Equation for a Complex Chirp

[Panda]

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]

The wavelength of A Sin(f(t)) is given by $f(t)= 2\pi$. In order to have that change you need that to be a function of t rather than a constant. The function $F_0(1- \frac{t}{9\pi}$ changes from F_0 to 1/3 F₀ as t changes from 0 to $6\pi$. You need
$$sin(F_0)(1-\frac{2t}{18\pi})$$

 

[Panda]

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.