If I build an analog receiver using a DDS where the DDS is my local oscillator (LO), based on a reference oscillator with phase noise ℒ(n), as I decrease the frequency that I tune to, my DDS frequency is reduced and I realize a reduction in phase noise of the LO and consequently of my system.

If I direct sample a similar spectrum, I will have a sampling clock instead of a DDS. That clock would necessarily be at least twice the frequency I want to sample. After I have sampled, I decide to tune (mix in the digital domain using an NCO which can also have phase noise) and decimate. Am I able to realize any reduction in phase noise as a result of either the mix (with a "low noise" NCO) or in the decimation process? If so, is are there rules about how the phase noise of my sampling clock would be affected in these processes to enable me to calculate my system's phase noise if I know my sampling clock's phase noise?

I wrote a post on ADC jitter which may be of some help.  Here is a link.

https://www.dsprelated.com/showarticle/1157.php

You also can look at references 1 and 2 at the end of my post.

regards,

Neil

Neil,

Thanks, much, for your reply. I found your jitter model interesting. The links at the bottom ended up leading me to AN-756 and AN-741 at Analog Devices which really answered my first question. Essentially, with a direct sampling receiver, I am able to recognize the same 20log(freq_tuned/sampling_clock) that a traditional DDS-based superheterodyne receiver would benefit from. In other words, the phase contribution from a 100MHz sampling clock receiving a 10MHz signal using direct sampling would be 20log(10/100) = -20dB. This is the same as using a DDS as a LO. I appreciate the reply and your original post.

Steve

Hi Steve,

Great!  Nice to see agreement of results.

Neil

This link directly explains DDS phase noise. I don't see any difference between DDS and NCO except that DDS is usually referred to a dedicated NCO commercial chip. So clock jitter and NCO phase issues are common between the two cases.

Remember you can't decimate unless your sampling frequency is high enough.

https://www.analog.com/media/en/training-seminars/...

I have seen "DDS" referred to the combination of an NCO with a D/A (meaning providing an analog output) whereas an NCO is providing a digitally generated source. I like that distinction since I also associate "synthesizer" when referred to as an RF source as a providing an analog output. 

Yes, synthesizer is a significantly overloaded term. It also applies to recombining polyphase channelizes channels that have perfect reconstruction.

An NCO is equivalent to a fractional divider of the master clock. In general when you divide any frequency tone with phase noise by $N$, the phase noise goes down by 20Log10(N). And similarly when you multiply a frequency tone by  N, the phase noise goes up by 20Log10(N). This is clear when you consider the case of a simple doubler: when you double the frequency, you also double the phase, and phase for small angles is directly proportional to sideband magnitude (and if you double a magnitude quantity, it increases by 20Log10(2)=6 dB).   

Consider a doubler as cos(2pift+phi)cos(2pift+phi), multiplying cosines is the sum and difference of the frequencies (and phases!) resulting in the following for the sum term:

cos(4pift+2phi)    Double the frequency and double the phase; if the phase was modulated as phase noise, the instantaneous phase deviation would double, and the phase noise spectrum would shift up by +6 dB.  

Dividing works the same way; if you divide a frequency by two, the phase is also reduced by 2. 

Ultimately there will be a noise floor (typically for digital frequency dividers are -155 to -160 dBc/Hz) after which no further improvement can be reached. 

Ahh yes, love this explanation. Thanks very much for passing it along!

A DDS or NCO has some noise sources that have been treated in literature fairly thoroughly, with a lot of tricks on how to mitigate noise effects in them.   Whether the mix is analog or digital, the noise sources in the DDS/NCO may be the same and may require the same mitigation if they're big enough to be problematic.

If the mix is digital instead of analog then a number of noise or distortion sources go away, so some of the manifestations of phase noise will likely be reduced.

Phase noise by itself is usually very narrow band, much narrow than a typical signal bandwidth, so even a lot of decimation filtering won't do much about phase noise.   Some of the other sources of spurs and distortion that can come from a DDS/NCO might be helped by filtering, though.   Since decimation filtering just helps in general with adjacent energy removal, quantization noise, etc., it's just kind of expected that things will be better after bandwidth reduction.