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I would like to simulate a circuit with a resistor and zener diode for various voltages in an excel spread sheet and need a way to model it.

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  • \$\begingroup\$ Watch out for tempco, the vz rise due to a rise in temp due to increase in current is typ worse than esr \$\endgroup\$
    – sstobbe
    May 20, 2017 at 15:23

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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&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.

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