# [time-nuts] DC Voltage Ramp?

Magnus Danielson cfmd at bredband.net
Mon Sep 5 06:24:43 EDT 2005

```From: "Tom Van Baak" <tvb at leapsecond.com>
Subject: Re: [time-nuts] DC Voltage Ramp?
Date: Sun, 4 Sep 2005 17:10:28 -0700
Message-ID: <000401c5b1ae\$39aea5a0\$1c12f204 at computer>

Tom,

> Thanks for all the info on PLL types.

You are welcome!

The trouble with PLLs is that you can do alot of understanding without too
much of deep math, but much of the material is only a narrow set of PLLs and
usually involves heavy math. However, balancing a higher order PLL is much
more difficult. A PLL of order three can be unstable for certain settings,
where as a second order PLL is stable. There are some design-rules that helps
out though.

Oh, a particular mistake I made in the quick there, I called the PLLs in the
listing of order n, where I meant to really say type n. The difference is that
you can have a PLL of order 2 for instance, but if it lacks a propper
integrator in the loop filter, it is still a type 1 PLL where as a PLL having
a propper integrator in the loop filter is a type 2 PLL. Thus, the PLL type
class is the count of integrators forming a loop. The order of the system is
the total number of poles. Beginners in PLLs may be a little confused, but the
oscillator is also an integrator. An integrator has its pole at origo in the
LaPlace plane (s = 0).

> [ snip ]
> > If you do Kalman filtering, it will change the tau as it learns the errors
> and
> > will perform better than any PLL since it will effectively adjust the tau
> to
> > the situation rather than some engineering decission had it a few years
> back.
>
> Is there a readable reference on Kalman filtering
> that doesn't require a PhD in math?

Yes, there is. I do recommend you to search the web for Kalman filtering. There
are several introductional texts which doesn't require much math at all. If you
fail, let me know and I might have a few pointers dug up for you.

As for the math, I don't have a PhD in anything, but it is all applied linear
algrebra which is taugth first year at most of the Unis EE courses. That it for
most people doesn't stuck is more of a testimony to the way they teach than the
complexity of the math. As for myself, I am a dropout that likes math but
doesn't exercise it except for within a very small region of problems, but
there I am fairly fluent on the other hand.

However, a mini-introduction to Kalman filtering is easy. The classical first
case of Kalman filtering is done on a one-variable system. Consider first that
you have a time-series of measuremens and we want to make an estimate of what
the average of that measurement is, then we just sum them all up and divide by
the number of measurements, just the normal averaging. Now, that is crude and
straighforward, but it also requires you to have the full time-series in
memory. Naturally, you can have a running sum of values and number of values
and divide in the end, we will soon come back to that. One of the crudenesses
is that we do not take into account the exactness of the measured samples, so
an inexact value may polute the average which may be formed from many other
values of better exactness. What we then can do is start weighing in the
samples such that less precise measurements weigh in lighter than more precise
measurements. The point with the Kalman filter is that you combine the weighing
in of samples with the running values of estimate and exactness of estimate.
So, for a 1-variable Kalman system, you take in a sample xn and its deviation
sigma(xn) and produces the estimate yn and estimate deviation sigma(yn) by
weighing it from the previous estimate y(n-1) and the deviation sigma(y(n-1)).
Kalman filters for n parameters is naturally a bit more complex, but is really
nothing else then applied linear algebra and there exist very good reading
material on how to apply it to the real world.

Kalman filters is standard in avionics, to the degree that maybe people should
question it more than they do. Kalman filters had the man on the moon for
instance. Proven in battle is surely not an overstatement, it is a fairly
unknown way of life these days. Good simple math applied on more and more
problems. GPS orbits etc.

> > If you do fancy PLL stuff, you can aid the PLL tracking with external
> sensors,
> > so that temperature measurements, accelerometers etc. can be used to feed
> > correction signals such that the PLL loop does not have to track it all in
> > by itself. The gain of such a solution is that a wider range of PLL
> parameters
> > may be chosen.
>
> I've seen OCXO with attached accelerometers - but
> was told that they did not feed back into the PLL in
> the expected way; instead if a jolt was detected it
> would simply quickly shorten the PLL time constant
> for a while. I suppose the same could be done to
> detect high slew rates in temperature.

It takes quite a bit of analysis to make it work right. It can however be done,
that is BTW how GPS receivers is made able to handle great dynamic changes,
they combine readings such as accelerometers etc. to aid the tracking loops
for the satellite carriers in order to maintain lock. Think of a F-16 or
whatever in wild flight, you have alot of dynamics going on and you still want
your precise location as you soon is to drop your GPS-steered smart-bomb. If
you drop in the wrong spot, your smart-bomb has no chance of finding its target
despite the fancy steeringsystem, since it doesn't have the propultion needed
to get there.

Not that I particularly care about dropping bombs anywere, but it sure helps to
understand what problems others have to solve to see why they solved a
particular problem. In this case there is a richness of public information that
we can use for certainly much more peacefull problems.

> > So, there is alot more to do then just to "lock it up". The performance
> you get
> > certainly can be improved as a result.
> >
> > Cheers,
> > Magnus
>
> Thanks again for a great posting.

Thanks for enjoying it and acknowledge the feeling!

Cheers,
Magnus

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