Lesson 3.1 · Module 3: Semiconductors & Active Switching

Diodes & LEDs: Forward Voltage and the I-V Curve

Diodes are one-way valves for electricity. LEDs are diodes that glow. This lesson shows how to give an LED exactly the right current.

The live, interactive simulation for this lesson opens here when JavaScript is on.

Key ideas

A diode only conducts forwards, and only after about 0.6 V (2 V for a red LED) of push.
Above that voltage, the current rises extremely steeply — so you must limit it with a resistor.
A Zener diode is built to conduct backwards at a set voltage, which makes it a voltage limiter.

Try this in the simulation

Pick the Red LED and adjust the resistor until about 10 mA flows.
Turn on the curve-tracer sweep and open the I-V tab to see the diode’s “hockey-stick” curve.
Make the source voltage negative: the diode blocks and no current flows.

How do diodes and LEDs work, and what is an I-V curve?

A diode lets current through in one direction only, and only after the forward voltage passes a threshold: about 0.6 V for silicon, less for a Schottky diode and around 2 V for a red LED. Past that point the current rises extremely steeply, so you must limit it with a resistor. An I-V curve plots current against voltage and shows this hockey-stick shape. A Zener diode is built to conduct backwards at a set voltage, which makes it useful as a voltage limiter.

What you’ll learn

How a diode blocks current in reverse and conducts in the forward direction.
How to pick the series resistor that gives an LED a safe current.
How to read an I-V curve for silicon, Schottky, Zener and LED parts.
How a Zener diode holds a voltage steady.

The formula, letter by letter

\begin{aligned}\htmlClass{mv mv-i_d}{\htmlStyle{font-size:1.33em}{\htmlData{sym=I_D:diode}{I_{\mathrm{D}}}}} &= \htmlData{sym=I_S}{I_{\mathrm{S}}}\left(\htmlData{sym=e}{\mathrm{e}}^{\htmlClass{mv mv-v_d}{\htmlStyle{font-size:1.00em}{\htmlData{sym=U_D}{U_{\mathrm{D}}}}}/\htmlData{sym=n}{n}\htmlData{sym=U_T}{U_{\mathrm{T}}}} - 1\right),\; \htmlData{sym=n}{n}=2\\ \htmlClass{mv mv-i_d}{\htmlStyle{font-size:1.00em}{\htmlData{sym=I_D:diode}{I_{\mathrm{D}}}}} &= \frac{\htmlClass{mv mv-v_s}{\htmlStyle{font-size:1.00em}{\htmlData{sym=U_s}{U_{\mathrm{s}}}}} - \htmlData{sym=U_D}{U_{\mathrm{D}}}}{\htmlData{sym=R_1}{R_1}} = \frac{\htmlData{funit=V,v=5}{\text{5.00 V}} - \htmlData{funit=V,v=1.7394891013026628}{\text{1.74 V}}}{\htmlData{funit=kΩ,v=1000}{\text{1.00 kΩ}}} = \htmlData{funit=mA,v=0.00326051089869736}{\text{3.26 mA}}\end{aligned}

Shown with this lesson’s starting values. In the simulation the numbers change as you move the sliders.

$I_{\mathrm{D}}$: Diode current (A · ampere) : The current through the diode.
$I_{\mathrm{S}}$: Saturation current (A · ampere) : A tiny leakage current that sets where a diode or transistor curve sits (about 1 pA to 1 nA).
$\mathrm{e}$: Euler’s number e ≈ 2.718 (no unit) : A fixed number used for anything that grows or decays smoothly, such as a capacitor charging. Not a variable.
$U_{\mathrm{D}}$: Voltage across the diode (V · volt)
$n$: Ideality factor (no unit) : A number from 1 to 2 that describes how close a diode is to the ideal formula. No unit.
$U_{\mathrm{T}}$: Thermal voltage (V · volt) : A fixed voltage set by temperature: about 25.9 mV at room temperature. It sets how steep a diode’s curve is. Datasheets usually write it V_T.
$U_{\mathrm{s}}$: Supply voltage (V · volt) : The source or supply voltage.
$R_1$: Resistance of R1 (Ω · ohm) : How strongly something opposes current.

Common questions

How do I calculate the resistor for an LED?

Subtract the LED’s forward voltage from the supply voltage, then divide by the current you want. For a 5 V supply, a red LED at about 2 V and 10 mA: (5 − 2) ÷ 0.010 = 300 Ω, so use the next standard value up, 330 Ω.

What is forward voltage?

The voltage that appears across a diode while it conducts. It barely changes as the current changes, which is why a resistor, not the diode, decides how much current flows.

What does a Zener diode do?

Connected backwards, it starts to conduct at a precise voltage (its Zener voltage) and then holds that voltage almost constant. With a series resistor it makes a simple reference or limiter.