# Voltage across Zener diode is higher than the Zener voltage

I have this circuit: Assuming that the knee current is 0.2 mA and that the Zener voltage at current 5 mA is 7V. I would like to find the voltage across the load. I am however confused with the question since I assumed that the voltage across a Zener diode cannot go above it's Zener voltage, i.e. 7V, even if the answer of this question is 7.12 V. How come?

• It is probably expecting you to use a more detailed zener model of the constant voltage model. Feb 19, 2020 at 23:09
• @DKNguyen Yes, that's what I thought, I've been looking in my notes and my book and I have not found such a model. Should I use the exponential diode model, or is there a special equation for the Zener diode I-V characteristic? Feb 19, 2020 at 23:15
• Where did you get the answer of 7.12 V? What else were you told about the zener diode besides its zener voltage? Feb 20, 2020 at 2:01

In the lower than rated current range, the Rs is inversely proportional to forward current until bulk series Rs dominates .

This really means the Rs is more logarithmic below rated current and more constant above rated current.

• Does that just mean $V_{Z0}$ = 1V? From 1/0.2mA = 5kOhm, and 0.2mA through 5K = 1V? Feb 19, 2020 at 23:53
• There is always k that scales Rs or Zo depending on size Feb 19, 2020 at 23:54
• Oh, I see what you mean. "Proportional" allows for some factor, not just 1:1. Feb 19, 2020 at 23:55

It is probably expecting you to use a more detailed zener model of the constant voltage model.

This is the model in Zener model in Sedra Smith. The slope is pretty linear so it basically models the Zener as a constant voltage in series with a resistance Rz.

You have the knee current, and the zener voltage and current deeper into the curve. But You seem to be missing the knee voltage required to calculate this slope. Do you have it?

• The DC voltage varies by 1.5 V for the voltage supply but other than that, nothing about knee voltage... Feb 19, 2020 at 23:37
• @IhdeneMalek Hmm I don't know how to fill in the gap. Feb 20, 2020 at 0:05