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I have this setup:

enter image description here

The problem with this setup is that when there is a 3.2 V voltage drop acriss the 160 Ω (vertical) resistor, then there's NOT a 3.2 V voltage drop across the Zener diode, in reality.

In reality, there is about 2.8 V or something like that. If I increase the 160 Ω (horizontal) resistor to e.g 10 kΩ, then the voltage drop across the Zener diode will be very low, like 1.5 V or so.

So that's the reason why I keep having a low value resistor before the Zener diode, but not too low because the resistor is protecting the Zener diode. Also there is a PTC resistor after the potentiometer in my real schematic.

I want to measure this voltage drop across the Zener diode. I have a 16-bit STM32 ADC (analog input channel) connected to the cathode of the Zener diode. When I measure the voltage, it looks like this:

enter image description here

The black line is the real measurement. The red line is the desired measurement.

I can write an equation for the orange line below using the sloped line equation:

$$y = mx + b$$

enter image description here

Question:

Is there any formula for the part where the measurement is bending? My goal is to find a correction formula that can correct its measurement. If I get, for example, 2.8 V, then the STM32 microcontroller should say it is actually 3.3 V. Like a look-up-table, but more like an equation, a formula.

This bending is caused by leakage current of the Zener diode. I need to find a formula for that, so I can curve-fit measurement data onto that formula and find its parameters.

ocrdu
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euraad
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    zeners are horrible at 3 V. You can get a much sharper characteristic at that voltage with a white LED. Have a look at [these](https://electronics.stackexchange.com/questions/394152/voltage-drop-on-diode/394160#394160) diode curves – Neil_UK Dec 20 '22 at 21:10
  • @greybeard Is there any formula for that? – euraad Dec 20 '22 at 22:18
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    Zeners need a specified current to maintain the knee. LEDs generally have a much sharper knee then zeners and are more tolerant to current variations. I have used them as zerers for many years and called them DED (Dark Emitting Diodes). There were some application notes published on this around 1990. I did one using the LED as the reference voltage for a high compliance current source. – Gil Dec 21 '22 at 00:12
  • Any "bends" in forward bias U/I diagrams for diodes are due to not using a linear scale for U or not using a log scale for I. For a (the?) basic semiconductor diode model including a lin/log graph prominently see [Shockley](https://en.m.wikipedia.org/wiki/Shockley_diode_equation). (I see that I need to exclude avalanche breakdown at least. What material I found on Zener diode reverse conductance (Zener&avalanche effects) I don't understand to the extent of claiming same for Zener effect reverse conductance with any confidence…) – greybeard Dec 21 '22 at 05:56
  • see also: [Zener breakdown modelling](https://electronics.stackexchange.com/q/617565) – greybeard Dec 21 '22 at 07:35
  • @Gil in this case, I think I will try to use the zener diode. I have no time to replace my SOT-223 with a LED. It does not even fit. But thanks for the information. I will try to use a 3.3V LED diode next time instead of an zener. – euraad Dec 21 '22 at 09:07
  • Different colors will give you different voltages. The same color from different manufacturers and or lots will also have some minor voltage variations. I usually bias them at about 1mA but that is up to you. – Gil Dec 21 '22 at 18:04

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