How to mathematically simulate a zener diode
Vf= Vz + Zzt*If

Background of my research


where Zzt ~= 1/Pd rating of part +/- 25% and depends on heatsink design at 85'C since Schockley effects reduces Vz with rising temp.  Vz depends on assumptions for test current, and I typically use 5~10% rated current for Vz and Iz at the onset on saturation. Since ESR is the incremental R from bulk resistance, this is related to the part Rja , Pd rating and heatsink Rca ['C/W]. Thus the junction temp rise is a product Rja * W =['C/W /[Ω] ] at rated power for Pd = (ESR * If+Vz) * If.
you can use this model for all diodes including LEDs , where the best thermally designed parts have ESR or Zzt=k/(Pd) with k=0.5 while most are k=1.


e.g. 3W LED looks like a zener with Vz=2.8V and ESR =1/3 ohms, then if in a string, ESR' = xS/yP for an array of xSyP White LEDs each with k/Pd = ESR per cell.

My model assumes Tj=80'C max. which I have computed on many spreadsheets for many different diodes and zeners, where ESR drops slowly with rising current /near&amp;above\ rated current and temperature for pulse mode.


I have jokingly in the past here called this Stewart's Theorem or Stewart's law for ESR on semiconductors but it is a good model for even BJT power switches in saturation and CMOS drivers and ESD diode protection inside CMOS.