[time-nuts] Triangle Waves

[Bob Camp]

On Feb 2, 2010, at 9:29 PM, Joseph M Gwinn wrote:

> time-nuts-bounces at febo.com wrote on 02/02/2010 09:13:26 PM:
> 
>> From:
>> 
>> Bruce Griffiths <bruce.griffiths at xtra.co.nz>
>> 
>> To:
>> 
>> Discussion of precise time and frequency measurement 
> <time-nuts at febo.com>
>> 
>> Date:
>> 
>> 02/02/2010 09:16 PM
>> 
>> Subject:
>> 
>> Re: [time-nuts] Triangle Waves
>> 
>> Sent by:
>> 
>> time-nuts-bounces at febo.com
>> 
>> Joseph M Gwinn wrote:
>>> time-nuts-bounces at febo.com wrote on 02/02/2010 08:19:26 PM:
>>> 
>>> 
>>>> From:
>>>> 
>>>> Bruce Griffiths<bruce.griffiths at xtra.co.nz>
>>>> 
>>>> To:
>>>> 
>>>> Discussion of precise time and frequency measurement
>>>> 
>>> <time-nuts at febo.com>
>>> 
>>>> Date:
>>>> 
>>>> 02/02/2010 08:20 PM
>>>> 
>>>> Subject:
>>>> 
>>>> Re: [time-nuts] Triangle Waves
>>>> 
>>>> Sent by:
>>>> 
>>>> time-nuts-bounces at febo.com
>>>> 
>>>> Joseph M Gwinn wrote:
>>>> 
>>>>> time-nuts-bounces at febo.com wrote on 02/02/2010 07:20:24 PM:
>>>>> 
>>>>> 
>>>>> 
>>>>>> From:
>>>>>> 
>>>>>> Bruce Griffiths<bruce.griffiths at xtra.co.nz>
>>>>>> 
>>>>>> To:
>>>>>> 
>>>>>> Discussion of precise time and frequency measurement
>>>>>> 
>>>>>> 
>>>>> <time-nuts at febo.com>
>>>>> 
>>>>> 
>>>>>> Date:
>>>>>> 
>>>>>> 02/02/2010 07:27 PM
>>>>>> 
>>>>>> Subject:
>>>>>> 
>>>>>> Re: [time-nuts] Triangle Waves
>>>>>> 
>>>>>> Sent by:
>>>>>> 
>>>>>> time-nuts-bounces at febo.com
>>>>>> 
>>>>>> Magnus Danielson wrote:
>>>>>> 
>>>>>> 
>>>>> [snip]
>>>>> 
>>>>> 
>>>>>>> Just a reality check question here... a simple triangle oscillator
>>>>>>> 
>>> is
>>> 
>>>>>>> very easily created by two op-amps, one for an integrator and one
>>>>>>> 
>>> for
>>> 
>>>>>>> Schmitt trigger operation. If you want better long-term
>>>>>>> 
>>>> stability open
>>>> 
>>>>>>> 
>>>>> 
>>>>>>> the loop and insert a 10 Hz from your favourite divider chain of a
>>>>>>> trusted 10 MHz or so. Would such a design be limiting your
>>>>>>> 
>>>> measurement
>>>> 
>>>>>>> 
>>>>> 
>>>>>>> goals considerable, and would any flaws be reasonably to 
>> overcome by
>>>>>>> better design?
>>>>>>> 
>>>>>>> Cheers,
>>>>>>> Magnus
>>>>>>> 
>>>>>>> 
>>>>>>> 
>>>>>> For beat frequencies in the 1-100Hz range one only need verify the
>>>>>> 
>>> ZCD
>>> 
>>>>>> jitter and delay variations etc., to within a few nanosec.
>>>>>> In the short term such jitter tantalisingly close to what a well
>>>>>> designed audio oscillator is capable of.
>>>>>> Unfortunately the trigger jitter in most counters is very large for
>>>>>> frequencies in this range so verifying the low jitter of an audio
>>>>>> oscillator requires using a ZCD or equivalent.
>>>>>> 
>>>>>> 
>>>>> Would integration of a 50% duty cycle square wave generate 
>> an adequate
>>>>> triangle wave?  Modern opamps make pretty good low-noise 
> integrators,
>>>>> although one would need to use a good integration capacitorto ensure
>>>>> linear ramps.
>>>>> 
>>>>> The square wave would come from a simple binary divider
>>>>> 
>>>> chain, which will
>>>> 
>>>>> clean many things up and ensure a stable duty cycle, whateverthe
>>>>> 
>>> nature
>>> 
>>>>> of the original signal source.
>>>>> 
>>>>> Joe Gwinn
>>>>> 
>>>>> 
>>>>> 
>>>> The integration function requires a low frequency cutoff (either a
>>>> servoloop or a resistor shunting the integration capacitor) to avoid
>>>> integrator saturation.
>>>> This inevitably distorts the triangle wave, however it should be
>>>> possible to reduce the triangular wave distortion by predistorting 
> the
>>>> integrator input current.
>>>> 
>>> Yes, there would need to be some kind of drift compensation (I favor a
>>> opamp servoloop), but given that we are trying to measure ZCD jitter
>>> (versus long-term wander), isn't this good enough?  The 
>> distortion will be
>>> small and stable, and so will not cause jitter.
>>> 
>>> Joe Gwinn
>>> 
>> Yes one shouldn't lose sight of the goal which isnt a perfect triangular 
> 
>> wave, but merely a low jitter one.
>> The major problem is the Johnson noise of the resistors used in the 
>> integrator.
>> 
>> If for example one uses a simple RC filter using 25k plus 10uF and 
>> drives it with a 10Hz square wave the output noise at dc is 
>> about 20nv/rtHz.
>> The output slew rate with say a 5V amplitude square wave is about 1V pp 
>> and the zero crossing jitter due to Johnson noise is on the order of 
> 3ns.
> 
> I've lost track of our jitter objective, and why we need to achieve it.
> 
> Also, if the intent is to measure the inherent jitter of a ZCD circuit, we 
> may be better off using a really clean sinewave, as it will be easier to 
> generate a clean enough sinewave than trianglewave.
> 
> The fact that we will use a triangle or trapezoid in practice will change 
> the numbers somewhat, but the ranking of proposed circuits by their 
> sinewave jitter should carry over correctly, so long as the same 
> fundamental frequency is used.
> 
> Joe Gwinn
> 

The objective is to check out a limiter that will have performance at better than 10 ns level when driven with a beat note in the 5 to 10 Hz range. A signal 5 to 10X better than the limiter target performance would be adequate. That puts the desired signal in the vicinity of 1 ppb avar at 1 second. 

Ideally the signal source would also provide a stable square wave "trigger" to drive the start channel of a counter or the sweep of a scope. I 'm sure some level of troubleshooting on the limiter will be needed eventually. Generating a good trigger off of a slow waveform isn't all that easy. The trigger also may be helpful in verifying the performance of the signal source it's self. 

Bob




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