[time-nuts] Triangle Waves

Joseph M Gwinn gwinn at raytheon.com
Wed Feb 3 02:29:52 UTC 2010


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




More information about the Time-nuts_lists.febo.com mailing list