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

[Magnus Danielson]

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