Two identical passive RC low-pass stages

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

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

Problem

Two identical passive RC low-pass stages, each with

RC = 300\,\mu\mathrm{s}

, are connected in cascade through a buffer so that neither stage loads the other. Each stage's impulse response is non-negative, has unit area, and has an rms width equal to its own

RC

(

300\,\mu\mathrm{s}

) and a

10

90\%

rise time of

2.2RC = 660\,\mu\mathrm{s}

. ((a)) Before any measurement, predict the rms width of the cascade's impulse response using the quadrature rule for cascaded stages. ((b)) Predict the cascade's

10

90\%

rise time using the same quadrature rule. ((c)) The cascade's rise time is then measured on the bench as

1008\,\mu\mathrm{s}

. State by what percentage this exceeds the quadrature prediction, and explain why the quadrature rule is exact for rms widths but only approximate for rise times.

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