Hi For moderate division ratios ( like 100 MHz down to 1 MHz ), the 20 log N stuff holds pretty well ….
Bob > On Sep 17, 2018, at 12:37 AM, Dana Whitlow <[email protected]> wrote: > > The act of squaring up the waveform alone might not do much harm, depending > on the extent > to which the phase noise on said waveform has already been filtered off. > But it's mainly when > the signal gets divided down by large ratios that the difference would > become really noticeable. > > For example, take the case of 10 MHz starting frequency; the phase noise > several MHz out > is likely to be nil. But divide the 10 MHz down to, say, 1 Hz; then > there's likely to be quite a > lot of phase noise within "folding range" of many Nyquist bands about 1 Hz. > > This, again, is why I wonder so much about our efforts in re-synthesizing > higher frequencies from > the 1PPS from GPS receivers. I don't know much the architecture of GPS > receivers, but it seems > to me it would sure be nice if there were some convenient way to extract a > clean signal at the > chipping rate, for use in generating standard reference frequencies. > > Dana > > > > > On Sun, Sep 16, 2018 at 9:15 PM, Bob kb8tq <[email protected]> wrote: > >> Hi >> >> It’s pretty easy to demonstrate that squaring up a sine wave, even with >> fairly simple >> circuits does not create crazy phase noise issues. People have been doing >> it successfully >> for a lot of years. In general faster saturated logic produces lower noise >> floors than slower >> logic. >> >> Bob >> >>> On Sep 16, 2018, at 4:33 PM, Dana Whitlow <[email protected]> wrote: >>> >>> I'd been thinking, in an admittedly non-rigorous sort of way, about this >>> matter for some years. >>> >>> As I see it, it is certainly true that the phase of an oscillator's >> output >>> is a continuous funciton >>> of time. It could be described as a continuous ramp, whose slope >>> corresponds to the frequency, >>> and with a little bit of non-flat random noise superimposed on it. >>> >>> Now if you square up the waveform and do digital things with it (such as >>> freq dividing, digital >>> phase detection, etc), you are really only glimpsing the phase noise at >>> transition times, and >>> are blind in between. Thus the very process amounts to sampling the >> phase >>> noise waveform >>> with a sampling phase detector. This view suggests that all the phase >>> noise power is aliased >>> and folded back into the band ranging from DC to Fsamp / 2, where Fsamp >> is >>> the frequency >>> of the waveform after frequency division. This is why the time domain >>> jitter of the oscillator's >>> waveform is unchanged by "perfect" frequency division (or >> multiplication). >>> >>> It is why I wonder about the wisdom of doing phase comparison at >>> unnecessarily low frequency- >>> all that noise would seem to be scrunched down into a bandwidth of half >> the >>> comparison frequency. >>> >>> Does this explanation help, and how does it sit with those of you who >> have >>> more expertise >>> than I? >>> >>> Dana >>> >>> >>> >>> >>> On Sun, Sep 16, 2018 at 4:06 PM, Attila Kinali <[email protected]> wrote: >>> >>>> Moin, >>>> >>>> On Sat, 15 Sep 2018 08:38:55 -0700 >>>> "Richard (Rick) Karlquist" <[email protected]> wrote: >>>> >>>>> On 9/15/2018 3:26 AM, Attila Kinali wrote: >>>>> >>>>>> possible logic family for the task. Otherwise the harmonics of the >>>>>> switching of the FF will down-mix high frequency white noise down >>>>>> to the signal band (this is the reason for the 10*log(N) noise scaling >>>>>> of digital divider that Egan[1] and Calosso/Rubiola[2] and a few >> others >>>>>> mentioned). >>>>> >>>>> Wow, I never knew this in 45 years of designing synthesizers! >>>>> I do remember that some of the frequency counter engineers at HP >>>>> talked about noise aliasing. I think this is another way of >>>>> describing the same problem. >>>> >>>> Yes. This effect has been known for a few decades at least. >>>> What kind of puzzles me is, that I have not seen a mathematically >>>> sound explanation of it, so far. People talk of aliasing and sampling, >>>> but do not describe where the sampling happens in the first place. >>>> After all, it's a time-continuous system and as such, there is no >>>> sampling. One could look at it as a (sub-harmonic) mixing system, >>>> but even that analogy falls short, as there is no second input. >>>> It also fails at describing why there is not infinite energy being >>>> down-mixed, as the resulting harmonic sum does not converge. >>>> >>>> If someone knows of a description that goes beyond handwavy arguments, >>>> I would very much appreciate hearing of them. >>>> >>>> The only way to explain the effect in a rigorous way, that I could >>>> figure out, is to apply Hajimiri and Lee's Impulse Sensitivity >> Function[1], >>>> and adapt from the oscillators they discribed to general periodic >> systems. >>>> (The step, as one can guess, is small, but hic sunt dracones) >>>> Doing this, it becomes obvious that the down-mixing is an inherent >>>> property of all systems that use or generate non-sinusoidal waveforms. >>>> It is this ISF that is the source of the down-mixing/aliasing effect, >>>> as it has a periodic waveform of sharp spikes. >>>> >>>> As the ISF is probably (this is my intuition and I have, unfortunately, >>>> no proof of this) related to the derivative of the produced output >>>> waveform, >>>> it becomes important to limit the slew rate of the output, to introduce >>>> a second pole in the ISF and thus limit the number of harmonics. >>>> Yet, it is also important to keep the input slew rate high, in order to >>>> keep the width/height of the ISF pulses low. >>>> >>>> A partial discussion of this can be found in the paper I presented >>>> at IFCS earlier this year[2]. Unfortunately, the write-up is not >>>> nice and I only realized after the deadline that I should have >>>> all written it using a different approach. Sorry for that. >>>> If something is not clear, do not hesitate to send me an email. >>>> >>>>> About 10 years ago, the frequency synthesizer chip vendors started >>>>> talking about a Figure of Merit (FOM) that predicted phase noise floor, >>>>> and it also included the 10 LOG N noise scaling. An application >>>>> engineer at ADI told me this was a characteristic of the sampling phase >>>>> detector that all these chips used. But I always wondered if the >>>>> frequency divider could come into play. The way FOM is defined, >>>>> it doesn't distinguish between phase detector and divider noise. >>>> >>>> The 10*log(N) also applies to the phase detector in PLL chips, >>>> where N becomes the ratio of the phase detector bandwidth divided >>>> by the phase detector input frequency. >>>> >>>> Given that the phase noise is dominated by the input source' phase >>>> noise, there will be no appreciatable difference in whether the >>>> down-mixing happens in the divider or the phase detector, as long >>>> as the bandwidth of all components is the same. If the bandwidth >>>> is different, we get into something akin Collins' zero crossing >>>> detector[3] where appropriately designed stages with different >>>> input bandwidths limit the energy that is down-mixed. >>>> >>>>> At Agilent, we used to make a lot of lab demos using a Centellax >>>>> (now Microsemi AKA Microchip) frequency divider that could divide by >> any >>>>> number between 8 and 511 up to 10 GHz. It was absolutely fabulous for >>>>> dividing 10 GHz down to 2.5 GHz. But 20 LOG N quit working if I tried >>>>> to divide down to 50 MHz. Now you have explained it. >>>> >>>> Hmm? Are you implying those chips somehow were able to give >>>> a 20*log(N) phase noise behaviour? If so, do you know how >>>> they achieved such a feat? >>>> >>>> >>>>>> If you divide by something that is not a power of 2, then it is >>>> important >>>>>> that each stage produces an output waveform with a 50% duty cycle. >>>> Otherwise >>>>>> flicker noise which has been up-mixed by a previous stage, will be >>>> down-mixed >>>>>> into the signal band, increasing the close-in phase-noise. >>>>> >>>>> Wow, another thing I never knew. >>>> >>>> I do not think that anyone was aware of this. A least I do not remember >>>> seeing this being mentioned in any of the papers I have read. I, myself, >>>> stumbled over it by accident. I was trying to design a sine-to-square >>>> wave converter and wanted to understand what happend to the noise. >>>> Especially the AM to PM conversion that a few people here have mentioned >>>> a few times. I was looking at Claudio's measurement [4, page 28] and, >>>> after applying Hajimir and Lee's ISF, I could (mathematically) explain >>>> everything but what Enrico so nicely labled as "bump". None of the >>>> explanations that I exchanged with Enrico, Claudio, Magnus and a few >>>> other people made sense with the complete data. An external influence >>>> didn't make sense as the flicker noise went from a straight ~6dB/oct >> line >>>> to a straight ~3db/oct line below 25MHz. This hunch got stronger when >>>> Claudio shared the complete circuit they used with me(see figure 3 in >> [2]). >>>> The feedback circuit, which stabilizes duty cycle, has a -3dB frequency >>>> of 0.28Hz, which is exactly the frequency where the bump is. And below >>>> it, the flicker noise behavior seems to go back to approximately >> 6dB/oct. >>>> For a complete explanation, see my paper[2] section 5.D "Scaling in a >>>> Multi-Stage Sine-to-Square Converter." >>>> >>>> >>>>> The conventional wisdom was to >>>>> divide by any number (even or odd) and then follow that divider >>>>> with a divide by 2 flip flop to get 50%. Now, that is in question. >>>>> The now correct answer is to us a variable modulus prescaler to >>>>> divide by P and P+1, controlled by a toggle flip flop to make >>>>> half the divisions at P and half at P+1. >>>> >>>> I don't think the modulus prescaler is a good approach. >>>> It will help reduce flicker noise, at the price of incrased >>>> white noise, as the two division values will generate two >>>> frequency spikes in the ISF that are close to each other. >>>> There is probably some residual even harmonic content due to >>>> the switching betwen the two scaler values, which will increase >>>> flicker noise, not as much as having non-50% duty cycle, but still. >>>> >>>> The right way to do it is to use both edges in case of odd division >>>> factors (as some of the divider circuits by Linear/Analog seem to do). >>>> Alternatively generate a ramp/sine output, ie use a Λ-divider >>>> or a DDS, as both have much lower harmonics content in the ISF >>>> and thus do not suffer from the down-mixing as much. If a square >>>> waveform is required afterwards, a square-to-sine converter with >>>> approriate bandwidth for the output frequency will solve that. >>>> >>>> >>>> >>>> Attila Kinali >>>> >>>> >>>> [1] "A General Theory of Phase Noise in Electrical Oscillators," >>>> by Hajimir and Lee, 1998 >>>> >>>> [2] "A Physical Sine-to-Square Converter Noise Model," >>>> by Kinali, 2018 >>>> >>>> [3] "The Design of Low Jitter Hard Limiters," by Collins, 1996 >>>> >>>> [4] http://rubiola.org/pdf-slides/2016T-EFTF--Noise-in-digital- >>>> electronics.pdf >>>> -- >>>> <JaberWorky> The bad part of Zurich is where the degenerates >>>> throw DARK chocolate at you. >>>> >>>> _______________________________________________ >>>> time-nuts mailing list -- [email protected] >>>> To unsubscribe, go to http://lists.febo.com/mailman/ >>>> listinfo/time-nuts_lists.febo.com >>>> and follow the instructions there. >>>> >>> _______________________________________________ >>> time-nuts mailing list -- [email protected] >>> To unsubscribe, go to http://lists.febo.com/mailman/ >> listinfo/time-nuts_lists.febo.com >>> and follow the instructions there. >> >> >> _______________________________________________ >> time-nuts mailing list -- [email protected] >> To unsubscribe, go to http://lists.febo.com/mailman/ >> listinfo/time-nuts_lists.febo.com >> and follow the instructions there. >> > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
