[time-nuts] Re: Measurement and correction of non-linearity of a TDC

[Magnus Danielson]

Hi Erik,

On 2024-06-09 08:54, Erik Kaashoek via time-nuts wrote:
> Is there someone on this list that has experience with the measurement 
> and correction of non-linearity of a TDC?
> It appears the TDC's I'm using have at least two types of non linearity.
> One seems to be related to the pulling by the clock used to create the 
> stop pulse.

"Apparent pulling of clock". It is a well known fenomena that nearby 
start will shift a stop pulse. It has limited counters of multiple 
brands, and basic isolation of the two trigger-paths is needed. Lack of 
isolation may come from ground-bounce in common power/ground connection, 
and good decoupling caps can be part of that solution. Some vendors have 
separated comparators to increase isolation between channels.

Through calibration mechanisms one can correct this, if one considers 
the non-linearity be from the other pulse rather from the core clock.

To separate trigger-shift and clock-pull, measure the internal clock 
output with a separate counter to see if you can observe a clock pull or 
not. Most often there is none.

You can also experience similar leakage from your core clock and even 
separately from reference clock if they are not the same. You need to 
back out to the period of those clocks to separate.

> The other is a small repeating non-linearity, every 54 steps of the 
> the TDC
> The attached graph shows the error in steps per step being measured. 
> There is still some noise in the error measurement as measuring the 
> linearity error proved to be rather difficult.
You have a sawtooth shaped non-linearity. Could be waiting-jitter. You 
should be able to simply apply a sawtooth of matching phase and period. 
Once corrected
> The larger oscillation around step 1250 with amplitude of 10 steps 
> could be pulling by the clock.  The repeating saw-tooth error has a 
> period of 54 steps and an amplitude of 4 steps. Each TDC step is about 
> 41 ps wide. Total width of the graph is about 100 ns or about 2400 steps.
> The same non-linearity appears on all 6 TDC samples that where measured.
> Does this make sense?

It does. I'm not convinced you actually have the actual clock pulled 
thought.

So, start with "predicting" the sawtooth and remove that. As you can see 
already from the graph it will not be perfect. Your big blurp mid-point 
will be easier to understand after that.

You also have a slow modulation over the full long period. It's like the 
shart spike in one direct is spread out in the other.

The spike in the middle seems to be a double derivate pattern. That's a 
hint of the system-order of the leakage.

One potential test you can do is to have an input signal of bad 
phase-noise. As you average, the finer-grained version of non-linearity 
will average out and you can see the larger shapes pretty OK. It can be 
a complementary approach. In fact, this is what the HP5328A/B was doing 
with the right options, but by modulating the reference clock and 
average out the non-linearities of quantization steps. I did a small 
simulation and paper on that.

Anyway, hope you have use of my ramblings.

Cheers,
Magnus

> Erik.
>
>
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