[time-nuts] Understanding Oliver Collins Paper "Design of Low Jitter Hard Limiters"

[Azelio Boriani]

Hi Raj,
welcome. Thank you for joining the group and thanks to Magnus for his
comment about the Collins' paper.

On Tue, Aug 21, 2012 at 11:51 PM, Magnus Danielson <
magnus at rubidium.dyndns.org> wrote:

> Hi Raj,
>
>
> On 08/21/2012 06:50 PM, raj_sodhi at agilent.com wrote:
>
>> Hello everyone,
>>
>> I am new to this forum.
>> It looks like a lively discussion on various topics.
>>
>> A colleague of mine here at Agilent pointed me to this paper entitled
>> "The Design of Low Jitter Hard Limiters" by Oliver Collins. In Bruce
>> Griffiths' precision time in frequency webpage, this paper is described as
>> "seminal."
>> (http://www.ko4bb.com/~bruce/ZeroCrossingDetectors.html)
>>
>
> This is indeed a good paper to read.
>
>
>  Since I'm trying to create a limiter that will accept frequencies ranging
>> from 1 MHz to 100 MHz,
>> I thought it would be good to understand the conclusions of this paper
>> (if not the mathematics
>> as well).
>>
>
> I agree that it could be very good to understand the paper for such a
> design.
>
>
>   The mathematics turned out to be quite challenging to decode. Has
>> someone on this forum unraveled the equations?
>>
>
> Both Bruce and me have been looking deeply into this paper (even if it
> where some time ago, so I re-read it quickly). Bruce deeper than me, but I
> think I can guide you into it.
>
>
>  It appears Collins has recommendations on the bandwidth and gain of a
>> jitter minimizing limiter, and then extends
>> this analysis to provide the bandwidth and gain of a cascade of limiters.
>>  But the application is still fuzzy.
>>
>
> You obviously have not paid attention to Chapter 1 where the application
> is very clear and obvious. In particular Dual Mixer Time Difference (DMTD)
> systems (of which one side is seen in Figure 1) is being discussed, but I
> think it is equally valid in your application, as it relates to the overall
> basic issue "Given a sine of a particular frequency, which limiter will
> provide me with minimum trigger jitter?"
>
>
>  In figure 5, he shows a graph showing the dependence of jitter on
>> crossing time.  Is the crossing time
>> (implied by equations 7) considered a design parameter one can vary?
>>
>
> Yes, k is the design parameter as the normalized crossing time.
>
>
>  Also, on figure 4, the "k" parameter has been varied to show the rising
>> waveform as a function of "k".
>>
>
> It essentially shows you how the filter bandwidth (as tau shifts with k)
> will affect the output signal as a function of the design parameter k.
>
>
>   The threshold is always assumed to be 0.5.  So could "k" be related to
>> "tau", the time constant of the RC filter?
>>
>
> That is formula 10.
>
> Actually, you can pick one of many different parameters as the one for the
> one degree of freedom parameter, and he has chosen the normalized crossing
> time k. Just about any other normalized parameter could have worked as well.
>
> Bruce observed that the same amount of contributed noise was assumed in
> the Collins paper, so you would like to read his notes of:
> http://www.ko4bb.com/~bruce/GeneralisedCollinsHardLimiterPaperV3B.pdf
>
> Oh, an interesting note is that the Collins paper considers what happens
> on a single transition, so that's why it is relatively clean from input
> frequency issues. What will change is the input slew-rate.
>
> The Collins paper does not very clearly advice you how to deal with 1:100
> input frequency design-range, even if it occurs as an example of variation,
> just scalled down a million times from your design problem.
>
> Another possible critique on the Collins paper is that it only consider
> white noise, and not flicker noise. For low frequencies, flicker would be
> noticeable if not dominant, where as for higher frequencies the white noise
> assumption works pretty well.
>
> Cheers,
> Magnus
>
>
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