3.146 FAQ-884 How to get a good fit with a very large or a very small parameter?

Last Update: 9/21/2017

When you do curve fitting, you might meet these problems:

• Origin returns missing value in standard errors when you perform fitting with a large parameter.
• Fit can not converge when you perform fitting with a very small parameter.

In both cases, we need to redefine the equations to avoid a very large or a very small parameter. For example:

• \(y = A \cdot x\); if A is a large parameter, we can redefine the equation as \(y=(A' \cdot 1E3) \cdot x\). After fitting, we can get \(A = A'\cdot 1E3\);
• \(y = A \cdot x\); if A is a small parameter, we can redefine the equation as \(y=(A' \cdot 1E-3) \cdot x\). After fitting, we can get \(A = A' \cdot 1E-3\);

Another actual example is the nonlinear implicit diode function:

\(f = Is \cdot {e^{(\frac{{V - I \cdot Rs}}{{k \cdot T}} - 1)}} + \frac{{V - I \cdot Rs}}{{Rsh}} - I\,\!\), k is in \(eV{K^{ - 1}}\,\!\) as a unit.

To do fitting with this function, firstly, we can reset the parameter \(Is\) to \(I's\), where \(I's=Is*exp(-20)\), then the parameter \(I's\) won't be too small.

\[f = I's \cdot [{e^{(\frac{{V - I \cdot Rs}}{{k \cdot T}} - 20)}} - {e^{ (- 20)}}] + \frac{{V - I \cdot Rs}}{{Rsh}} - I\,\!\]

In this way, we can avoid the very small parameter and finally get the fit converge.

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Keywords:good fit, not converge, missing value in standard error,diode function