# MDS with DDC?

I'm not sure if I'm in the right section here -- please move this post if not.

Can someone tell me what the minimum detectable signal (MDS) should  be using a digital down converter (DDC)?  Assume I have a 14-bit A/D  with 74 dB SNR which feeds the DDC.  Say the A/D operates at 65 MHz (fs)  and then the DDC down-converts a 10 kHz BW (bw) anywhere in the first  Nyquist zone to baseband.  I think this means a processing gain of 10  log (fs / bw), for 10 log (65 MHz / 10 kHz) = 38 dB extra reduction in  the A/D noise floor, but I'm not quite sure what this means.  Does it  mean I would be able to resolve a signal just above 74 + 38 = 112 dB  below the full-scale of my A/D (well below the LSB)?  Would my MDS be  limited by the A/D noise floor, or the A/D floor lowered by the DDC  processing gain?

There is dither too.  I know that the spurious free dynamic range (SFDR) of the A/D  can be increased by adding dither.  Is this necessary to take advantage  of the 38 dB of processing gain?  Do the spurs of a NON-dithered A/D  remain after the DDC processing?  I think they would, but maybe that means that I can't resolve anything lower than the A/D noise floor.

Many thanks for any help!

• Hi,

I think this would best be addressed by pointing you to a seminar on our website on the fundementals of analog to digital conversion:

http://www.analog.com/library/analogDialogue/archives/39-06/Chapter%202%20Sampled%20Data%20Systems%20F.pdf

Your analysis calculates the improvement in SNR over the final 10KHz bandwidth, but your question is the minimum detectable signal level.   I think you are asking what the noise density is for 1Hz, which is the noise spectral density.  On page 42 of the seminar,  it walks through how to take the SNR and calculate the spectral noise density for any bandwidth.  Note that this is for an ideal ADC, which would have uniform white noise (perfect DNL).  In real world applications you will need to be sure the noise of signal presented to the converter is 5-10dB above the calculated spectral density to avoid errors.

Dither does help with that, and there is an excellent article by Brad Brannon,  a collegue of mine at ADI, that explores those issues.  Here is a link:

http://www.wirelessdesignmag.com/ShowPR.aspx?PUBCODE=055&ACCT=0004160&ISSUE=0106&RELTYPE=PR&Cat=0&SubCat=0&ProdCode=00000&PRODLETT=B&SearchText=brannon&CommonCount=0

As far as the spur content, the spurs in any portion of the ADC output spectrum would be preserved, the DDC will not filter them out.

Let me know if review this material and still have further questions.

Regards,

David

• Thanks, David.  That seminar is indeed a great help, and also Brannon's article.  It still doesn't quite answer my question though.

To use the example from pg 42 of the seminar, the SNR in the 30 kHz channel BW is improved by 30 dB, from 65 dBfs (dB relative to full scale) at the ADC to 95 dBfs after digital filtering.  Does this mean that a -92 dBfs signal at the input of the A/D will be 3 dB above the noise after the digital filtering?  Or will I only be able to resolve a signal at about -65 dBfs but it will have an SNR of 30 dB after filtering?

• Hi,

Hi, sorrry for the delay.  At the output of your filter, the signal would be 3dB higher than the sum of the noise power in the full 30kHz bandwidth.

Regards,

David

• Well, that's truly magic!  And good to hear -- thank you.