Propagation of error in a curve fit

[misty iron]

So I did an experiment where I have to measure the voltage V and current I for a solar cell to get its IV characteristics. I did a curve fitting to match my result of I vs V, and I can calculate the resistances by taking the derivative of IV curve and it’s reciprocal would be the resistance.

But here’s the thing, there’s an uncertainty of 0.01V and 0.01mA for the voltage and current measurement and how do I calculate the propagation of error for my resistance from my curve fitting model?

The curve fitting equation is
I(V) = A*exp(BV) + C*exp(DV)
And the resistance calculation is
R = -1/I’(V)

[runic pollen]

dont really know much about this but you can "fake" how the error should propogate for your equation by replacing V with (V + error) then moving the error as far outside of the expression as possible

[misty iron]

But the thing is that it’s not that straight forward, the relationship is obtained from an experimental result with I vs V, both I and V have their own uncertainties, and I used MATLAB to do the curve fit

[misty iron]

heres what i came out with, aint sure if its correct

[mossy gulch]

Is there a reason you're using instantaneous resistance? Do you have data that is that detailed and violating ohm's law? If you're roughly steady state (solar cell and a load), none of that should be necessary.

I tried digging into using instantaneous resistance, but I think it's going to be wrong because the partial derivative of R_est w.r.t. I is going to be zero which means your propagation of error of R_est will be independent of your deltaI

Can you upload your data?

[misty iron]

Propagation of error from the uncertainties of measurement and curve fitting

Wait I will upload my calculations and my data later (hours later)

[misty iron]

Also, it shouldn’t be obeying ohms law as it’s following Shockley’s equation (together with photocurrent and hence the IV curve)

Because solar cells are actually series of pn junctions

[misty iron]

These are how the IV curve look like

[mossy gulch]

If the curve is fit to all of these data points and they all have error/noise shouldn't the propagation of error function include the error contribution of every data point?

[misty iron]

Not necessarily

I mean if you mean even distribution of error, not necessarily

I have less uncertainty at V=0 and higher uncertainty at open circuit voltage because the circuit cannot go to infinity resistance

I think I got it, my equation is for error propagation is correct, just that I have higher curve fit uncertainties near open circuit voltage due to limited points being plotted

[mossy gulch]

mean even distribution of error likely creates some symmetry but every input/paramater of your predictive function contributes some error that is weighted by a partial derivative.

Do you have a mathematical expression for your predictive function? It might be cleaner than you think to pull out the partial derivatives

[misty iron]

It’s a curve fit from experimental data

I don’t think it will be symmetrical