of 7 mV maximum; this means that, for example, a differential voltage of 1 V and 1.007 V should be amplified. But the question is, does the output change when we change the 1.007000 V to 1.007001 V? Also, in some op-amps, the offset voltage is "nullable". Does this affect the sensitivity?

If the answer is no, then which parameter indicates the minimum voltage? So we know if this op-amp is good to use in the μV or even nV range?

Thank you for your time and knowledge.

• I think you're thinking about this in the wrong way, but I'm too tired right now to properly work out how to explain things. You're not going to find any op amps that can amplify nanovolts, though; that takes some real specialty equipment. Nov 28 '21 at 7:39
• Using twisted pairs for Diff and using a shield helps improve sensitivity by balance cancelling noise . Using a common mode signal as a guard is even a better shield. Nov 28 '21 at 8:39
• The opamp's 'input offset voltage' spec is not a threshold, it's an error source. Nov 28 '21 at 13:13
• Obligatory reference on measuring not nano- but femto-amperes, from 1993: electronicdesign.com/technologies/test-measurement/article/… Nov 28 '21 at 17:19
• Just to clarify your question: Do you wish to distinguish the difference between $0\mathrm V$ and $1 \mu \mathrm V$, or $1 \mathrm V$ and $1.000001 \mathrm V$? Those are very different problems. How quick of a change do you want to see? Do you wish to only use an op-amp, and consider things like analog switches, diodes, and/or transistors to be "cheating", or not? Again, those are very different problems. It may not be obvious to you, but the question is kind of sliding into "give me a 4-year course in analog circuit design, in the space of one Stackexchange answer, please". Nov 28 '21 at 19:53

Opamps are analog. There is no smallest step to them.

Instead there are various noise sources at play, which will be given in datasheets..You weigh those against your signal magnitude to obtain a signal-to-noise ratio (SNR).

When you know SNR you can calculate the necessary integration time needed to discern a certain voltage step.

However, it is not possible to just integrate arbitrarily long to attain arbitrary precision. There is a fundamental precision limit. As you speak about nanovolt measurements I assume you have a low source impedance and current noise is inconsequential.

In this case the base precision is given by the point where the 1/f slope of input voltage noise density crosses 1 Hz. E.g. for the OPA211:

It has very low wideband noise, but due to 1/f noise, it is impossible to make a DC voltage measurement, more precise than 6 nV, regardless of how long you integrate.

Due to 1/f noise the precision has a lower bound. So what you should be looking for is opamps with low 1/f voltage noise, e.g. zero-drift opamps.

Alternatively, you can do AC voltage measurements, but I will not go into this as your question doesn't suggest you can modulate the source easily.

The input offset voltage and current is inconsequential in my opinion. These are static offsets, that you can easily compensate in software unless you let them saturate the opamp due to ultra gains of 1000 or something. The noise discussed above is dynamic and cannot be simply removed in software. For the LM358, I could only find a plot down to 10 Hz:

Without thinking too much, one can guess that the noise at 1 Hz will be about $$\\sqrt{10}\$$ times higher, so this will lead to the base precision of about 174 nV, for integration times that are at least a few seconds long.

• Tirdad as @TimWescott mentions in comments, this is only about the opamp. If you want to actually measurr something you would also require a voltage reference and ADC and probably some gain setting resistors. Each of those will have their own share of both 1/f and wideband noise. And I agree that going into all of this would be excessive. My answer explains what to consider for each single element though and you can do similar analyses for each of the other elements. The sentiment is that 1/f fundamentally limits DC precision Nov 29 '21 at 1:21
• yes. I'm going to set a suitable gain and measure it using an ADC. then apply some error correction. I thought the op-amps have a resolution like an ADC. Nov 29 '21 at 6:27
• Indeed. Many decades ago, one of the most illuminating pieces of advice I read went something like this: "It's easy to make a sensitive instrument. It's hard to make a sensitive instrument insensitive to all the things that can disturb its operation." I think it was C. L. Stong in his Scientific American column. Nov 29 '21 at 14:59

There's no minimum threshold, but...

Input offset voltage can add a significant error to the small voltage you're trying to measure. This is only a problem if the signal is DC: a bit of DC offset doesn't change the peak to peak or RMS value of an AC signal, it just shifts the whole signal. If you can switch the voltage to be measured on and off, and you use an ADC after the opamp, you can also measure the offset without signal, then turn on the signal, measure again, and substract, which removes the offset. You can also trim the offset with a circuit that shifts the input voltage, and in this case the important spec becomes drift versus temperature.

Offset can be a problem for another reason: if the circuit has a lot of gain (say, 10000) and the opamp has an offset of 1mV, then it will output 10V. If the opamp only has a 5V power supply then it will clip, so that won't work.

Another issue is noise, which can obscure the signal. You can average with a lowpass filter or take many measurements with your ADC to remove the noise, but if that takes too long, then you need a lower noise opamp.

There's no minimum voltage that can be amplified by operational amplifiers.

nV voltage signals, from operational amplifiers point of view, have the same dignity of mV or V signals.

RF amplifiers, for example, amplify nano Volt signals arriving from the antenna.