# [time-nuts] time-nuts Frequency Divider

Bruce Griffiths bruce.griffiths at xtra.co.nz
Fri Apr 3 21:10:18 UTC 2009

```Magnus

The input noise of a logic inverter or other trigger device used as a
clock shaper is important.
If we have a logic inverter device with the following characteristics:

Input noise: 100uV rms
Intrinsic jitter: 1ps rms

Then the input signal slew rate at the threshold crossing has to be
greater than

3x1E-4/1E-12 = 3E8 V/s or 300 V/us

to ensure that the output jitter isnt increased by more than 5% from the
intrinsic jitter.

With a 1.4V pk 10MHz sinewave input the maximum slew rate is ~89V/us (at
the zero crossing).
For such an input signal the output jitter will be about 1.14 ps.
This increases to about 1.4ps if there is a threshold offset of 1V.
This can be reduced to about 1.05ps by amplifying the slope of the input
signal by ~ 3.4x.

The intrinsic jitter (RJ. DDJ isn't important when the input signal is a
low distortion sinewave) of a 74AC04 inverter is about 1ps.
However the equivalent input noise is unknown.
The noise could, in principle, be determined by measuring the output
jitter as a function of the input signal slew rate.

Whilst AM and other noise associated with the source can be reduced by
filtering, the input noise of a trigger circuit cannot (except perhaps
for the trigger circuits input current noise).

Magnus Danielson wrote:
> Bruce Griffiths skrev:
>
>> Ulrich
>>
>> Your experience with the SR620 illustrates the point I was making quite
>> well.
>> It really does matter what you do in front of the limiter circuit built
>> into the counter.
>> A bandpass or any other filter by itself is ineffective unless the
>> signal is exceptionally noisy.
>>
>> By using the inverter in the 74HCT4046 you have added a low gain limiter
>> stage the bandwidth of which is smaller than that of the SR620 input
>> circuit.
>> This has the effect of increasing the slew rate of the input signal
>> whilst producing an output with less jitter than the SR620 input circuit
>> would without this low pass filtered limiter circuit (the inverter from
>> the 74HCT4046). The slew rate at the 74HCT4046 inverter output is
>> greater than that of the input signal which means that the jitter due
>> the counter input circuit noise is smaller than when this low gain low
>> bandwidth limiter isn't used.
>> The input circuit of the SR620 has a wide noise bandwidth (~ 470MHz
>> assuming a single pole response with a 300MHz 3dB high frequency cutoff)
>> and a correspondingly high total input noise (~350uV rms).
>> If the slew rate of the SR 620 input signal at the trigger point the
>> jitter due to this noise dominates the trigger circuit output jitter.
>> The HP5370 time interval counter input circuit has a lower noise
>> bandwidth (~160MHz??) and is quieter (~ 100uV rms) than the input
>> circuit of the SR620 and thus the HP5370 jitter (without the 74HCT4046
>> limiter) for the same 10MHz signal should be less than that of the SR620
>> (without the 74HCT4046 limiter).
>>
>
> As a curiosity, there are various variants of the original 4046 which
> has different sensitivity on the input side... one of them has several
> inverters in a row to get the needed gain where as the other variant
> does not. This difference made a huge difference in some applications.
>
>

The appropriate device (one that will have the least output jitter) to
use will vary with the input signal zero crossing slew rate.
That is it depends on both the input signal frequency and amplitude.

>> If one uses a state of the art trigger circuit with a noise bandwidth of
>> 1GHz or more then the total input noise will be even larger so it
>> becomes even more important to use an optimised cascade of limiter+ low
>> output pass filter stages to increase the slew rate of the counter
>> input  trigger circuit at the trigger threshold.
>> Careful optimisation of the gain of each stage and the corresponding
>> output filter cutoff frequency for each stage is necessary to minimise
>> the output jitter of the counter trigger circuit.
>> There is also an optimum number of such stages that minimises the
>> trigger jitter.
>>
>> The optimisation problem for Limiter stages with gaussian wideband input
>> noise was solved in the 1990's.
>> Unfortunately the optimum number of stages, associated gains and output
>> filter bandwidths depends on the input signal frequency and amplitude so
>> that in general it isn't possible to use the same limiter cascade for a
>> wide range of signal amplitudes and frequencies and minimise the jitter
>> for each frequency and amplitude.
>>
>
> Actually, you can make a cascade setup which is approaching optimum and
> insert signal at the stage where the signals slewrate matches the range
> for each stage. Since the gain steps is larger later in a slew rate
> amplifier chain, the last stages may have a little coarse slew rate
> range, but additional mid-range amplifiers that can act as alternative
> input amps could curcumvent that such that a wide range but and fairly
> good trigger jitter could be achieved.
>
> The comparator level is fed to whatever stage is the first stage.
>
> Such an approach could lead to much improved jitter values for lower
> frequency signals with associated gain in measurement accuracy.
>
> It is easy to make a pre-amplifier set that achieves this, but you want
> to integrate the control algorithms for automatic use.
>
>
That would constitute an interesting design challenge.
>> Thus such circuits aren't usually employed in general purpose frequency counters.
>>
>
> Certainly true. A generic counter is usually equipped with triggers such
> that they can measure slewrate without too much difficulty.
>
>
>> However if the input signal frequency and amplitude are known and stable
>> then using such a limiter filter cascade is feasible.
>>
>
> Indeed.
>
> Cheers,
> Magnus
>
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>

Bruce

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