Zener diode and voltage regulation

Why it matters

A Zener diode is the cheapest voltage reference you can buy, and it appears inside almost every instrument: as a reference for comparators and ADCs, as a shunt regulator for low-current sensor supplies, and as an over-voltage clamp on input lines. Designing one correctly is a classic worst-case problem: it must keep regulating at the lowest input and heaviest load, and must not overheat at the highest input and lightest load.

Key ideas

Breakdown by design. A Zener diode is a heavily doped p-n junction built to operate in reverse breakdown. Once the reverse voltage reaches V_Z, the current rises steeply while the voltage changes only slightly, so the device behaves like a battery V_Z in series with a small dynamic resistance r_z. In the forward direction it behaves like an ordinary diode (≈ 0.7 V drop).

Two breakdown mechanisms.

• Zener (field) breakdown dominates in very heavily doped junctions, roughly V_Z below about 5 V. Its temperature coefficient is negative.
• Avalanche breakdown (impact ionisation) dominates above about 6 V. Its temperature coefficient is positive.
• Diodes near 5–6 V have the smallest temperature coefficient, which is why 5.6–6.2 V references are popular. Temperature-compensated references put a forward-biased diode (−2 mV/°C) in series with a positive-coefficient Zener.

Operating window. Regulation needs a minimum current I_Z(min) (the knee current) to keep the diode in breakdown. The maximum current is set by the rated power: I_Z(max) = P_Z(max) / V_Z.

The shunt regulator. A series resistor R_S from the unregulated supply feeds the parallel combination of the Zener and the load. The resistor drops the difference V_in − V_Z; the Zener absorbs whatever current the load does not take. If the input rises, the Zener current rises; if the load draws more, the Zener current falls. The circuit is simple but wasteful: the resistor and Zener burn power even at no load, so it suits currents of tens of mA. For more current a transistor (emitter follower) is added, which leads to the series regulators of a later topic.

When does it stop regulating? If the Zener is not in breakdown it is an open circuit and the output is just the divider V_in·R_L/(R_S + R_L). The Zener regulates only while this divider voltage is at least V_Z.

Figures of merit. Line regulation is the change in output per change in input; load regulation is the change in output from no load to full load, often quoted as a percentage. Both improve as r_z falls and R_S rises.

Formulas

I_S = (V_in − V_Z) / R_S — current through the series resistor (A); V_in input (V), V_Z Zener voltage (V), R_S series resistance (Ω). Valid while the Zener is in breakdown.

I_Z = I_S − I_L, with I_L = V_Z / R_L — Zener current and load current (A).

P_Z = V_Z · I_Z — Zener dissipation (W). Worst case at maximum V_in and minimum I_L.

R_S(max) = (V_in(min) − V_Z) / (I_L(max) + I_Z(min)) — largest series resistor that still keeps regulation at the worst case.

R_S(min) = (V_in(max) − V_Z) / (I_L(min) + I_Z(max)) — smallest series resistor that keeps the Zener within its rating.

R_L(min) = R_S · V_Z / (V_in − V_Z) — smallest load that still lets the Zener reach breakdown (ignoring I_Z(min)).

ΔV_o / ΔV_in ≈ (r_z ∥ R_L) / (R_S + r_z ∥ R_L) — line regulation (ripple rejection) using the dynamic resistance r_z (Ω).

Load regulation (%) = (V_NL − V_FL) / V_FL × 100.

Worked examples

Example 1 (standard). V_in = 15 V, V_Z = 5 V, R_S = 100 Ω, R_L = 250 Ω. Find I_S, I_L, I_Z and P_Z.

1. Check breakdown: the open-Zener divider gives 15 × 250/350 = 10.7 V > 5 V, so the Zener is in breakdown and V_o = 5 V.
2. I_S = (V_in − V_Z)/R_S = (15 − 5)/100 = 0.1 A = 100 mA.
3. I_L = V_Z/R_L = 5/250 = 0.02 A = 20 mA.
4. I_Z = I_S − I_L = 100 − 20 = 80 mA.
5. P_Z = V_Z·I_Z = 5 × 0.08 = 0.4 W.

Answer: I_S = 100 mA, I_L = 20 mA, I_Z = 80 mA, P_Z = 0.40 W.

Example 2 (GATE level). An unregulated supply varies from 18 V to 24 V. A 12 V Zener with I_Z(min) = 5 mA and r_z = 5 Ω must supply a load current between 10 mA and 50 mA. (a) Find the largest usable R_S. (b) With R_S = 100 Ω, find the worst-case Zener dissipation. (c) Estimate the output ripple for 1 V peak-to-peak ripple on the input.

1. (a) Worst case for regulation is lowest input with heaviest load: R_S(max) = (V_in(min) − V_Z)/(I_L(max) + I_Z(min)) = (18 − 12)/(0.050 + 0.005) = 6/0.055 = 109 Ω. Choose the standard 100 Ω.
2. (b) Worst case for dissipation is highest input with lightest load: I_S = (24 − 12)/100 = 120 mA; I_Z = 120 − 10 = 110 mA; P_Z = 12 × 0.110 = 1.32 W. Pick at least a 2 W Zener.
3. (c) R_L ≥ 12 V/50 mA = 240 Ω ≫ r_z, so r_z ∥ R_L ≈ r_z. ΔV_o ≈ ΔV_in·r_z/(R_S + r_z) = 1 × 5/105 = 0.048 V.

Answer: R_S(max) ≈ 109 Ω; P_Z(max) = 1.32 W; output ripple ≈ 48 mV peak-to-peak.

Common mistakes

• Computing I_Z without first checking that the Zener is actually in breakdown; with a heavy load (small R_L) it may be off.
• Using I_S = (V_in − V_Z)/R_L: the load resistor does not carry the dropped voltage, the series resistor does.
• Sizing R_S at nominal conditions instead of the two worst cases (minimum input with maximum load; maximum input with minimum load).
• Saying all Zeners have a positive temperature coefficient; low-voltage (Zener-mechanism) devices have a negative one.
• Forgetting that removing the load is the worst case for Zener dissipation.

For GATE IN

Expect numericals on Zener current and power, the permissible range of R_S or R_L for regulation, line and load regulation using r_z, and the output of a Zener with a load when it may or may not be in breakdown. Also expect conceptual questions on Zener versus avalanche breakdown and their temperature coefficients. Practise the "assume ON, solve, check I_Z > 0" routine.

Quick check

1. A 9 V Zener is fed from 15 V through 120 Ω with no load. What is I_Z?
2. In Q1, what load resistance makes I_Z fall to zero?
3. Which breakdown mechanism has a positive temperature coefficient?
4. Why is the no-load condition the worst case for Zener dissipation?

Answers: 1. 50 mA. 2. 180 Ω. 3. Avalanche breakdown. 4. All of the series-resistor current then flows through the Zener.