# [time-nuts] Basic regenerative-divider questions

Magnus Danielson magnus at rubidium.dyndns.org
Sat Sep 29 11:34:52 EDT 2007

```From: Enrico Rubiola <rubiola at femto-st.fr>
Subject: Re: [time-nuts] Basic regenerative-divider questions
Date: Sat, 29 Sep 2007 16:55:49 +0200
Message-ID: <351770DB-4C41-4475-82B0-0E0B205F6904 at femto-st.fr>

Dear Enrico,

> I worked on low-noise regenerative dividers long time ago.
> See my home page http://rubiola.org , click on "more journal articles"
>
> 22. E. Rubiola, M. Olivier, J. Groslambert, Phase noise in the
> regenerative frequency dividers (PDF, 670 kB),
> IEEE Transact. Instrum. Meas. vol.41 no.3 pp.353-360, June 1992. ©IEEE.

For convenience:
http://www.femto-st.fr/~rubiola/journal-articles/rubiola1992im-regenerative-divider-noise.pdf

> Notice that you can divide by 4 with a single divider,
> using the 3rd harmonics internally generated by the double balanced
> mixer.
> Dividing 80 MHz, you feed a 20 MHz back to the mixer.
> A 60 MHz signal is generated by the mixer.
> 80 MHz - 60 MHz = 20 MHz, here you go.

Which is what the NIST articles explicitly exercises. They create a double-
frequency oscillation loop having 1/N and (N-1)/N times the input frequency.
A very quick introduction is available in
http://tf.nist.gov/timefreq/general/pdf/1800.pdf

Care to comment on that strategy Enrico?

It should be noted that both the 1/N and (N-1)/N frequencies is actually
equally available, just that usually the (N-1)/N variant is filtered out.
You could also acheive 3/4, 4/5, 5/6, 7/8 etc. divisions.

Similarly, both frequencies could be output and also their difference could be
included by addition of a mixer (and isolational amps) resulting in an (N-2)/N
output. For the 1/4 case you could thus get 1/2 as a side-effect.

Naturally, for higher N values would the (N-1)/N be close to the (N+1)/N which
results from the 1/N addition with the input frequency.

The same basic strategy could also be used get values beyond the input
frequency if we choose to use the sum frequency rather than the difference
frequency for the high frequency, i.e. by choosing (N+1)/N over (N-1)/N.
It would result in the same synchronous regenerate interlocked system.
It would allow for 3/2, 4/3, 5/4, 6/5, 7/6, 8/7, 9/8 ratios.

A similarly post-processing would only be meaningfull for the sum-products of
the two outputs, thus resulting in (N+2)/N ratios, giving 4/2 (2/1 = 2), 5/3,
6/4 (3/2 = 1,5), 7/5 (1,4), 8/6 (4/3), 9/7, 10/8 (5/4 = 1,25).

In all these, the 1/2 frequency is notched out from the system. If it where to
be included, a trinary oscillation scheme could be used where the 1/2 frequency
support itself through the input frequency and the lower and upper frequencies
would interlock around the 1/2 frequency rather than the input frequency.
This would be equalent to having an 1/2 frequency divider followed by a 1/N
divider. Could be an interesting solution when more compact solutions is
needed.

> Another issue is the correction of the phase noise of a digital divider
> using a double-balanced mixer.
>
> D. Huffman, Extremely low noise frequency divider,
> Microwave Journal November 1985, pp. 209--210

Isn't this the same as the Richard Karlquists

http://www.karlquist.com/FCS95.pdf

Cheers,
Magnus

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