[time-nuts] Triangle Waves

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Feb 3 02:13:26 UTC 2010


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




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