Help fitting transcendental exponential relationship to experimental data
in [Matlab]
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From: bcoss COSS on 14 Jul 2010 18:39 I am trying to fit diode data to a model that contains all four components of current conduction across a diode, namely: Thermionic emission, Tunneling, generation-recombination, and leakage. (if you are a very interested reader please see: doi:10.1016/0038-1101(91)90031-S) There are several papers that successful use this model, yet I am unable to fit my data using Matlab. The main issue is the appearance of the total current on both the lhs and rhs of the equation: Itotal = Ite*exp[ (x-Itotal*Rs) / kT] + Igr*exp[ (x-Itotal*Rs) / 2*kT] + Itun*exp[ (x-Itotal*Rs) / E0 ] + (x - Itotal*Rs) / Rshunt Where x is voltage, Itotal is the experimentally measured current, k is the boltzmans constant in eV and T is temperature in kelvin. Ite, Igr, Itun, E0, Rs, and Rshunt are my parameters I want to extract. I was using lsqnonlin and lsqcurvefit to no great effect: function nlcft_V = full_current_fit(P,x,y) % This function is called by LSQNONLIN. % P is a vector which contains the coefficients of the % equation. x and y are the option data sets that were % passed to lsqnonlin. global T; q = 1.602e-19; k = 1.38e-23; nlcft_V = P(1).*(exp(((q/k).*(x-(P(2).*y)))./T)-1)... + P(4).*(exp(((q/(2*k)).*(x-(P(2).*y)))./T)-1)... + P(5).*(exp((q*(x-(P(2).*y)))./P(6))-1)... + (x-(P(2).*y))./P(7); Function call: [result, resnorm,residual,exitflag]=lsqnonlin(@full_current_fit,x0,[], [], options, xdata,ydata); I am totally stuck and have tried every trick I know. Anybody solve a similar problem and would care to share some insight? Mad internet karma to the kind soul who can help me 0 : - )
From: bcoss COSS on 14 Jul 2010 23:22
I may have found my own solution, but ask for any additional suggestions It appears that there is a tutorial on linear and nonlinear coeffecient fitting...I am reading this now. It is called Medium scale non-linear curve fitting. It does not help me with the transcendental part of the problem, but I believe a self consistent loop added to the top of that tutorial code could provide the solution. Thoughts anyone? |