|
|
# Improvements
|
|
|
|
|
|
We will not discuss here the software improvements but give another
|
|
|
approach that might improve the results. As explained in the result
|
|
|
section, the fact that the incoming pulse is not a Dirac impulse
|
|
|
decreases the sinewave quality and then the precision of the results.
|
|
|
Some modifications of the fitted mathematical model could be done to
|
|
|
take the pulse shape into account. Figures 1 & 2 show the real pulse
|
|
|
shape when arriving in the
|
|
|
filter.
|
|
|
|
|
|
![](/uploads/24d655247b381770d692439b65d53a03/pulse.PNG)
|
|
|
*Figure 1 - Pulse shape. It does not look exactly as a Dirac
|
|
|
pulse*
|
|
|
|
|
|
![](/uploads/d9afa9541fe9e5b3a1709904ce064918/pulsezoom.PNG)
|
|
|
*Figure 2 - Zoom on the pulse shape*
|
|
|
|
|
|
Once the corresponding mathematical model of the pulse is found, its
|
|
|
Laplace transform can be multiplied with the LC circuit transfer
|
|
|
function (Expressed in the following
|
|
|
equation).
|
|
|
|
|
|
![](/uploads/45e65cd23898a72589c3721eca4e61bf/transfer.PNG)
|
|
|
|
|
|
The inverse Laplace transform of the system "pulse + filter" can be
|
|
|
deduced, giving a best suited mathematical model for the fitting.
|
|
|
Indeed, the distortion should now be taken into account in the model.
|
|
|
|
|
|
The hardest part of the job is to find a best suited mathematical model
|
|
|
for the pulse than can be easily converted in the Laplace domain. Tests
|
|
|
were done with the following model giving the result plotted in figure
|
|
|
3.
|
|
|
|
|
|
![](/uploads/5648cfcc83963a9e9214379bc92b3646/model.PNG)
|
|
|
|
|
|
![](/uploads/5fd940aa65cb9ad7bfbc916f3700714b/plot_model.png)
|
|
|
*Figure 2 - Plot of the example of the mathematical model*
|
|
|
|