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Circuits, electronics and noise

Zener shunt regulator current

Current left for the Zener diode after the series resistor’s current has supplied the load.

Ref: ELN-15
Rev: v1
Field: Circuits, electronics and noise
Result: I_z [A]

I_{z} = \frac{V_{s} - V_{z}}{R_{s}} - I_{load}

A series resistor Rs feeds a Zener diode clamped at Vz in parallel with the load. The current through Rs is (Vs − Vz)/Rs. The Zener takes what the load does not use, Iz = (Vs − Vz)/Rs − Iload. When that drops to the knee current (or below zero) the diode is not clamping and regulation is lost. Check the power Vz × Iz at the smallest load.

Current left for the Zener diode after the series resistor’s current has supplied the load. A low or negative result means the regulator has lost regulation, and the Zener needs a minimum knee current.

Calculator

Solve for

I_zZener currentComputed

V_sSupply voltage

550

V_zZener voltage

230

R_sSeries resistor

101,000,000

I_loadLoad current

1e-40.1

Current through the series resistor0.02091 A
Zener power dissipation, Vz Iz0.05564 W
Voltage across the series resistor6.9 V

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Zener current (A) current value 0.01091 A

R_sSeries resistorKey driver

−0.009990.68

V_sSupply voltage

−0.01030.126

I_loadLoad current

−0.07910.0208

V_zZener voltage

−0.06450.0203

The 5.1 V Zener carries 0.01091 A (10.91 mA) and dissipates 0.05564 W while the load takes 0.01 A.
If the load rose past 0.02091 A the Zener current would fall below zero and the output would sag.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (A)	Local step	Change in result
R_s Series resistor	10 to 1,000,000 Ω	−0.009993	0.68	0.69	+10%	−17.4 %
V_s Supply voltage	5 to 50 V	−0.0103	0.1261	0.1364	+10%	+33.3 %
I_load Load current	1e-4 to 0.1 A	−0.07909	0.02081	0.0999	+10%	−9.17 %
V_z Zener voltage	2 to 30 V	−0.06455	0.0203	0.08485	+10%	−14.2 %

Sweep of Load current

Load current (A)	Zener current (A)
1e-4	0.02081
2.371e-4	0.02067
5.623e-4	0.02035
0.001334	0.01958
0.003162	0.01775
0.007499	0.01341
0.01778	0.003126
0.04217	−0.02126
0.1	−0.07909

Sweep one variable

Vary

Zener current (A)Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

I_z

Zener current

Result · A

What the equation gives you. Everything else feeds it.

V_s

Supply voltage

V · typical 5 to 50

The supply voltage, in V. A higher supply raises the current through Rs and so the Zener current. Raising it by 10 % (to 13.2) moves the result by +33.3 %, from 0.01091 to 0.01455 A.

V_z

Zener voltage

V · typical 2 to 30

The Zener voltage, in V. A higher Zener voltage reduces the series resistor’s current and so the Zener current. Raising it by 10 % (to 5.61) moves the result by −14.2 %, from 0.01091 to 0.009364 A.

R_s

Series resistor

Ω · typical 10 to 1,000,000

The series resistor from the supply to the Zener node, in Ω. A larger resistor cuts the supply current and so the Zener current. Raising it by 10 % (to 363) moves the result by −17.4 %, from 0.01091 to 0.009008 A.

I_load

Load current

A · typical 1e-4 to 0.1

The current drawn by the load, in A. More load current takes current away from the Zener, one for one. Raising it by 10 % (to 0.011) moves the result by −9.17 %, from 0.01091 to 0.009909 A.

Worked example with the values above

Voltage across Rs: Vs − Vz = 12 − 5.1 = 6.9 V.
Current through Rs: 6.9 / 330 = 0.020909 A.
Iz = 0.020909 − 0.01 = 0.010909 A.

Assumptions and limits

Ideal diodes with zero forward drop for the rectifier formulas, and a resistive load.
A sinusoidal supply and, for the ripple formula, a small ripple compared with the peak.

Common mistakes

Using the peak value where an RMS or average value is needed.
Forgetting that a full-wave rectifier recharges twice per supply cycle, so the ripple frequency is 2f.
Ignoring the minimum Zener current, or its power rating.

Statistics and uncertainty

Rectifier formulas assume an ideal diode, so a real diode drop of about 0.7 V lowers the results for small peaks. Zener results depend on the supply, the Zener voltage tolerance and the load current, so use worst cases.

Where it is used

Power supplies, battery chargers and meter circuits.
Simple voltage references and regulators for sensors and microcontroller inputs.

Maths you need

Average and RMS values: the mean and root-mean-square of a waveform
Diode: conducts in one direction
Capacitor discharge: ΔV = I Δt / C

Related formulas

Practise this formula