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I am working on a simulation and need to insert this graph as a current source and of course I can only do this by inserting the graph equation. However I'm not sure on how to obtain the equation of this graph. The graph shown is not symmetrical to each other but I only need the equation of the general shape which means it can be assumed to be symmetrical.

Thank you in advance.

current leakage vs time graph

Misha Lavrov
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nurinnadz
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  • in short : Yes , it is possible. But its hard in some cases. In your case if you know some data points you could use polynomial interpolation to get atleast a good approximation – The Integrator Jun 01 '18 at 15:40
  • At first glance this looks like a sine wave that has had some shrinkage applied to it. –  Jun 01 '18 at 15:41
  • I suggest giving a load of data points of one period to a computer, with linear interpolation between the data points,, to a computer, and find the lower-order Fourier co-efficients. – DanielWainfleet Jun 01 '18 at 15:54

2 Answers2

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Equations of the form $f(x) = \dfrac{\sin^a(bx)}c$ seem to be a good approximation for your given curve.

For example ,

with $a =23,b=40,c=10$

enter image description here

NOTE : for your curve $a$ should always be odd . $b$ and $c$ are just scaling factors , $c$ can also be kept constant as it keeps the graph bounded between $y= [0.1,-01]$

The Integrator
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My best fit:

$$f(x)=a\cdot\sin^7(bx)$$

where you have to adjust $a$ and $b$, so that it fits your scaling. The picture was generated with $a=3.444,b=1$, but this is special to the used axes scaling and has to be adjusted for your exact application.

enter image description here

To the question in your title

No. There is not an explicite formula for every possible function graph (in a strict set theoretic sense). But we can aproximate almost surely any function appearing in applciations to any desired accuracy if we want to.

M. Winter
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