Exponentials

Generates a real rising and falling exponential signal

Description

The Exponentials component outputs a rising exponential signal from the time step, ${T}_{0}$, for the duration of the period, ${T}_{r}$. A decaying exponential signal is then generated. The equations of this component are

 $y={\begin{array}{cc}\mathrm{offset}& t<{T}_{0}\\ \mathrm{offset}+{\mathrm{out}}_{\mathrm{max}}\cdot \left(1-\mathrm{exp}\left(-\frac{t-{T}_{0}}{{\tau }_{r}}\right)\right)& {T}_{0}\le t<{T}_{0}+{T}_{r}\\ \mathrm{offset}+{y}_{r}\cdot \mathrm{exp}\left(-\frac{t-{T}_{0}-{T}_{r}}{{\tau }_{f}}\right)& t\ge {T}_{0}+{T}_{r}\end{array}$ ${y}_{r}={\mathrm{out}}_{\mathrm{max}}\cdot \left(1-\mathrm{exp}\left(-\frac{{T}_{r}}{{\tau }_{r}}\right)\right)$

Connections

 Name Description $y$ Real output signal connection

Parameters

 Symbol Default Units Description Modelica ID ${\mathrm{out}}_{\mathrm{max}}$ $1$ - Height of output for infinite $\mathrm{riseTime}$ outMax ${T}_{r}$ $0.5$ $s$ Rise time riseTime ${\tau }_{r}$ $0.1$ $s$ Rise time constant riseTimeConst ${\tau }_{f}$ ${\tau }_{r}$ $s$ Fall time constant fallTimeConst $\mathrm{offset}$ $0$ - Offset of the output signal offset ${T}_{0}$ $0$ $s$ Time offset startTime