Zener diode calculator

How this is calculated

A zener regulator is a resistor from the supply to the output and a zener from the output to ground. The resistor carries the load current and the zener current together, and the zener takes whatever the load does not:

I_Z = (V_in − V_Z) / R − I_load

That one line contains the whole design problem. The zener only regulates while it carries some minimum current — below it the knee softens and the voltage sags — and it may only carry so much before it exceeds its power rating. Every term on the right moves: the supply has a range, the load has a range, the zener's voltage has a tolerance and the resistor has one too. The zener current is smallest at the lowest supply, the highest load, the highest zener voltage and the resistor at the top of its tolerance; it is largest at the opposite corner of all four. Each corner gives one bound on R:

R ≤ (V_in,min − V_Z,max) / (I_load,max + I_Z,min)

R ≥ (V_in,max − V_Z,min) / (I_load,min + I_Z,max)

where I_Z,max is the current at which the zener reaches the share of its rating you allow. The page also includes the zener's dynamic impedance: a real zener's voltage rises with its current, V_Z = V_Z0 + r_Z·I_Z, which slightly relieves the starved corner and slightly worsens the hot one. Resistor tolerance then narrows the window from both ends. Every figure on the page, and every row of the table, is evaluated at all sixteen corners rather than at the two the formulas name, so nothing depends on having guessed the worst case correctly.

The window can be empty

Put the two bounds side by side and ignore the small effects, and the condition for any resistor to exist is

(V_in,max − V_Z) / (V_in,min − V_Z) ≤ (I_load,min + I_Z,max) / (I_load,max + I_Z,min)

The left side is the headroom ratio — how much the voltage across the resistor swings, as a ratio — and the right side is how much the current through it is allowed to swing. A zener regulator works only if the supply's headroom swings by less than the currents can absorb. Neither side contains R, so this is decided before any resistor is chosen, and no resistor can rescue a design that fails it.

The ratio is what makes it bite. The default 12 V rail moves by 2.4 V and a 9 V battery running from 9.6 V fresh to 7 V flat moves by 2.6 V — almost the same swing — but for a 5.1 V zener the first is a headroom ratio of 1.4 and the second of 2.4, because the headroom the battery's swing is a ratio of is so much smaller. That is why zener regulators on batteries so often work on the bench with a new cell and fail in the field, and it is the same arithmetic that sinks an LED on a low-headroom rail, where the LED resistor calculator shows a small forward-voltage spread turning into a large current spread.

At the defaults the window runs from 173 Ω to 226 Ω, a factor of 1.30, and the page buys 220 Ω — the largest catalogue value inside it. That resistor needs a 1 W rating, not the 1/4 W part the circuit's size suggests: at 13.2 V with the zener at the bottom of its tolerance it drops over 8 V and dissipates about a third of a watt.

Why the largest resistor that fits

Anywhere inside the window works, so the choice is about what else R sets, and every one of those things improves as R rises. The current the circuit draws from the supply when the load is idle falls. The zener's worst-case dissipation falls, because at the hot corner it takes everything the resistor passes. And the regulation improves: the resistor and the zener's dynamic impedance form a divider for any change in the supply, so

ΔV_out / ΔV_in = r_Z / (R + r_Z)

which is the ripple rejection. At the defaults it is −22.9 dB, so a volt of ripple on the input arrives as 72 mV at the output. The one thing a larger R costs is margin at the starved corner, and the "keep the zener above" figure already is that margin — so the page rounds the resistor down to the largest catalogue value at or under the top of the window, never to the nearest.

The smallest zener that works

The top of the window does not depend on the zener's power rating at all — only on the supply, the load and the minimum zener current. The bottom does. So the rating the design needs is the worst-case dissipation at the top of the window, divided by the share of the rating you are prepared to use. Below that rating the window is empty; at it, the window is a single value. The page reports it as its own figure because it turns a failed design into a shopping answer: at the defaults, 381 mW of zener rating would do, so the 500 mW part is enough and a 250 mW one would not be.

The dissipation to design for is the counter-intuitive one. The zener runs hottest when the load is lightest, not heaviest, because every milliamp the load stops taking is a milliamp the zener must absorb. If the load can ever be switched off, disconnected or held in reset, the zener must survive the full resistor current alone at the highest supply. That is why the default load minimum is zero.

When a zener regulator is the wrong part

A zener shunt regulator draws its worst-case current all the time, whether the load needs it or not, and that is its real limitation. It suits references, bias rails and loads of a few tens of milliamps from a supply that does not move much. Past that, three alternatives. Put an emitter follower after the zener and the zener only has to supply the base current, which divides the load range it must absorb by the transistor's gain. Use a linear regulator, whose quiescent current is fixed and small; its drop still turns into heat, which the heatsink calculator sizes. Or, where the drop is large, use a buck converter. On a battery, a zener regulator's standing current matters more than anything else it does, and the battery life calculator shows what a few milliamps drawn continuously cost against a device that otherwise sleeps.

FAQ

How do I calculate the resistor for a zener diode?

Take the lowest supply voltage, subtract the highest zener voltage, and divide by the largest load current plus the minimum zener current. That is the largest resistor that keeps the zener regulating. Then check the other end: at the highest supply and the lightest load, the zener takes everything the resistor passes, and its dissipation there must stay inside its rating. If it does not, no resistor works, and the design needs a bigger zener, a steadier supply or a different circuit.

What minimum zener current should I use?

Datasheets give a knee current, I_ZK, typically 0.25 to 1 mA for small zeners, below which the voltage is no longer specified. Staying well above it — a quarter to a half of the test current is common — keeps the zener where its dynamic impedance is low and its voltage is the one on the datasheet. Low-current zeners specified at 50 µA exist for battery work.

Why does my 9 V battery zener regulator stop working as the battery drains?

Because the window closes. A 5.1 V, 500 mW zener feeding 20 mA from a battery that runs from 9.6 V to 7 V has a headroom ratio of 2.4, and no resistor satisfies both corners: the largest one that keeps the zener regulating at 7 V lets it dissipate 304 mW at 9.6 V with the load off, past the 250 mW that half its rating allows. A 1 W zener opens the window; so does a follower transistor, or a low-dropout regulator.

What wattage resistor do I need?

The page reports the resistor's worst-case dissipation, which occurs at the highest supply, and the standard rating that keeps it under half its rating. A resistor at its full rating runs hot enough to drift and discolour the board.

Does the zener voltage change with temperature?

Yes, and the sign depends on the voltage. Below about 5 V zeners have a negative temperature coefficient, above about 6 V a positive one, and parts near 5.6 V come closest to zero, which is why that voltage is popular for references. The tolerance field is where to add the drift over your temperature range.