# How to measure bit resolution

I have a system that has a bit resolution of 1.9uV (gain 20), to increase the bit resolution the gain stage was increased at the input of 180V/V which lowers the effective bit resolution to 0.21uV.

I have a DAQ system that is able to record signals in the uV range. I am wondering how can I verify that I am getting the noted effective bit resolution? Is this feasible or at this bit resolution we just trust the data sheet and calculations?

If so how is the bit resolution measured or verified in general?

• 1.9/180 is not 0.21. Apr 26 at 10:35
• 1.9 was already a gain of 20, forgot to mention Apr 26 at 10:39
• @enhzflep it's excessively hard to "apply 1.9 µV"; what device gives you a voltage with that accuracy, and how to you connect it to the device under test without voltage drop or static and HF fields being more important factors than that? Apr 26 at 12:06
• @enhzflep and you'd be right imaginging you'd be monitoring the signal where it entered the device and compare that to what the device under test says! But the physical setup is a bit more involved, possibly. Apr 26 at 12:27
• Are you clear on resolution vs. ENOB? Which do you want to measure? If you short the input and look at the output you'll see discrete steps due to noise, the smallest height of which will show the the resolution. Apr 26 at 17:46

You should get a suitable, linear signal generator with a dynamic range that is suitable to your system. If you can do an automated measurement even better, but essentially what you are doing is a simple manual characterisation of your system with a calibrated and accurate source. This will not only provide you with a good understanding of the linearity, but at the small voltage levels when you get down to the noise floor, you can essentially extrapolate beyond the resolution into the noiose, to obtain what you think is the bit resolution of your system in question. Hope this helps and gives you a lead on how to proceed ...

• I think the part worth stressing is "get a suitable,…", i.e, this is a calibration job, and you'll need a calibrated, low-noise reference, not just some random adjustable power supply. In the µV range, you need shielding, and/or load impedances for external static E-fields to be sunk into, if the DAQ inputs are high-ohmic. I wouldn't know how to calibrate something this well! Apr 26 at 12:04

I am wondering how can I verify that I am getting the noted effective bit resolution?

This is a very cheap and very good DC test I have used on all the ADC/DAQ systems I have ever brought into life. It's not 'calibration' as such, which requires very expensive hardware, but it will tell you whether you have any missing codes, what your differential linearity is, and what your real resolution and noise level is.

It is totally passive, so it's as low noise as you can get. No instrumentation noise, no power supply noise, no ground loops, the only noise you're going to see is the noise of your ADC itself.

simulate this circuit – Schematic created using CircuitLab

Charge C1 to some suitable voltage, and let it discharge into R1. For verifying no missing codes and differential linearity, it doesn't really matter whether the discharge is dominated by the DAQ input current (maybe linear), dominated by R1 (exponential), or a mix of both. Choose R1 and C1 to give you many (10s to 1000s) of readings per expected resolution step, and write a program to analyse what you get. If you use a big electrolytic, relaxation or reforming currents may confound your predictions of what should happen to the voltage, at least until it's settled down, however it will be smooth and zero noise. Plastic caps will be more predictable.

Your two pole SW2 could be a plug and socket, to allow you to mount the components in a small shielded box right at the DAQ terminals, for minimal RF/mains hum pickup without even the switch-isolated wires to V1 contaminating anything. Repeat the experiment with the components further away from the DAQ, to see whether your cabling is picking anything up.

• So I am measuring the capacitor discharge using the DAQ? For the connection to the DAQ, Can I use one for a channel and one to ground or each end goes to a channel and the DAQ ground is floating? Apr 26 at 14:20
• You'd use it on a single-ended channel. If you wanted to do a differential channel, you could either use one of these with each output going to the + and - inputs of the diff channel - this would give you an uncontrolled common mode, which could be a valid regime in which to test it. Or you could use two of these, each one from ground to one of the active inputs, this would allow you to control the common mode. Basically connect this up instead of the signal you want to measure. Apr 26 at 15:58