A decoupling stage behaves as an RC low-pass with

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Signals, systems, control and digital signal processing · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Linear systems, the impulse response and convolution

Problem

RC = 200\,\mu\mathrm{s}

. A technician injects a rectangular test pulse of area

5.0\,\mu\mathrm{V\,s}

and width

500\,\mu\mathrm{s}

, and measures a peak output of

9.2\,\mathrm{mV}

. They argue: "The ideal impulse response should peak at

h(0) = 1/RC = 5000\,\mathrm{s^{-1}}

, so for a pulse of area

5.0\,\mu\mathrm{V\,s}

the peak should be

(5.0\,\mu\mathrm{V\,s})(5000\,\mathrm{s^{-1}}) = 25\,\mathrm{mV}

. I measured only

9.2\,\mathrm{mV}

, which is

63\%

low. Since I trust the pulse generator's area, the stage's true time constant must be about

63\%

longer than its nameplate value, i.e.

RC \approx 326\,\mu\mathrm{s}

, not

200\,\mu\mathrm{s}

." ((a)) Find the error in this reasoning. ((b)) Give the correct interpretation of the

9.2\,\mathrm{mV}

reading, and show it is consistent with

RC = 200\,\mu\mathrm{s}

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