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:

${\displaystyle V_{R}={\frac {V_{\mathrm {out} }}{2}}}$

${\displaystyle V_{C}=V_{\mathrm {out} }\left(1-e^{-t}\right)}$

${\displaystyle V_{\mathrm {out} }=\pm \mid V_{\mathrm {dd} }\mid }$

The system is assumed to begin with ${\displaystyle V_{\mathrm {out} }=V_{\mathrm {dd} }}$, ${\displaystyle V_{C}=0}$, ${\displaystyle V_{\mathrm {dd} }=1V}$ and ${\displaystyle V_{\mathrm {ss} }=-1V}$