Hold-Up Time Capacitor

Q: How do you calculate Hold-Up Time Capacitor?

Use the formula t = C × (V_max² − V_min²) / (2 × P_load). Hold-up time is the duration a power supply can maintain its output after the input power is interrupted, using energy stored in the bulk electrolytic capacitors. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for Hold-Up Time Capacitor?

The Hold-Up Time Capacitor formula is t = C × (V_max² − V_min²) / (2 × P_load), where t—Hold-up time (s); C—Bulk capacitance on the DC bus (F); V_max—DC bus voltage when fully charged (V); V_min—Minimum DC bus voltage for regulation (V); P—Load power (W).

t = C × (Vmax² − Vmin²) / (2 × P)

Quick answer

This calculator solves t = C × (V_max² − V_min²) / (2 × P_load) for Hold-Up Time. With Bulk Capacitance 100 µF, Max Voltage (charged) 12 V, Min Voltage (cutoff) 26.4 V, Load Power 10 W, the result is -2.765 ms. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Bulk Capacitance

Max Voltage (charged)

Min Voltage (cutoff)

Load Power

Hold-Up Time (ms)

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Formula

t = C × (V_max² − V_min²) / (2 × P_load)

Description

Hold-up time is the duration a power supply can maintain its output after the input power is interrupted, using energy stored in the bulk electrolytic capacitors. The energy available is E = ½C(Vmax² − Vmin²), where Vmax is the fully charged DC bus voltage and Vmin is the minimum voltage at which the downstream converter can still regulate. For server and telecom power supplies, the typical requirement is 20 ms (one full cycle of 50 Hz mains) of hold-up time to ride through brief power interruptions without disrupting the load.

Variables

t — Hold-up time (s)
C — Bulk capacitance on the DC bus (F)
V_max — DC bus voltage when fully charged (V)
V_min — Minimum DC bus voltage for regulation (V)
P — Load power (W)

Practical Notes

Example: 400 V DC bus, 300 V minimum, 200 W load, 20 ms required: C = 2 × 200 × 0.02 / (400² − 300²) = 8/70000 ≈ 114 µF. Use 120 µF or 150 µF standard value. The hold-up capacitor is typically the largest and most expensive component in the power supply. For higher power or longer hold-up times, consider adding a separate energy storage stage with supercapacitors.

Symbols and units

Symbol	Meaning	Default unit	Accepted units
t	Hold-Up Time	ms	ps, ns, µs, ms, s, min, h
C	Bulk Capacitance	µF	pF, nF, µF, mF, F
Vmax	Max Voltage (charged)	V	pV, nV, µV, mV, V, kV
Vmin	Min Voltage (cutoff)	V	pV, nV, µV, mV, V, kV
P	Load Power	W	µW, mW, W, kW

Step by step

1. What you know: Bulk Capacitance 100 µF, Max Voltage (charged) 12 V, Min Voltage (cutoff) 26.4 V, Load Power 10 W
2. The relation: t = C × (V_max² − V_min²) / (2 × P_load)
3. Substitute: C = 100 µF, Vmax = 12 V, Vmin = 26.4 V, P = 10 W
4. Result: Hold-Up Time = -2.765 ms

Worked examples

Minimum range

Given: Bulk Capacitance 100 nF, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW

Result: Hold-Up Time = -2.091 µs

Low range

Given: Bulk Capacitance 1 µF, Max Voltage (charged) 3.3 V, Min Voltage (cutoff) 7.26 V, Load Power 100 mW

Result: Hold-Up Time = -0.2091 ms

Typical

Given: Bulk Capacitance 100 µF, Max Voltage (charged) 12 V, Min Voltage (cutoff) 26.4 V, Load Power 10 W

Result: Hold-Up Time = -2.765 ms

High range

Given: Bulk Capacitance 1 mF, Max Voltage (charged) 0.23 kV, Min Voltage (cutoff) 0.506 kV, Load Power 1 kW

Result: Hold-Up Time = -101.6 ms

Maximum range

Given: Bulk Capacitance 10 mF, Max Voltage (charged) 2.3 kV, Min Voltage (cutoff) 5.06 kV, Load Power 10 kW

Result: Hold-Up Time = -10.16 s

Solving for each variable

Solve for Hold-Up Time

Bulk Capacitance 100 nF, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW → -2.091 µs

Solve for Bulk Capacitance

Hold-Up Time 100 µs, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW → -4.783 µF

How Hold-Up Time changes with Bulk Capacitance

Bulk Capacitance (input)	Hold-Up Time (result)
10 µF	-0.2765 ms
25 µF	-0.6912 ms
50 µF	-1.382 ms
75 µF	-2.074 ms
100 µF	-2.765 ms
150 µF	-4.147 ms
0.2 mF	-5.53 ms
0.4 mF	-11.06 ms
0.7 mF	-19.35 ms
1 mF	-27.65 ms

The same result in other units

Unit	Value
ns	-2765000
µs	-2765
ms	-2.765
s	-0.002765

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Frequently asked questions

How do you calculate Hold-Up Time Capacitor?

Use t = C × (V_max² − V_min²) / (2 × P_load). With Bulk Capacitance 100 µF, Max Voltage (charged) 12 V, Min Voltage (cutoff) 26.4 V, Load Power 10 W, Hold-Up Time works out to -2.765 ms.

What is the formula for Hold-Up Time Capacitor?

The formula is t = C × (V_max² − V_min²) / (2 × P_load). Hold-up time is the duration a power supply can maintain its output after the input power is interrupted, using energy stored in the bulk electrolytic capacitors.

How do you find Bulk Capacitance when you know the other values?

Rearrange for Bulk Capacitance: with Hold-Up Time 100 µs, Max Voltage (charged) 0.33 V, Min Voltage (cutoff) 0.726 V, Load Power 10 mW, Bulk Capacitance is -4.783 µF.

What units does Hold-Up Time Capacitor use?

Hold-Up Time is shown in ns, µs, ms, s. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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