In this article I have explained how to calculate and the find the value of the zener diode resistor using simple formulas.
What is a Zener Diode
Zener diodes are semiconductor devices which are used for regulating an input DC voltage to any desired output voltage. The regulated output voltage value directly depends on the value of the zener diode.
However, all zener diodes being vulnerable to high currents, strictly require a current limiting resistor to control the maximum current through the zener diode.
This resistor also decides how much maximum current the output load can acquire. Thus, the zener diode resistor must be selected in such a way that it ensures proper safety to the zener diode from excessive current, and also allows sufficient current for the output load, so that it can operate optimally.
As shown in the figure below, R1 and the zener diode D1 reduces the input voltage VIN to the desired output voltage VOUT.
The operating voltage of the zener diode is fixed by the manufacturer of the device. While selecting a zener diode we match its operating voltage with the required VOUT voltage.
Power Dissipation
Another important parameter of a zener diode is its power dissipation, which is given by the formula:
P = VOUT x IMAX
Just as VOUT is decided by the load, Imax is also determined by the load. Imax is also determined by the resistance and wattage of the resistor R1.
To be precise, VOUT and Imax are both decided by the minimum and the maximum values of the load current.
This is because, first the current has to flow through the resistor R1 before passing through the zener diode and the load. Therefore the R1 current can be expressed from the following formula:
IR = IZ + IL (Equation#1)
- Here, IR = current through resistor R1
- IZ = current through zener diode D1
- IL = current through the output load
Calculating Current through Zener Diode Resistor
If we consider the input voltage VIN and the output voltage VOUT to be relatively steady and constant, the current flowing through resistor R1 will be proportional to the voltage across it (by Ohms law). This can be expressed with the following equation:
IR = ( VIN - VOUT) / R (Equation#2)
Combining (Equation#1) and (Equation#2), we get:
(VIN - VOUT) / R = IZ + IL (Equation#3)
As assumed earlier, the (VIN - VOUT) is much constant. Therefore when the load current is minimum (let's call it ILmin), the current through the zener diode will be maximum (let's call it ILmax). Substituting these factors in the above equation#3, we get:
(VIN - VOUT) / R = ILmax + ILmin (Equation#4)
If suppose we have a load that demands only maximum current, then the current through the diode will be always negligible. Therefore the above equation can be reduced to the following equation:
(VIN - VOUT) / R = ILmax (Equation#5)
The above equation is simply telling us that the resistor R1 should be selected not only to protect the diode but also to supply adequate current for the load.
Now, we can rearrange the above equation as follows:
R = (VIN - VOUT) / ILmax (Equation#6)
Once the above equation is solved and we get the value of R, we can easily calculate the power of the resistor using the following equation:
P = (ILmax)2 x R (Equation#7)
The above calculations thoroughly explains how to calculate a zener diode resistor!
Maximum Reverse Current
It is also possible for us to determine the maximum reverse current of the zener diode. This can be done by rearranging the Equation#4, and substituting it in Equation#5:
Imax = ILmax - ILmin (Equation#8)
The above equation simply illustrates that the zener diode adjusts its current dissipation and compensates for the maximum and minimum load currents.
It also illustrates that the zener diode pulls current through the resistor to generate a voltage drop across the resistor, which proportionately reduces the voltage for the load.