Exponential Chirp

Generate a chirp whose frequency varies exponentially with time

 Description The Exponential Chirp component generates a constant amplitude chirp whose instantaneous frequency, $f$, varies exponentially with time. The chirp begins at time ${T}_{0}$ and ends after duration ${T}_{d}$. The instantaneous frequency varies from ${f}_{1}$ to ${f}_{2}$.
 Equations $f={f}_{1}\mathrm{exp}\left(\left(t-{T}_{0}\right)\mathrm{logk}\right)$ ${\mathrm{int}}_{f}=\left\{\begin{array}{cc}{f}_{1}\left(t-{T}_{0}\right)& \mathrm{logk}=0\\ \frac{f-{f}_{1}}{\mathrm{logk}}& \mathrm{otherwise}\end{array}$ $y={y}_{0}+\left\{\begin{array}{cc}A\mathrm{sin}\left(2\pi {\mathrm{int}}_{f}\right)& {T}_{0}\le t\le {T}_{0}+{T}_{d}\\ 0& \mathrm{otherwise}\end{array}$ $\mathrm{logk}=\frac{\mathrm{log}\left(\frac{{f}_{2}}{{f}_{1}}\right)}{{T}_{d}}$

Connections

 Name Description Modelica ID $y$ Real output signal y $f$ Instantaneous frequency f

Parameters

 Name Default Units Description Modelica ID ${y}_{0}$ $0$ $1$ Offset of output signal offset $A$ $1$ $1$ Amplitude of sine wave amplitude ${f}_{1}$ $1$ $\mathrm{Hz}$ Initial frequency freqHz1 ${f}_{2}$ $10$ $\mathrm{Hz}$ Final frequency freqHz2 ${T}_{0}$ $0$ $s$ Start of chirp startTime ${T}_{d}$ $2$ $s$ Duration of chirp duration