A mains-hum filter is a single-stage 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 = 2\,\mathrm{ms}

, impulse response

h(t) = (1/RC)e^{-t/RC}

for

t \ge 0

, zero for

t < 0

. It is at rest before

t=0

. ((a)) A rectangular test pulse

x(t) = 5\,\mathrm{V}

for

0 \le t \le 3\,\mathrm{ms}

(zero otherwise) is applied. Using the convolution integral, calculate the output voltage at

t = 1, 2, 3, 4, 5, 6\,\mathrm{ms}

and sketch the output with numbers on both axes. ((b)) The same filter is instead driven, in normal use, by a

50\,\mathrm{Hz}

mains hum tone of peak amplitude

100\,\mathrm{mV}

. Using the frequency response of the filter, calculate the peak amplitude and the phase of the output tone, and state which general relation between input spectrum, output spectrum and frequency response this calculation uses.

Browse the problem library