Solving a Trickier-Than-Usual Circuit Equation with Mathematica 8.0”

[Zavata]

Hello,

I'm working on a simple electronic circuit with two resistors and two diodes.

I have experimental data of the current-voltage characteristic and am trying to fit the corresponding equation - the resistors and diodes are unknown.

With basic circuit analysis, I get this tricky (messy) equation:

Id - (Vd-Rs*Id)/Rsh - Is1*(Exp[(Vd-Rs*Id+n2*vt*Log[1-(Id-(Vd-Rs*Id)/Rsh)/Is2])/(n2*vt)] - 1) = 0
where the current-voltage characteristic is Id(Vd), Rs is a series resistor, Rsh is a parallel shunt resistor and Is1, n1, Is2, n2 are the saturation current and ideality factors of the two diodes.

To achieve this, I've installed Mathematica 8.0 for Students and have written a small code.


**************************


(* Creation of an implicit function *)

vt = 0.0256;
function =
Last[Last[
Last[NDSolve[{Id[Vd, Rs, Rsh, Is1, n1, Is2,
n2] - (Vd - Rs*Id[Vd, Rs, Rsh, Is1, n1, Is2, n2])/Rsh -
Is1*(Exp[(Vd - Rs*Id[Vd, Rs, Rsh, Is1, n1, Is2, n2] +
n2*vt*Log[
1 - (Id[Vd, Rs, Rsh, Is1, n1, Is2,
n2] - (Vd - Rs*Id[Vd, Rs, Rsh, Is1, n1, Is2, n2])/
Rsh)/Is2])/(n1*vt)] - 1) == 0,
Id[0, Rs, Rsh, Is1, n1, Is2, n2] == 0},
Id, {Vd, -1.5, 1.5}, {Rs, 1, 3000}, {Rsh, 100, 10000}, {Is1,
10^-7, 10^-2}, {n1, 1, 20}, {Is2, 10^-7, 10^-2}, {n2, 1, 20}]]]]


(* Data *)

data = {{-1.20006167888641, -0.000335911958245561}, \
{-1.00005328655243, -0.000308143673464656}, {-0.380005955696106, \
-0.000220252826693468}, {-0.119975663721561, -0.000175646884599701}, \
{-0.740023016929626, -0.000272983132163063}, {-0.0199853703379631, \
-0.0000520107132615522}, {0.0399897247552872,
0.0000320119106618222}, {0.0600147768855095,
0.0000576710590394214}, {0.119977183640003,
0.000138641073135659}, {0.3599793612957,
0.000222295187995769}, {0.76000714302063,
0.000279692729236558}, {1.30006861686707, 0.00035656921681948}};
ListPlot[data]

(* Fit *)

fit = NonlinearModelFit[
data, {function[Vd, Rs, Rsh, Is1, n1, Is2, n2]}, {{Rs, 400}, {Rsh,
8000}, {Is1, 2*10^-4}, {n1, 1}, {Is2, 2*10^-4}, {n2, 1}}, {Vd}]


**************************

I get three problems.


1. NDSolve doesn't converge conveniently for values of Vd near 0.

NDSolve::mconly: "For the method \!\(\"IDA\"\), only machine real code is available. Unable to continue with complex values or beyond floating-point exceptions."


2. If I keep all these data points, there isn't enough memory for the fit calculation.

General::nomem: The current computation was aborted because there was insufficient memory available to complete the computation.


3. If I eliminate a few data points, I get the following error:

NonlinearModelFit::nrlnum: "The function value {0.000335912 +function[-1.20006,400.,8000.,0.0002,1.,0.0002,1.],0.000308144 +function[-1.00005,400.,8000.,0.0002,1.,0.0002,1.],0.000220253 +function[-0.380006,400.,<<4>>,1.],<<1>><<1>><<1>>,0.000272983 +function[-0.740023,400.,8000.,0.0002,1.,0.0002,1.],0.0000520107 +function[-0.0199854,400.,8000.,0.0002,1.,0.0002,1.]}\\n is not a list of real numbers with dimensions {6} at {Rs,Rsh,Is1,n1,Is2,n2} = {400.,8000.,0.0002,1.,0.0002,1.}."

I suspect this error is a consequence of the first one.



Some help please...
Does someone know if Mathematica can actually do this fit?
Or, is the function too messy?
Any idea for working out this problem?
Eventually, should I try another method or program?



Thanks in advance for any help.

A bright and sunshiny day to you!
Alexandre

 

[mmwave]

Hello Alexandre,

Thank you for sharing your project with us. It seems like you are facing some challenges with fitting the data to your equation. I can offer some suggestions that may help you in your analysis.

Firstly, it is always helpful to have a clear understanding of the theoretical basis for your equation and the physical meaning of each of the parameters. This will not only help you in choosing appropriate initial values for your fit, but also in interpreting the results.

Secondly, I would recommend trying to fit your data using a simpler equation first, and then gradually adding complexity as needed. This will help you identify any potential issues with the data or the fit itself.

Thirdly, make sure to check the quality of your experimental data. Are there any outliers or errors that could be affecting your fit? It may be helpful to plot your data with error bars to get a better understanding of the variability in your measurements.

Lastly, if you continue to face difficulties with Mathematica, you may want to try using a different software or method for your fit. Some popular alternatives include MATLAB, Python, and Origin.

I hope this helps and wish you the best of luck in your research. Have a great day!