Exponential Chirp

Generates a real sine signal, which varies exponentially in frequency over time

Description

The Exponential Chirp component generates a sine wave signal at the output, $y$. Its equation is

where $f$ is the instantaneous frequency,

 $f={f}_{0}\cdot {k}^{\left(t-{T}_{0}\right)}$

and $k$  is the exponential rate of change of frequency with respect to time,

The instantaneous frequency of the generated sine wave varies exponentially from ${f}_{0}$ at time ${T}_{0}$ to ${f}_{1}$ at time ${T}_{0}+{T}_{r}$

For example, if ${f}_{0}=1$, ${f}_{1}=1000$, and ${T}_{r}=3$, then the frequency will be 1Hz at time ${T}_{0}$, 10Hz at time ${T}_{0}+1$, 100Hz at time ${T}_{0}+2$, and 1000Hz at time ${T}_{0}+3$.

Connections

 Name Description $y$ Real output signal connection $f$ Instantaneous frequency

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{amplitude}$ $1$ - Amplitude of the sine wave amplitude ${f}_{0}$ $1$ $\mathrm{Hz}$ Initial frequency of the sine wave freqHz1 ${f}_{1}$ $10$ $\mathrm{Hz}$ Final frequency of the sine wave freqHz2 $\mathrm{offset}$ $0$ - Offset of the output signal offset ${T}_{0}$ $0$ $s$ Time offset startTime ${T}_{r}$ $2$ $s$ Duration of the chirp duration