Equation for a Complex Chirp

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Equation for a "Complex" Chirp

Can anyone give me a general equation for a sinusoidal frequency dropping chirp.

I want to calculate a waveform where the frequency drops a given fraction over a given number of cycles.

The capacitance of the circuit I am trying to analyse changes with applied voltage and time of excitation resulting in a chirped waveform that drops from Fo to Fo/3 over about 10 cycles.
 

HallsofIvy

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The wavelength of A Sin(f(t)) is given by [itex]f(t)= 2\pi[/itex]. In order to have that change you need that to be a function of t rather than a constant. The function [itex]F_0(1- \frac{t}{9\pi}[/itex] changes from F_0 to 1/3 F0 as t changes from 0 to [itex]6\pi[/itex]. You need
[tex]sin(F_0)(1-\frac{2t}{18\pi})[/tex]
 
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OK now, I sorted it out on my own eventually, Sadly when I compare the calculations to the measurements it looks like the frequency decays exponentially, so it's back to the drawing board.
At least by deriving the linear case myself I know how to tackle the exponential case.
I haven't even started the amplitude decay yet, this is going to be a nasty equation.
 

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