# Fitting to Equations with Different Variables

I have a model that determines the conductivity given raw data and a few input parameters. One of the parameters is unknown (substrate thickness). We have an expectation that the data should fit a Drude model, which describes the conductivity using a different, microscopic set of parameters.

Is there a built-in way to find the substrate thickness as that which creates the best match to a Drude fit?

You haven't given us much to go on- I don't know anything about the Drude model, but if you can write an equation with unknown coefficients it seems like you should be able to do a curve fit to it. That would depend on the data having sufficient sensitivity to the coefficients that it actually constrains the model, of course.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com
The question is more about the technique. I want to fit to 2 functions with distinct fit parameters, yielding one function.

i.e. fit a,b,c of f1 and d of f2 to yield a best fit with f1=f2

So you have f1, and you know the coefficients for it? But you want f2 to match f1, but you need the coeficient that makes it so? I suppose you could fill a wave with f1 values, and then do a curve fit of f2 to the f1 data set.

Are they mathematically equivalent? But you can't solve the equality analytically? You might be able to use FindRoots.

John Weeks
WaveMetrics, Inc.
support@wavemetrics.com