Example Analog Filter

Figure E.1: Simple RC lowpass.

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

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

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