Zener dynamic resistance

The Zener dynamic resistance $r_z$ is the slope-resistance of a Zener diode in its Reverse breakdown region — the small but non-zero resistance that makes the regulated voltage shift slightly when the current through the Zener changes:

$r_z=\frac{\Delta V}{\Delta I}{|}_{\text{breakdown}}$

$\Delta V$ is the change in the Zener’s terminal voltage caused by a change $\Delta I$ in its current, evaluated on the steep breakdown part of the curve.

Why it is not zero, and why that matters

An ideal voltage reference would hold exactly $V_Z$ no matter how much current flows — a perfectly vertical breakdown line, $r_z=0$. Real Zeners have a breakdown line with a slight tilt, so the voltage creeps up a little as the current rises. That tilt is $r_z$. It is small — typically a few ohms to a few tens of ohms — but finite, and it is the entire reason a Zener voltage regulator does not perfectly hold its output: when the load or supply changes, the Zener current changes, and the $r_z$ converts that current change into a small output voltage change.

In the linearised Zener model the device is an ideal source $V_{Z0}$ in series with $r_z$, so the terminal voltage is $V_Z=V_{Z0}+I_Z{r}_z$. A regulator’s line/load regulation figures are essentially $r_z$ divided by the series resistance. Choosing a Zener with low $r_z$ directly buys a better regulator.

The same idea as the forward diode

$r_z$ is the breakdown-region analogue of the Diode small-signal resistance $r_d=V_T/I_D$ of a forward-biased diode. Both are the inverse slope of the device’s $i$–$v$ curve at the operating point; both quantify how much the “constant” voltage actually moves with current. The forward-diode Voltage reference (three diodes in series) and the Zener regulator are the same circuit idea, with $r_d$ playing for forward diodes the role $r_z$ plays for the Zener. Treat $r_z$ as a small series resistance whenever you need to predict how stiff a Zener-based reference really is.