English: Transient Analysis of a comparator-based hysteretic oscillator (i.e., a relaxation oscillator implemented with a Schmitt trigger and an RC network) with R=C=1 (unit). The system properties are:

${\displaystyle V_R=\frac{V_{\mathrm{o}\mathrm{u}\mathrm{t}}}{2}}$

${\displaystyle V_C=V_{\mathrm{o}\mathrm{u}\mathrm{t}}(1-e^{-t})}$

${\displaystyle V_{\mathrm{o}\mathrm{u}\mathrm{t}}=\pm \mid V_{\mathrm{d}\mathrm{d}}\mid }$

The system is assumed to begin with ${\displaystyle V_{\mathrm{o}\mathrm{u}\mathrm{t}}=V_{\mathrm{d}\mathrm{d}}}$, ${\displaystyle V_C=0}$, ${\displaystyle V_{\mathrm{d}\mathrm{d}}=1V}$ and ${\displaystyle V_{\mathrm{s}\mathrm{s}}=-1V}$