# Estimating parameters for diode model from experimental data

I have got a set with experimental data of the voltage drop on a diode an its corresponding current. The general model of a diode is $$I = I_s \left( e^{V/nV_T} - 1 \right)\ ,$$ and I want to estimate parameters $$I_s$$ and $$\beta = 1/nV_T$$ to fit the model with my data.

My first attempt was making a least squared error approximation by defining an error function with my set of data $$\{V_i,I_i\}$$, $$E(I_s,\beta) = \sum_i \left[ I_i - I_s \left( e^{V_i/nV_T} - 1 \right) \right]^2\ ,$$ such that solving the system of equations $$\partial E / \partial I_s = 0$$ and $$\partial E / \partial \beta = 0$$. This approach leads to two non-linear equations that I tried to solve numerically with the Newton-Raphson method, but the system and its jacobian seems to not have a ''good behaviour'', and the solutions blow up.

I thought about doing the same but using a logarithmic scale to make a kind of linear regression, but if I try to remove the exponential term I get the following, $$\ln(I+I_s) = \ln I_s + \beta V\ ,$$ being not possible to isolate $$I_s$$ in a way that I can do a simple linear regression.

What could be a correct approach for fitting the diode model?

• Can you share the data? May 7, 2021 at 17:38
• @Jan I would like to but I'm not allowed to share it for the moment. Sorry May 7, 2021 at 17:40

If you have enough points with large voltages ($$V\gg \beta^{-1}$$), you can use the asymptote $$\log I =\log I_s + \beta V$$ to get (usually) a very good estimation of the parameters: