# [time-nuts] A new take on the all-hardware GPSDO concept

Charles Steinmetz csteinmetz at yandex.com
Mon Sep 12 18:15:02 EDT 2016

```Nick wrote:

> Ok. Is it the case that the loop filter bandwidth is related to the time constant?

They are two ways of expressing the same thing, with the proviso that TC
applies strictly only to first-order, linear time-invariant systems --
in electronics, circuits with with one real pole.

T = RC, where "T" is the time constant and "R" and "C" are resistor and
capacitor values.

So, a single-pole LP filter consisting of a series 10k resistor and a
shunt 100nF capacitor has T = .001 seconds (=1mS).  Its frequency
response (i.e., the -3dB or "corner" frequency) is given by:

f = 1/(2 x pi x T), or 159.16 Hz.

Checking, we note that the reactance of a capacitor is given by x =
-1/(2 x pi x f x C).  When f = 159.16 Hz, the reactance of a 100nF
capacitor is -10k ohms, which is the value that produces a -3dB response
of 159.16 Hz in the LP filter with a 10k resistor.

> Jim Miller's 10 kHz GPSDO that’s been referenced here has either solved this problem, or the 10 kHz output of the Jupiter is substantially better than the Venus’ 10 MHz output, or the design doesn’t give the results time-nuts expect from a GPSDO. Which of those applies?

I have no idea how the Jupiter generates its 10k output -- it was
speculation on my part that its stability must be no better than the
PPS.  I have not looked at the Miller circuit for a long time (also,
note that Mr. Miller published at least two different GPSDO designs, so
one also has to be careful to know which one is under discussion).  I
recall that I did not have much hope that the better of the two would
give TN-quality results, and was very surprised to find that when Tom
tested one, it performed quite well (although, the loop time constant
was clearly way too low -- as it is in the Tbolt with factory default
settings).  I suppose the answer to the question is to be found in ADEV
plots of the Jupiter's 10kHz output.  Perhaps there are some already
published on the web?

There was some discussion of this on the list back in mid-February 2008.

Best regards,

Charles

```