# Thermal Model Eon (v,i,T,R,Rg) (Effect of Rg in Switching losses)

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Hello,

I think this might be a very fundamental question but I could not find any discussion in the forum related to the topic...

I need some help to know the source of the Eon Formula shown in the following video tutorial (figure attached):

At minute 8:30 it is mentioned that we can add a formula to our Turn-On losses thermal model to include the effect of Rg.

I would like to know what is the logic/reasoning behind that expression. It looks like "lookup()" is taking information from the custom table EonVsRg (defined at minute 7:40 to 8:22 ) but I would like to understand exactly what is that expression doing. Finally, there is the last term "(1/19.68)" which I also would like to know from where it came from. Is the (1/19.68) a parameter that we can get from the manufacturer datasheet?

Hope I can hear back from somebody soon.

Hello,

From https://cms.wolfspeed.com/app/uploads/2020/12/C3M0280090J.pdf, you will find that in Figure 25 there is the attached plot for Rg vs. E: I would probably use a simple formula for the gate resistance dependence on turn-off losses since that is basically a linear relationship. So, you could find the slope of the Eoff line, e.g., m = (y_max - y_min)/(x_max - x_min) ~= (7.9 - 4.0)/(20 - 2.5) = 0.22 uJ/Ohm. Then, your equation would be E+(m*(Rgoff - Rgoff_nominal)) or E+(0.22*(Rgoff-2.5)).

As for your question on how exactly the EonvsRg custom lookup table and formula in our video were developed, it isn’t shown in the video directly, but 19.68 is the value of Eon at 2.5 Ohms (the nominal value also for the Eon plots in the data sheet). So for the equation E*lookup(‘EonvsRg’,Rg)*(1/19.68):

- E is the lookup table data itself, and everything after that is a scaler

- lookup(‘EonvsRg’,Rg) provides the user-specified Rg value to the custom table named EonvsRg that is saved in the thermal description and is used to determine what the loss should be. You also have to divide by the loss value at the nominal Rg (19.68 uJ) to get the multiplier factor correct for the new Rg.

You might choose to use this approach from the video for Eon in this case, as the behavior is a non-linear fitting. Further, you can just scale your entire data set based on the plot itself if you are only interested in simulating at one Rg value. Note that having the equation really only helps if you plan to try out the effects of different Rg values, but if you know the multiplier it’s easy to include that effect just as a scaling coefficient.

These tips are useful for other manufacturers as well, by the way. As for what Wolfspeed actually does for the Rg dependence in all of the PLECS thermal descriptions models that you can download from their website, they use a more complex higher order fit. But again, I think that would certainly be overkill for the Eoff behavior at least in this case.

Let me know if you have any questions.

Regards,

Kris

answered Sep 30, 2021 by (1,288 points)
selected Oct 3, 2021 by Erick P.