Example Analog Filter

Figure C.1: Simple RC lowpass.

Figure C.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 [21], we have

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

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