Power Supply Hold-Up Time Formulas

Hold-up time formulas: the energy a bulk capacitor gives between two voltages, the time it can carry a load and the capacitance needed for a given time.

The formulas

C is the bulk capacitance in farads, V1 the voltage at the start of the outage, V2 the lowest voltage at which the converter still works, and P the power drawn from the capacitor in watts, which is the output power divided by the converter efficiency. The load is taken as constant power, which is the case for a switching converter. The values are examples. The capacitance falls with age and cold, so allow a margin.

Worked example: 470 µF, from 380 V to 300 V, at 500 W

1. E = ½ × 470e-6 × (380² − 300²) = 12.78 J
2. t = 12.78 / 500 = 25.57 ms

Hold-up time by load (same capacitor)

Frequently asked questions

Why use a constant-power load?

A switching converter draws more current as the voltage falls, to keep its output power, so the capacitor energy is used at a constant rate.

What sets the lowest voltage?

The converter data sheet, which gives the lowest input at which the output stays in regulation.

Does a bigger capacitor always help?

It gives more time, but it also increases the inrush current at start and the size, so the design is a compromise.

Should I allow for ageing?

Yes. An electrolytic capacitor loses capacitance over its life and when it is cold, so size it with a margin.

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