[time-nuts] Triangle Waves

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Feb 3 02:29:16 UTC 2010


Bruce Griffiths wrote:
> 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 capacitor to 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.
>
> Bruce
>
Make that 25K plus 2uF producing ~2V pp quasi triangular wave with a 
slew rate of around 40V/s and a noise bandwidth of about 5Hz producing a 
zero crossing jitter of around 1.1ns due to Johnson noise from the 25K 
resistor.

To ensure this isnt degraded by the logic supply noise an extremely low 
noise logic supply (at least for the output stage) is necessary.

Bruce




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