# Zener diode as a Voltage regulator, where do the formulas come from?

I'm currently studying the above circuit and trying gain a better understanding of it, I found the following forumlas to calculate Rs Max and Rs Min:

$$R_Smax = R_L(\frac{V_{in}}{V_z}-1)$$

Which I think comes from:

$$V_{in} = IR_{total}$$ $$V_{in} = I(R_S+R_L)$$ $$\frac{V_{in}}{(R_S+R_L)} = I$$ $$\frac{V_{in}}{(R_S+R_L)} = \frac{V_z}{R_L}$$ $$V_z = \frac{V_{in}R_L}{(R_S+R_L)}$$

Hence:

$$R_Smax = R_L(\frac{V_{in}}{V_z}-1)$$

If this is where it came from it doesn't seem right to me, Isn't the Zener Diode and Resistor L in a paralell circuit? because if the formula came from there it's like saying the zener diode is in series with Rs, but from what I see in the circuit drawing is that Resistor L is in paralell with the zener diode, so why not use the loaded potential divider formula? as opposed to the potential divider? plus it's like saying that the current Is is gonna be the same as the current in IL....

$$I_S = I_Z + I_L$$

The above is true right?

if someone can explain this to me I'd be grateful, it's been bothering me for days.

• From my practics I have found that there is a minimal zenner current, this current is bigger when diode has higher power rating. If the current trough zenner is below this minumum current, then it will not stabilze the voltage. The max current is calculated from max power rating and zenner voltage, everthing else is as you described Is=Iz+Il – Marko Buršič Sep 13 '15 at 22:01