[time-nuts] Re: The SI second and the ease of realization (was: leap seconds finally being retired?)

[Magnus Danielson]

Hi Rick,

On 2022-11-26 03:54, Richard (Rick) Karlquist wrote:
>
>
> On 11/25/2022 1:55 PM, Magnus Danielson via time-nuts wrote:
>
>> error hunts in and a remaining phase-shift often being the end 
>> result, looking like a phase-step. A higher degree compensation may 
>> track in the phase-step. Do look at Gardner book.
>
> Gardner was the book that taught me how to do phase locked loops.
Yes. I think it is extremely good at teaching all the key aspects in 
such a way that one can get the needed understanding. I strongly advice 
people to get it and read it. Other books provide additional insights 
and details that Gardner does not explicitly do. If I only got to keep 
one book on PLLs, Gardner will be my keeper. Best and Wolaver books have 
their benefits, and I prefer the Wolaver book over the Best book. I find 
that I dip my nose into all three depending on the particular problem I 
want to check things, which I rarely do since once learned, many things 
can be very quickly derived directly. Wolaver has an elegance to it with 
rich set of illustrations of many techniques, while providing necessary 
support in math. It does have jitter peaking well described and also how 
PLL lock behaves with parallel injection locking. I then have additional 
books for more specific contexts, such as the clock recovery of signal 
and the effect on bit error rates and such. Jitter peaking becomes 
extremely important there.
>
> The 5061 had an analog dual integrator using a then $100 op amp, 
> specifically to address the problem you are describing.  Len Cutler 
> went to a lot of trouble to get this right.  The 5071 of course also 
> has a dual integrator, but it's just DSP code.

Yes, once you have DSP code, doing it becomes more an issue of setting 
up the coefficients properly. A DSP integrator can be made effectively 
non-lossy while actual analog integrators have a shelfving of their gain 
due to both open loop gain of op-amps and leakage of integrating 
capacitor circuit (both internal and surrounding circuits). So, for the 
5061 time, the op-amp needed was for sure expensive. Modern technology 
for sure have simplified this, but long term memory is best kept digital 
rather than analog, and for the time-constants this is where DSP side 
shines over analog, while for much shorter time-constants it should be 
kept in analog domain.

The issue at hand is often analyzed in terms of the loops error 
function, that is how the output of the loop is in error with the input. 
For a PLL this ends up being a high-pass function. As one then expose it 
to a disruption and look at the error, depending on the degree of the 
loop, it will be able to zero, get a constant error or unbounded error 
for various types of signals. So the degree of the loop to handle 
frequency jump of a locked oscillator is defined fully by the fact that 
an frequency jump forms a second degree function and a third degree 
function is needed to combat that to zero it, while a second degree 
function can only keep it within some limit. It's all classical control 
theory, for which Len for sure needed to know well. One just need to 
learn it and realize it's applicability to the problem at hand.

Got a 5060, 5061, 5062 and 5071 among other units in my collection.

> Len was also responsible for the dual integrator in the E1938A oven 
> control loop, which was amazing.

Oven control is quite similar control-wise, but many treat it with less 
care than they should.

Cheers,
Magnus