Friday, March 18, 2011

All about numbers BIG and small

I am writing up another post right now on analog scopes vs digital scopes vs sampling scopes, and I realized that many abbreviations I use may not be familiar.  So here are some of the most commonly used big numbers in digital oscilloscopes.
  • 1 S/s – this is 1 sample every 1 second, or very slow
  • 1kS/s – 1 kilo-sample per second, 1000 = 1e3
  • 1MS/s – 1 mega-sample per second, 1,000,000 = 1e6
  • 1GS/s – 1 giga-sample per second, 1,000,000,000 = 1e9
  • 1TS/s – 1 tera-sample per second, 1,000,000,000,000 = 1e12
And of course, memory is specified normally in terms of samples.  So if somebody tells you their scope has 10M of memory, it’s not mega-bytes but megasamples.  This simplifies the math.  A scope with 10M of memory running at 1MS/s can store 10 seconds of data continuously!
Now numbers also get small:
  • 1ms – 1 millisecond – at 1kS/s, sample pts are .001 seconds apart = 1e-3
  • 1us – 1 microsecond – at 1MS/s, .000001 seconds apart = 1e-6
    • This is really a greek mu, a funny looking u, but it’s easier to type u
  • 1ns – 1 nanosecond – at 1GS/s, .00000001 seconds apart = 1e-9
  • 1ps – 1 picosecond – at 1TS/s, .0000000001 seconds apart = 1e-12
  • 1fs – 1 femtosecond = 1e-15
  • 1as – 1 attosecond = 1e-18
Now why do I mention femtoseconds and attoseconds?  First, in equivalent time mode, samples can get 100fs apart on a realtime oscilloscope and 10fs apart on a sample oscilloscope.  Second, even though real-time sampling at its fastest puts sample points 10ps apart, jitter software performs calculations that can result in random jitter numbers measured in femtoseconds.  I’ve seen random of 140femto-seconds on a Tektronix DPO72004C.

And why do I mention atto-seconds?  It turns out that in some calculations (such as perfectly gaussian low-noise jitter with the right clock recovery), the mean “time interval error” is measured in atto-seconds, or “as”.  I’m not sure how meaningful an atto-second really is, but it certainly looks better than rounding to zero!

So that’s your brief intro to the world of abbreviations in scopes.  Now I can post with a clear conscience!

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