A programmer samples a sinusoid of amplitude using a software loop whose pass length…

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition · Digital electronics, embedded systems and data acquisition

Electronics for Measurement, Ch The microcontroller as laboratory hardware

Problem

A programmer samples a

1\,\mathrm{kHz}

sinusoid of amplitude

2\,\mathrm{V}

using a software loop whose pass length depends on which instructions execute, intending a

100\,\mu\mathrm{s}

(

10\,\mathrm{kHz}

) sampling interval. Averaged over

10\,000

samples, the measured mean interval is exactly

100.00\,\mu\mathrm{s}

, matching the intended rate exactly. Individual intervals scatter about this mean with an rms of

2.3\,\mu\mathrm{s}

. The programmer argues: "the mean interval equals the intended value exactly, so the record must be indistinguishable from one taken by a hardware timer, and no extra noise should appear on the digitised waveform." ((a)) Explain why this reasoning is wrong. ((b)) Compute the rms voltage scatter that the

2.3\,\mu\mathrm{s}

rms timing jitter adds to the sampled sinusoid, and express the resulting signal-to-noise limit in decibels.

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