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Example Analog Filter

Figure E.1: Simple RC lowpass.
\begin{figure}\input fig/rc.pstex_t

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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Laplace Analysis of Linear Systems