Demo 3.3: Zener Diodes and LEDs

The demonstration on diodes drew the whole characteristic and then stayed away from one end of it. Past about −75 V an ordinary silicon diode breaks down, the current runs away, and nothing limits it, so that region was labelled as the end of the device and left alone.

This demonstration is about two diodes that are not ordinary. A Zener is built to live in that region: it breaks down at a chosen, low voltage, does it very steeply, and is packaged to survive the heat. That turns the steepest part of the curve into something useful, a voltage that hardly moves however much current you push through it. A light emitting diode is at the other end of the same family: the same junction with a wider band gap, so that the carriers recombining across it give up their energy as a photon rather than as heat.

Both are ordinary diodes in every other respect, and both need the same thing from you: something in series to decide how much current flows.

The rectifier left something unfinished

The previous demonstration got as far as a smoothed supply, and it is still not a fixed voltage. It ripples, it sags as the load increases, and it rises and falls with whatever the mains is doing. A regulator is a circuit that holds its output steady while its input wanders about above it, and the simplest one there is is a resistor and a Zener diode.

The idea is worth stating before you see it. The resistor takes the difference between the supply and the Zener voltage. The Zener holds the output where it wants it by swallowing whatever current the load does not take. If the supply rises, the Zener takes more; if the load takes more, the Zener takes less; and the output barely moves either way.

It works only while there is current to spare, and every failure of this circuit comes from that one sentence.

How to use it

The breakdown region puts a Zener and an ordinary diode on the same axes and lets you sweep the applied voltage through the knee. Step through the standard Zener voltages along the top and watch the dynamic impedance change with them, which is not a detail: it is the number that decides how good a reference the part is.

A voltage regulator is the circuit. Supply, series resistor, Zener and load, with every current and every power on the page. It opens on the worked example from the lecture, and beside the live values there is a panel doing the same calculation the way you would do it on paper.

Choosing the components is the design problem. The supply varies, the load varies, and the series resistor has to work at all four combinations of the extremes at once. There is a range of values that works rather than a single answer, and the demonstration checks every standard value against all four corners.

Light emitting diodes covers colour, wavelength and forward voltage, the series resistor calculation, and the reason two LEDs must never share one resistor.

Zener Regulators and Light Emitting Diodes

A diode built to live in breakdown, a diode built to give off light, and the arithmetic each of them needs.

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Every diode breaks down in reverse. A Zener is one built to do it on purpose.

The demonstration on diodes showed the avalanche region at the far left and treated it as the end of the device.
In an ordinary silicon diode it happens near −75 V, and nothing limits the current once it starts.
A Zener breaks down at a chosen, low voltage, does it very steeply, and is packaged to survive the heat.
That turns the steepest part of the curve into something useful.
The result is a voltage that hardly moves however much current you push through it.

Zener voltage

Power rating

12.6 V Zener ordinary diode, breaks down near −75 V

Iz(min) = 5.00 mA, below which it is on the soft kneeIz(max) = 30.98 mA, past which it is over its 0.4 W rating

Applied voltage-12.90 V

Sweep left through the knee. It stops at -12.91 V, where the part reaches its 0.4 W rating.

Current

-30.04 mA

in breakdown, and holding

Power in the Zener

387.5 mW

97% of the 0.4 W rating

What happens past Iz(max)

Yes, it damages it. Nothing inside the diode limits the current.
Past the knee the slope is the dynamic impedance, 10 Ω here, so another volt applied is another 100.00 mA.
What limits the current is whatever is outside the diode, which in every circuit in this demonstration is the series resistor.
Iz(max) is a property of the package rather than the junction. This part reaches its 0.4 W at 30.98 mA, and it is sitting at 12.91 V by then rather than at 12.6 V.
That is why the paper figure P / Vz, which gives 31.75 mA, is optimistic: it assumes the part is still at nominal when it is not. The gap is worst on the low-voltage parts, which have the highest dynamic impedance.
Beyond Iz(max) the junction heats faster than the case can shed it, the leakage rises, the heating rises with it, and the part shorts. The failure is thermal runaway and it is quick.
That region is shaded rose on the graph, and the slider will not go into it.

How flat is flat

At Iz(min), 5.00 mA, this part sits at about 12.65 V.
At Iz(max), 30.98 mA, it sits at about 12.91 V.
That is the whole usable range of current, and the voltage moved 260 mV across it.
The slope is the part's dynamic impedance, 10 Ω here, and a smaller number means a better reference.
Step through the voltages along the top and watch that impedance change.
It falls to a minimum around 6 to 9 V and rises either side, because two mechanisms are at work.
Below about 5 V the breakdown is Zener tunnelling; above it the breakdown is avalanche; near the crossover the two partly cancel.
The same crossover is where the temperature coefficient passes through zero, which is why precision references are built around 6.2 V parts rather than round numbers.

A Zener is always fitted the other way round

Every other diode in this module is connected so that current flows the way the arrow points.
A Zener regulator is connected so that it does not: the cathode, the end with the band, goes to the positive side.
That is not a trick. It is the whole point, because the useful behaviour is in the reverse characteristic.
Fitted the way an ordinary diode would be, a 12 V Zener is simply a diode with a 0.7 V drop, and the circuit around it will do nothing that was intended.

Why an ordinary diode cannot do this

Turn the ordinary diode's trace on. It never reaches breakdown anywhere on this graph, because it does not break down until about −75 V.
Two things make the Zener different.
Its junction is far more heavily doped, which narrows the depletion layer so that breakdown happens at a low and controllable voltage.
And it is built and packaged to carry the resulting current continuously without the heat destroying it.
An ordinary diode taken into avalanche is not regulating. It is failing.

The two mechanisms share a name

Strictly, only the low-voltage parts are Zener diodes.
Below about 5 V the field across that very thin depletion layer tears electrons out of their bonds directly, which is Zener tunnelling.
Above about 5 V the breakdown is the avalanche multiplication from the previous demonstration.
Everybody calls them all Zener diodes anyway, and for circuit purposes it makes no difference.
It does explain why the temperature behaviour changes sign partway along the range.

Walkthrough

Step 1: Find the region the last demonstration avoided

Open The breakdown region and sweep the applied voltage from right to left.

Forward, it is an ordinary diode. Through zero and into reverse, nothing happens at all: a few femtoamps, exactly as before. Then at about −12.6 V the current turns sharply downwards and rises very fast.

Turn on the ordinary diode’s trace for comparison. It does nothing anywhere on this graph, because it does not break down until roughly −75 V. Two things make the Zener different: its junction is far more heavily doped, which narrows the depletion layer so that breakdown happens at a low and controllable voltage, and it is built and packaged to carry the resulting current continuously. An ordinary diode taken into avalanche is not regulating, it is failing.

Step 2: Ask how flat the flat part really is

Read the panel underneath the graph.

Push 5 mA through the 12.6 V part and it sits at about 12.62 V. Push ten times that, 50 mA, and it sits at about 13.10 V. Ten times the current for less than half a volt. That is what makes it worth calling a reference, and the slope is the part’s dynamic impedance, 10 Ω here.

Now step along the Zener voltages at the top and watch that impedance change: 28 Ω at 3.3 V, down to 7 Ω at 9.1 V, back up to 20 Ω at 18 V. It has a minimum in the middle, and the reason is that two different mechanisms are at work. Below about 5 V the field across that very thin depletion layer is strong enough to tear electrons out of their bonds directly, which is Zener tunnelling. Above about 5 V the breakdown is the avalanche multiplication from the diode demonstration. Near the crossover the two partly cancel, and so do their opposite temperature coefficients, which is why precision references are built around 6.2 V parts rather than round numbers.

Step 3: Work the lecture example

Open A voltage regulator and press The lecture example: 45 V supply, 1 kΩ series resistor, a 12.6 V Zener, and no load connected.

The paper working is in the panel below, and it is four lines:

across R  = 45.0 − 12.6 = 32.4 V
I(R)      = 32.4 / 1000  = 32.40 mA
P(R)      = 32.4 × 32.40m = 1.050 W
P(Zener)  = 12.6 × 32.40m = 408.2 mW

Which is why the lecture concludes that you need a Zener rated above 0.4 W and a resistor rated at 1.5 or 2 W. Note how far that resistor is from the quarter-watt part in most drawers.

Now look at the live readouts above it. The simulation says 32.08 mA rather than 32.40, and the output sits at 12.92 V rather than 12.6. That gap is the dynamic impedance: a real Zener passing 32 mA sits above its nominal voltage by that current times its 10 Ω. The paper calculation is the one to do, and it is right to within a per cent or two, which is about the accuracy a Zener regulator is worth anyway.

Step 4: Notice when the Zener suffers most

The lecture example has no load connected, and that is not an oversight in the question.

Look at where the current goes: all 32 mA of it through the Zener. Now connect a load and watch the Zener’s share fall as the load’s share rises. The two always add to the current through the resistor, because that is Kirchhoff at the output node.

So the Zener dissipates most when the load draws least, and the worst case of all is no load. A regulator that survives at full load can destroy itself the moment the load is unplugged, which is exactly the opposite of the intuition most people bring to it. The 0.408 W in the lecture is the number that sizes the part precisely because it is the worst the Zener will ever see.

Step 5: Break it in the two available ways

Press Load too heavy. The output collapses to well under 5 V and the demonstration says it has stopped regulating.

What has happened is that the series resistor cannot pass enough current to supply the load and still leave some for the Zener, so the Zener has come out of breakdown and is doing nothing at all. What remains is an ordinary voltage divider, whose output moves with both the supply and the load. There is nothing subtle about the fix: raise the supply, lower the series resistance, or take less current.

Then press Supply too low. Same symptom, different cause. If the supply cannot even reach the Zener voltage, there is nothing for the Zener to hold.

Finally, go back to the lecture example and drag the series resistor down to 200 Ω. Now the opposite failure: the Zener is dissipating well over a watt against a 400 mW rating.

Step 6: Do the design properly

Open Choosing the components. This is where the two failures above become the two bounds on one number.

R must be small enough that at the lowest supply with the heaviest load, there is still current left over for the Zener. That gives R(max) = (Vs_min − Vz) / (I_load_max + I_z_min).
R must be large enough that at the highest supply with no load, the Zener is not asked to dissipate more than it can. That gives R(min) = (Vs_max − Vz) / (P / Vz).

Anything between those two works, and there is usually a good spread. Pick a standard value nearer the middle so that neither bound is close.

Then look at the table of four corners underneath, because that is where the design is actually decided. The two that matter are the first and the last, and they pull in opposite directions: lowest supply with the heaviest load is where regulation collapses, highest supply with no load is where the part overheats. A resistor that survives both survives the other two automatically.

Step 7: Meet the other end of the family

Open Light emitting diodes and read the table.

The last two columns are the interesting pair. A shorter wavelength is a more energetic photon, a more energetic photon needs a wider band gap, and a wider band gap needs more voltage to push carriers across it. Infrared at 940 nm runs at 1.3 V; red at 630 nm is a 1.97 eV photon and runs at 2.0 V; blue at 470 nm is a 2.64 eV photon and runs at over 3 V. That is why a blue LED cannot be driven from a single alkaline cell however much current you offer it.

Two things on that table are worth pausing over. White is not a wavelength: it is a blue LED with a phosphor on top that re-emits part of the blue as yellow, which is why it has a blue LED’s forward voltage. And green appears twice, because the traditional gallium phosphide green runs at about 2.1 V while the modern high-brightness green is the same indium gallium nitride as the blue and wants 3.2 V. Anyone who learns “green is 2.1 V” from a parts drawer and then buys a modern one gets a surprise.

The resistor calculation is the same one as always, and it is the one from the demonstration on pull-up and pull-down resistors seen from the other side: R = (Vs − Vf) / I, choose the current first, and round the resistor up.

Step 8: Find out why LEDs must not be paralleled

Scroll to the panel at the bottom of that tab: two LEDs sharing one resistor, with a mismatch slider.

Set the mismatch to zero and they share equally, 50-50, which is the situation that never occurs in practice. Now drag it to 100 mV, which is well inside a single data sheet bin.

The split becomes 87 per cent and 13 per cent. One LED gets 12 mA and the other gets 1.7 mA: one is bright, one is barely lit.

The reason is the exponential, and it is worth being precise. Being in parallel, the two must share a voltage. At a common voltage, a difference in forward voltage of ΔV changes the current by a factor of e^(ΔV/nV_T), and with n ≈ 2 for an LED that is a factor of about seven for 100 mV. Worse, the bright one runs hotter, heat lowers its forward voltage further, and the imbalance grows.

The fix is one resistor per LED, so that each branch has something with a positive slope to set its own current. If they must be in one string, put them in series instead: series parts are forced to share a current, which is the quantity you actually care about.

Check your understanding

Quiz

Select 0/1

In a Zener regulator, when does the Zener diode dissipate the most power?

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Quiz

Select 0/1

A 12 V Zener with 9 Ω of dynamic impedance is passing 5 mA, then the supply rises so that it passes 50 mA. Roughly what happens to the output voltage?

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Concept Match

Match each item to what it does

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Quiz

Select 0/1

Two nominally identical red LEDs are connected in parallel behind a single resistor. Their forward voltages differ by 100 mV. What happens?

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Quiz

Select 0/3

Which of these would let a Zener regulator supply more load current? Select all that apply.

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Wrap-up

Five things to take away.

A Zener is a diode built to live in reverse breakdown, at a chosen low voltage, steeply enough that its voltage barely moves with current. It is fitted the opposite way round to every other diode you have met.
Dynamic impedance is the slope in breakdown and the reason the output is not flat. It has a minimum around 6 to 9 V, where the tunnelling and avalanche mechanisms cross over and their temperature coefficients cancel.
In a regulator the resistor sets the total current and the Zener shares it out. The Zener takes whatever the load does not, so the worst case for its power is no load at all.
Sizing the resistor is two bounds, not one number, and they come from the two ways the circuit fails: too large and it starves at the lowest supply with the heaviest load, too small and it cooks at the highest supply with no load.
An LED is a diode with a wider band gap, so its forward voltage tracks the photon energy. It has no useful resistance, so its current must be set by something else, and two of them must never share one resistor.

That completes the diode material. Everything here has used devices with two terminals, where the only choice available was which way round to fit them. The next step in analogue electronics is the three-terminal device, where a small current or voltage at one terminal controls a much larger one between the other two, and where the load line you drew across a diode’s curve becomes the tool for choosing an operating point deliberately rather than merely observing one.