SIZING

Start with the energy you need

E = ½C(V₁² − V₂²)

You can't use all of a supercapacitor's energy, because electronics stop working below a minimum voltage. Usable energy is the energy at full voltage V₁ minus the energy left at the cutoff voltage V₂.

Usable energy comes from the voltage range you can actually use.

SOLVING FOR C

How big must it be?

C = 2E / (V₁² − V₂²)

Example: a sensor burst needs 6 mJ, and the supercapacitor swings from 3.3 V down to 2.0 V. Then C = 2 × 0.006 / (3.3² − 2.0²) = 0.012 / 6.89 ≈ 1.7 mF. Real designs add margin for leakage and aging, since end of life is often defined as a 20% capacitance loss.

Always add margin for aging and leakage.

HOLD-UP TIME

How long can it carry a load?

t = C(V₁ − V₂) / I

For a constant current I, the voltage falls in a straight line, so hold-up time is t = C(V₁ − V₂)/I. Example: a 1 F capacitor supplying 0.5 A while falling from 5 V to 3 V lasts 1 × 2 / 0.5 = 4 seconds.

A constant-power load drains faster, since it draws more current as the voltage falls.

THE ESR DROP

Resistance takes its cut instantly

ΔV = I × ESR

When a load switches on, the voltage drops at once by I × ESR, before the capacitance has even begun to discharge. Example: a 2 A pulse through 0.1 Ω of ESR drops 0.2 V immediately and wastes I²R = 0.4 W as heat. If the cutoff is close, that drop alone can trip it.

Check both: the energy budget and the instant drop.

SIZING CHECKLIST

Before you pick a part

Voltage range Highest safe voltage and lowest usable voltage

Load profile Peak current, its duration, and constant current or constant power

Energy Usable energy from ½C(V₁² − V₂²), plus margin

ESR The instant drop and heating at peak current

Life and temperature Aging, leakage, and derating in the real environment

Series stacks Cells must be balanced so none exceeds its rated voltage

Key idea Sizing is arithmetic plus margin.

UNIT 40 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered usable energy, hold-up time, and the ESR drop, with worked examples.