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# Few clarification on SNR/SNDR calculation

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#### dkumar

##### Member level 3
snr calculation

HI all,
I need some clarification on calculating SNR/SNDR.

I did cadence simulation of a sample and hold circuit and then took the FFT of the output. ( i did that keeping in mind the proper method of dealing sample data FFTs)

now i want to calculate the SNR/SNDR and i want to use matlab. I have following confusion.
(i save the FFT in .csv file)

1.As my data output is from sample and hold it is just sampled and not quantized.To calculate the SNR/SNDR so i need to quantize it? like to 0/1?

2.If no, i can then use the FFT output ( that is in dBs) directly or should i convert all the data back to non-dB format then use them?

3.If i use the direct dB format i plan to do the following for SNDR:
a. take the max. value ( will be my signal)
b. sum all the other dB values and remove signal from the sum.
c. Take the difference.

but this doesnt seem correct to me as it would give really a bad SNDR since all the noise summed values will be huge summation and signal component will be just a small number.

4.So, when i plan to convert the dB to non-dB (using 20*log(non-dB)) then i plan to do following for SNDR:
a.again take the maximum
b.sum all the other values and remover the signal from the sum.
c.divide the maximum by the sum. and then convert to dB.

this was all for SNDR.

for SNR, i have to remove the distortion components. So , if my circuit is fully differential , can i just remove all the odd harmonics from the signal band and then do the same as above.

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on the second though: i read somewhere, someone used fourier and fourier2ch instances in analogLib in cadence for calculation of THD and SNDR. if you have any idea about these components please help me understand them as well.

sndr calculation

refer this site

I think

in SNR , how to calculate the noise (thermal nosie etc....)

harminic component include in noise

i think the SNR and SNDR is sam reslut

i don`t know how to substrate or add harminic component to noise

sndr of quantized signal

You do not need to quantize the output of a SHA to calculate the SNR/SNDR. Moreover, you can do the calculation both in the dB- or V-domain. Just keep in mind that you are ***integrating*** not just summing the FFT bin values!
Last, even if your circuit is differential, you should still exclude the even harmonics from your SNR (and includethem in the SNDR).

fftw snr example

Hi dkumar,

Here is some help from a digital designer.

1 - You don't need to quantize it. Quantizing is equivalent to adding quantization noise, would you agree? So, since matlab handles double values, and the fftw libraries that it uses also do (www.fftw.org), there is no point in doing any quantization, and you still measure a higher SNR.
In case your question was related to scaling the signal to the interval from -1 to 1, if you only want to have the SNR measure, you also don't need it. If you would like to plot the magnitude of the fft, then you should scale it and divide by the number of samples that you gave to the fft function, and (I think) multiply everything by 2.

2 - The fft is an efficient algorithm (or set of algorithms) for calculating the N complex samples (equally spaced from 0 to 2*pi*(N/(N+1))) of the frequency domain of a signal, from a set of N samples from the time domain.
So, after calling the fft function in matlab, you get complex values. If you want to have the magnitude, use "abs(fft(...))". If you want to have it in dB, use "20*log10(abs(fft(...)))". If you want to have the phase, use "angle(fft(...))".
For calculating the SNR, I would prefer to use linear, as numeric integration of the noise spectrum power can be calculated by a simple sum of values from abs(fft(...)).

3 and 4 - Here are my recommendations:
- Use linear, instead of logarithmic, i.e. use values from abs(fft())
- Since you work with analog, be careful, as your maximum could be either at the frequency of your sine wave stimulus, or at DC. Running "plot(linspace(0, 2*pi*(N/(N+1)), N), abs(fft(...)))" can help you checking that.
- Be sure to have coherent sampling, i.e. the set of values that you provide to the fft contains exactly an integer number of periods of your sine wave. You can notice it in the plot of the fft, when your sine wave is a single, thin and tall line, instead of a not so tall, fat "mountain". This could be difficult to have in analog domain, I am not sure, so, you might think about using some windowing function on your data (Hanning, for example). I never used windowinf funtions but I can also tell you that providing a greater amount of data to the fft helps you reaching coherent sampling.
- When you see that the energy of your sine wave is only one sample of the fft plot (or only 3, if you use certain windowing functions), you can proceed to the following step.

Now I should add some sample code:
N = length(data);
sp = (eps + abs(fft(data))) * 2 / N; % Using eps, machine epsilon, you avoid getting -inf dB because of the fft getting to 0, even after you divide it by N, the number of samples that you provided to the fft function. Use eps and not realmin

s = ...; %Provide the index to your sine wave position, in sp
bw = ...; % provide the index to the end of your bandwidth of interest (could be pi, less than that, or a sub-multiple, in case you have some oversampling in your system)

sig_pow = 20*log10(sp(s)); % signal power
sp(s) = (sp(s-1) + sp(s+1)) / 2; % remove signal from the fft spectrum

noise_and_harms_power = 10*log10(sum(sp(2:bw).^2); % for calculating SINAD later, which I think is your SNDR
% I think you should use 2:bw, to avoid DC, as we also do in digital

harms = 0;
for h=2*(s-1):s-1:bw
harms = harms + sp(h+1)^2; % integrate the power of the harmonics
sp(h+1) = (sp(h) + sp(h+2)) / 2; % remove the harmonics from the fft spectrum
end

thd = -sig_pow + 10*log10(harms); % Total harmonic distortion

snr = sig_pow - 10*log10(sp(2:bw).^2); % snr calculation

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I hope I have helped you.
rmiguel

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