# [time-nuts] Linear Interpolator

Stephan Sandenbergh stephan at rrsg.ee.uct.ac.za
Thu Jun 29 05:04:54 EDT 2006

```Hi All,

Thank you for all the very helpful hints and info. However, I am still
confused by some topics related to the analogue interpolator.

I can see that designing an analogue interpolator can be tricky, at least as
(or probably more) tricky than the DAC feeding the OCXO.

Question 1 is relating to what TvB wrote.

--

Tom van Baak wrote:

Since you're asking about time interval counters in relation to your GPSDO
design, I want to tempt you to do some math first:

1) You know, or can measure, the ADEV of your GPS engine (M12M, or Res-T,
etc.).

.

.

.

You may in fact find your current 3.33 ns guess is fine. Or maybe you'll
find that it's not near good enough and you are leaving good performance on
the table. Let us know what you come up with. Perhaps it will shed light on
why the classic HP GPSDO used a ~100 ps TIC.

--

The M12+T outputs a 1PPS with 2ns 1sigma accuracy if the sawtooth correction
has been implemented (at least this is what the datasheets claim). Also the
sawtooth is output as a number between -127 and +127 in ns. This postulates
that you would probably never now the 1PPS position better than 2ns, and
this is with a sawtooth correction of 1ns resolution.

So why would you want an interpolator of greater accuracy than 1ns?

Question 2: If you want 1ns resolution (without interpolation), you will
need a 1GHz clock (also an EMI beast) to do the capturing. If one go for say
a 100MHz (10x slower) you will be left with a resolution of 10ns. With this
kind of resolution sawtooth correction is somewhat futile. But, the 1PPS
jitter along with some clocking uncertainty will probably give you better
resolution (say about half) due to the dithering effect. Why isn't it
possible to let the 100MHz clock decide the MSB bits in your phase error
word and then "linearly interpolate" in software by letting the sawtooth
error decide your LSBs? Now you will be sawtooth corrected with an absolute
uncertainty of 10ns. Your actual uncertainty would probably be less due to
dithering. Isn't this a better alternative to rounding the sawtooth error to
the nearest 10ns?

Question 3: Is it possible to calculate/estimate the actual resolution due
to dithering? Maybe you need the frequency spread of the 1PPS?

Question 4: I will probably be much better off EMI wise with a much slower
clock. Also, I would at least like to max out the M12+T's 2ns resolution.
Thus, can anyone maybe point me to some good interpolation ICs?

Regards,

Stephan Sandenbergh

```