Equation for a Complex Chirp

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SUMMARY

The discussion centers on deriving an equation for a sinusoidal frequency dropping chirp, specifically transitioning from F0 to F0/3 over 10 cycles. The participant initially formulated the function F(t) = F0(1 - t/(9π)), which describes a linear frequency drop. However, upon comparing calculations to measurements, they observed an exponential decay in frequency, prompting a reevaluation of their approach. The participant acknowledges the complexity of incorporating amplitude decay into their analysis.

PREREQUISITES
  • Understanding of sinusoidal waveforms and frequency modulation
  • Familiarity with mathematical functions and calculus, particularly derivatives
  • Knowledge of circuit capacitance behavior under varying voltage
  • Experience with waveform analysis and measurement techniques
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  • Research exponential decay functions in signal processing
  • Explore advanced techniques for modeling chirp signals in MATLAB
  • Study the impact of amplitude decay on waveform characteristics
  • Investigate the relationship between circuit capacitance and frequency modulation
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Electrical engineers, signal processing specialists, and researchers involved in waveform analysis and chirp signal modeling will benefit from this discussion.

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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.
 
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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})
 
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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