Electronic – Active resistor for gain Control for reference pin in instrumentation op amp

What parameters of a real op amp determine the lowest voltage it can amplify?

It's all about signal (desired) to noise (not desired) ratio (SNR). The LM358 has an equivalent input voltage noise of 55 nV per sqrt(Hz). Now that probably sounds confusing but it isn't. Let's say your bandwidth is 10kHz\$^1\$ - the total noise will be 55 nV x sqrt(10,000) = 5.5 uV RMS.

If your signal level is 500 uV then your SNR is 20 log (500/5.5) = 39 dB.

Is this acceptable? I don't know but it would be fine for a telephone conversation.

Does it mean that it is not possible to amplify signals on the order of 2mV?

No the 2mV figure tells you that with a gain of 100 you will see an output offset voltage (an error) of 0.2V - this shouldn't normally be a problem in an AC amplifier.

\$^1\$ The onus is on the designer to incorporate filtering that sufficiently removes noise above 10 kHz - for instance a 1st order filter (a simple capacitor across the gain setting feedback resistor) is usually enough but, for this type of filter the "noise bandwidth" will be a bit bigger than that determined by the CR components (\$\pi/2\$ bigger). In other words a 10kHz filter will have a noise bandwidth of 15.7 kHz and this would raise the noise from 5.5 uV RMS to 6.9 uV RMS.

1) Yes. The usual way to handle this for an AC signal is to construct the feedback so that it has unity gain at DC, and your required higher gain above your minimum signal frequency. That way, only 1x the input offset voltage gets onto the output, rather than gain times.

2) The problem with bias current is that the resistance of the DC path attached to either input must be low enough to source this current, without developing excessive voltage drop. Think of input bias current as being due to current sinks at the input terminals, these are biasing the bases of the input transistors. If the input AC signal is AC coupled, then the R to ground at the input needs to be small enough.

3) Yes, as for input offset voltage, but multiplied by those R to ground input resistors.

You don't want to damage the equipment you are feeding into. It doesn't matter what filtering or feedback you use in your amplifier to control gains and offsets, you must assume that at some point, your amplifier output will hit the rails. If the equipment you are feeding will be damaged by that, then you must take additional steps to protect it.

One solution is to run your amplifier from low enough voltage rails that output saturation will be OK.

Another good solution is to use a pair of anti-parallel silicon diodes to ground after a suitable current limiting resistor from your output. This will clip the output voltage to +/- 0.7v from ground, and allow a signal of +/- 500mV or so with minimal distortion or gain error.

^{simulate this circuit – Schematic created using CircuitLab}

Not all of these AC coupling components are required, but I've shown them all to discuss what they do. Depending on the DC level of your source, the DC input requirements of the thing you're driving, your amplifier offsets and required system gain, none to all of these will be useful.

a) Input AC coupling, R1C1, prevents any input DC reaching the opamp.

b) Feedback AC coupling, R2C2, gives unity gain at DC, and high frequency gain of 11. Any input offsets appear at the output without the gain that the signal has. With a gain as low as 11, typical input offsets are unlikely to be a problem at the output, even if that gain is not rolled off at DC.

c) Output AC coupling, C3R4, removes any amplifier output DC from the final output.

d) The input bias currents will flow through R1 and R3, generating an offset voltage across these resistors. These voltages balance each other and do not create an amplifier output offset. For the amplifier shown which is FET input, these will be very low, and even megohm values for these resistors would be OK. With a bipolar input amplifier, values like this would be more appropriate.

e) The input offset current is the difference between the input currents. The difference in voltage generated on R1 and R3 does cause an output offset.

f) You may for input filtering or gain bandwidth reasons want R1 and R3 to be different values. This mismatch will generate an output offset voltage with the input bias current, but it will rarely be a problem, especially if you can AC couple the output.

g) Output protection of R5D1D2 limits the output voltage to around +/- 700mV, R1 limits the current into the diodes to something they and the amplifier can handle. This form of output protection will only work if +/-700mV is safe for your load, +/- 500mV signal level is adequate (600mV signals will start to get seriously distorted), and R1 is not so big that it limits output current excessively into the load, or its stray capacitance. If all of these are not met, you will need to do something more clever.