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Example Analog Filter

Figure E.1: Simple RC lowpass.
\includegraphics{eps/rc}

Figure E.1 shows a simple analog filter consisting of one resistor ($ R$ Ohms) and one capacitor ($ C$ Farads). The voltages across these elements are $ v_R(t)$ and $ v_C(t)$ , respectively, where $ t$ denotes time in seconds. The filter input is the externally applied voltage $ v_e(t)$ , and the filter output is taken to be $ v_C(t)$ . By Kirchoff's loop constraints [20], we have

$\displaystyle v_e(t) = v_R(t) + v_C(t), \protect$ (E.1)

and the loop current is $ i(t)$ .

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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition)
Copyright © 2024-09-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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