[time-nuts] DIY TimePod
Chris Caudle
chris at chriscaudle.org
Tue Jun 14 18:01:41 EDT 2016
On Tue, June 14, 2016 2:35 am, John Swenson wrote:
> The idea here is around a 80MHz sample clock with a
> maximum input/ref signal of around 25MHz.
Without some pretty steep low pass filtering that will violate the Nyquist
criterion (for 80MHz sample clock the input must be strictly limited to
less than 40MHz). You can't even get the first odd harmonic in of a 25MHz
square wave input.
> This is based on the TimePod with ADCs, which is
> supposed to work with square waves.
The ADC's would have a low pass filter in front. Think of it in terms of
the Shannon information capacity, the amount of information conveyed is
determined by the bandwidth and the signal to noise ratio. The bandwidth
is determined by the sample rate, the signal to noise ratio by the number
of (effective) bits of the ADC.
I forget which ADC someone mentioned recently as being in the TimePod.
Isn't it a 16 bit converter? So that is getting around 96dB integrated
signal to noise ratio per converter, and you are starting with 6dB.
> When you feed a square wave into this you have several samples at say
> 50, then it jumps to 50,000 stays there for several samples, then jumps
> down to 50 again.
The key thing you are missing which happens with a multi-bit ADC is that
the signal has a finite rise time, so it doesn't "jump" to 50,000, it has
a transition region where you get several samples of different values.
Those samples fit an infinite number of possible signals, but only one
signal which is limited to the Nyquist criterion bandwidth. Using those
samples and the knowledge of the system bandwidth you can interpolate
where the zero crossing must have been.
With a single bit quantizer (and no feedback to shape the noise), you get
very little information about the signal values in the transition region.
> This still seems like a binary sample. The difference
> is that every now and then the sample hits during a ramptime of the
> square wave and will give some intermediate value,
No, every time you will sample during the transition, because the "square"
wave still has a finite rise time, and if you have properly bandwidth
limited the signal as required by the Nyquist sampling criterion (input
signal must be less than half the frequency of the sampling clock) then
you know what the upper limit on the rise time is.
--
Chris Caudle
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