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 niloun Community Member Offline Posts: 47 SAR ADC SNR variations for different FFT numbers Sep 30th, 2017, 1:51am   Hi everyoneI would like to calculate the dynamic specifications of an SAR ADC that I have designed in Cadence. I have imported the output data (D0~D8) of my SAR ADC from Cadence into Matlab to calculate the FFT.I have done this process for N=64 , N=512 and N=4096, and I don’t understand why the SNR is increased when the number of FFT points is increased?I have used an integer number of cycles, however, when I use a Hann window the extent to which the SNR varies for N=64 , N=512 and N=4096 declines considerably. 1- Does SNR change when we increase N (FFT number)? I think it shouldn’t change because total noise power is constant.2- Are we allowed to use both integer number of cycles and a Hann window? Thanks in advance Back to top IP Logged
 carlgrace Senior Member Offline Posts: 231 Berkeley, CA Re: SAR ADC SNR variations for different FFT numbers Reply #1 - Oct 2nd, 2017, 8:50am   The noise floor of the FFT itself declines when you use a longer FFT. If the SNR is improving as you increase the length of the FFT, that means that you are being limited by the FFT and not the ADC. When you get to the point the ADC is limiting SNR using a longer record won't improve SNR.You should consider using a prime number of cycles rather than just an integer. An integer is OK, but you may get some samples landing on top of each other which will make it appear like you have less data.Also, if you are using coherent sampling correctly (integer/prime number of cycles) using a Hann window should be needed (all your input power should fall into a single FFT bin). Back to top IP Logged
 niloun Community Member Offline Posts: 47 Re: SAR ADC SNR variations for different FFT numbers Reply #2 - Oct 3rd, 2017, 1:17am   Thanks so much for the answer.carlgrace wrote on Oct 2nd, 2017, 8:50am:The noise floor of the FFT itself declines when you use a longer FFT. If the SNR is improving as you increase the length of the FFT, that means that you are being limited by the FFT and not the ADC. When you get to the point the ADC is limiting SNR using a longer record won't improve SNR. I understand that noise floor declines when FFT size increases because of the formula below (-10log(n/2)): But what I don’t understand is that the noise power must be distributed between noise bins (either 62 or 510) and the total power of the noise bins should be constant hence the snr must remain constant. I don’t find any theoretical reasons for total noise power variations and it is confusing me. What do you exactly mean by SNR being limited to FFT?carlgrace wrote on Oct 2nd, 2017, 8:50am:You should consider using a prime number of cycles rather than just an integer. An integer is OK, but you may get some samples landing on top of each other which will make it appear like you have less data. Yes I totally understand what you mean and I have used prime/integer number of cycles, “integer number of cycle” is a term used in Stanford lecture notes meaning the same thing you just explained: carlgrace wrote on Oct 2nd, 2017, 8:50am:Also, if you are using coherent sampling correctly (integer/prime number of cycles) using a Hann window should be needed (all your input power should fall into a single FFT bin). Fine, but according to Stanford lecture notes, windowing will distribute the sigbin power between some bins: Back to top IP Logged
 sheldon Community Fellow Offline Posts: 751 Re: SAR ADC SNR variations for different FFT numbers Reply #3 - Oct 3rd, 2017, 9:02am   Niloun,  Comments:1) Carl's approach includes an integer number of clock and signal    periods, for example: 13 periods of the signal and 256 periods    of the clock. So, the signals will be periodic in the data record    used for the FFT2) The reason for using the approach Carl suggest is to assure that    the clock and signal are not harmonically related. For example,    if the clock is 100MHz and the signal is 10MHz, there are only    10 lsb levels tested in the simulation. So the SNDR/SINAD will    be correct, but the SNR and THD will be incorrect. Since all the    energy will be concentrated in 10 bins of the FFT 3) If you follow the guidelines that Carl suggests, you can use the    Rectangular window which means that there is no signal spreading4) For Delta Sigma, #1 is still applied but you will need to use a    window function                                                                     Sheldon Back to top IP Logged
 niloun Community Member Offline Posts: 47 Re: SAR ADC SNR variations for different FFT numbers Reply #4 - Oct 3rd, 2017, 9:53am   Thanks Sheldonsheldon wrote on Oct 3rd, 2017, 9:02am:Niloun,1) Carl's approach includes an integer number of clock and signal    periods, for example: 13 periods of the signal and 256 periods    of the clock. So, the signals will be periodic in the data record    used for the FFT2) The reason for using the approach Carl suggest is to assure that    the clock and signal are not harmonically related. For example,    if the clock is 100MHz and the signal is 10MHz, there are only    10 lsb levels tested in the simulation. So the SNDR/SINAD will    be correct, but the SNR and THD will be incorrect. Since all the    energy will be concentrated in 10 bins of the FFT I totally understand, I had done my calculations as you and Carl said, for example, when using 64 FFT points I choose Fin according to the formula below:(Fin/Fs)=(cycles/FFTpoints)If Fs=200K and I have 64 FFT points I choose cycles to be 7 so I will have: Fin=7/64*200K=21.875KAnd if I choose 512 points and 51 cycles Fin will be 51/512*200KBut it’s not helping and ENOB improves when FFT number is increased. Back to top IP Logged
 sheldon Community Fellow Offline Posts: 751 Re: SAR ADC SNR variations for different FFT numbers Reply #5 - Oct 3rd, 2017, 10:13am   Which goes back to Carl's other comment, that the noise floor of the FFT is above the noise floor due to quantization noise. You need to increase the number of FFT points until the noise floor is constant. Back to top IP Logged
 niloun Community Member Offline Posts: 47 Re: SAR ADC SNR variations for different FFT numbers Reply #6 - Oct 3rd, 2017, 10:35am   sheldon wrote on Oct 3rd, 2017, 10:13am:Which goes back to Carl's other comment, that the noise floor of the FFT is above the noise floor due to quantization noise. You need to increase the number of FFT points until the noise floor is constant.   As I know the noise floor of the FFT is the sum of SQNR (obligatory noise due to quantization) and processing gain(10log(N/2)), so theoretically FFT noise floor is always under SQNR. How is it even possible for the FFT noise floor to go beyond SQNR?What kind of FFT limitation forces noise floor to go beyond SQNR? Back to top IP Logged
 sheldon Community Fellow Offline Posts: 751 Re: SAR ADC SNR variations for different FFT numbers Reply #7 - Oct 3rd, 2017, 4:05pm   Niloun,    Oops, misspoke. You are confused. You are assuming that the FFT noise floor is the same as the total noise. The SNR calculation uses the total integrated noise across the Nyqvist band, from 0 to Fsample/2.As you increase and decrease the number of FFT points, you are raisingand lowering the noise in the individual FFT bins. However, the total noise, calculated by integrating across the band is constant.                                                                         Sheldon Back to top IP Logged
 sheldon Community Fellow Offline Posts: 751 Re: SAR ADC SNR variations for different FFT numbers Reply #8 - Oct 3rd, 2017, 4:12pm   In answer to the last question, you can't do better than the quantization limited noise floor for the total noise of the  ADC. The resolution of the FFT is limited by the number of bits. However, by increasing the number of FFT bins, you can decrease the FFT noise floor. So, you can lower the FFT noise floor to as much as you want at the cost of increased simulation time. However, the SNR won't change because every time you make the FFT bin size smaller, you more bins.                                                                       Sheldon Back to top IP Logged