[time-nuts] Triangle Waves

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Feb 3 02:57:11 UTC 2010


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
>
>    
Figure 8 (attached) from Collin's paper indicates that the jitter of a 
100Hz wien bridge oscillator is of the order of a few hundred nanosec or so.
This was taken using a 3 stage limiter and a 1 sec counter gate time.
It may be feasible to do better.

It would also appear to be feasible to produce a 10Hz sinewave with ns 
jitter by low pass filtering a square wave using a combination of active 
and passive RC filtering.

Bruce
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