How to calculate SNR and ENOB using the accuracy table?

[Hesham]

Hello
In the specs document SNR and ENOB are not mentioned explicitely, it only contains the "Absolute Accuracy Table"
How can I calculate SNR and ENOB using this table?

[Ima U]

Hi,

From my understanding, you would like to know how to calculate the signal to noise ratio (SNR) and effective number of bits (ENOB) since it is not found in the spec.  I am assuming you are referring to the DSA and High speed digitizers.  Here is a great knowledge base that explains how to SNR.  As for ENOB, you will need to refer to this KB.

I hope this helps!

[Hesham]

I am using NI 6221 and NI 6115 DAQs
The specs sheet doesn't contain any information about SNR, SINAD, SFDR, ...
I think ur links is talking about something else
Anyway, thank u for ur reply 🙂

[ChrisR.]

SNR and ENOB are typically a function of signal frequency and amplitude. However, you can estimate low-frequency SNR and ENOB from a board's noise specifications. The underlying assumption in the following is that nonlinearity is not a significant factor, which is probably close to true in the case of the 6221 and 6115.

SNR just means Signal-to-Noise Ratio. Consider the first line of the 6221 accuracy table, which states noise of 244 uV rms on the +/-10V range. The biggest sine wave that fits in +/-10V is 10V/sqrt(2) rms. Thus the SNR is 10V/sqrt(2) / 244uV = 28980. Expressed in decibels, that is 20xlog10(28980) = 89dB.

The formula for ENOB is based on the fact that a "noiseless" ADC has quantization noise of 1LSB/sqrt(12). Thus ENOB = log2((total range)/(noise x sqrt(12))). Taking again the case of the 6221 on the +/-10V range, this works out to log2(20V/(244uV x sqrt(12))) = 14.5 bits.

The 6115 specs don't list noise in rms, but the dynamic specs list noise (not including quantization) of 0.35 LSB rms. Adding 1/sqrt(12) LSBs of quantization noise gets us total noise of sqrt(0.35^2 + 1/12) = 0.45 LSB rms. On the 10V range that works out to 0.45/2048 x 10V = 2.2mV rms. Then we calculate SNR and ENOB as above to arrive at SNR = 70dB and ENOB = 11.4 bits.

Note that the SNR and ENOB numbers you compute will depend on range. Smaller ranges typically have more noise relative to the amount of signal they can accommodate, so the SNR and ENOB will be lower.

Chris

[Hesham]

Thanks Chris!

ur reply is really helpful

But I still have two questions:

1. Does this mean that absolute accuracy doesn't affect SNR?
2. In the "Absolute Accuracy Table" the sensitivity is given, how it comes that it is less than the LSB?

[ChrisR.]

Does this mean that absolute accuracy doesn't affect SNR?

Yes. SNR and ENOB are affected by noise and linearity. These also affect absolute accuracy, but there are other factors that affect absolute accuracy that have no effect on SNR and ENOB.

In the "Absolute Accuracy Table" the sensitivity is given, how it comes that it is less than the LSB?

If you have sufficient noise/dither in your system, you can resolve less than 1 LSB by averaging. (See http://zone.ni.com/devzone/cda/tut/p/id/3016#toc5 and http://zone.ni.com/devzone/cda/tut/p/id/3488 .) You'll notice that in the 622x accuracy table, the sensitivity is just 0.4 times the rms noise. I believe the idea is that if you average 100 samples, your noise decreases by a factor of 10. The peak noise induced error would be roughly 4 times the rms value, so you end up with a multiplier of 0.1 x 4 = 0.4. Of course if you average a different number of samples, or none at all, the "sensitivity" would change. So just ignore that column and use the noise column instead.

Chris

[Hesham]

Thank u Again 🙂

But please be patient with me because I still have two other questions

1. I understood from u that the quantization noise is already included in the rms noise entry in the accuracy table of 6221. Is that correct?
2. u said that we neglected the effect of nonlinearity on SNR. What shall we do if we want to consider it?

[ChrisR.]

I understood from u that the quantization noise is already included in the rms noise entry in the accuracy table of 6221. Is that correct?

Yes.

u said that we neglected the effect of nonlinearity on SNR. What shall we do if we want to consider it?

Actually, nonlinearity doesn't affect SNR, but it does affect ENOB, because ENOB is usually defined to include the effect of distortion. I don't have a formula that modifies ENOB to include nonlinearity effects, because it would really depend on overall nonlinearity, not just worst-case nonlinearity, which is what is specified. For example, the 6221 has an INL spec of 76 ppm of range. That means that over the range of -10V to +10V, the nonlinearity somewhere could be as bad as 760uV. But it could be perfect almost everywhere else, and the net effect on the ENOB would be very small. I think you'd need something like an rms nonlinearity spec to be able to add its contribution to the noise. As a guess, I'd say maybe the rms nonlinearity of the 6221 is something like 0.5 LSBs, which is about 150uV. We'd add that to the rms noise of 244uV as follows: total = sqrt(150uV^2 + 244uV^2) = 270uV. So the ENOB would drop to 14.4 bits. Remember this is just a guess. The best way to know for sure is to measure it.

Chris

[Hesham]

I am really grateful

Thanks