# Calculators: Power Supply Hold-up Time

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Often, you need to calculate that a power supply will remain operating for a required period of time. In the mean time, allowing, say, the microcontroller to perform cleanup functions before being rudely interrupted. Some equipment requires being able to ride through a short interruption (like the constant interruption of power from rectified AC, where filtering is a simple example of obtaining hold-up), usually for industrial, mobile or aeronautical applications.

These calculators cover the three most common situations: resistive, constant current, and constant power.

Enter new numbers and see the remaining output value change. Floating point format ("1.1E-6") works; engineering units ("1.1u", etc.) do not.

Note that the units are simply ratios, so their actual units do not matter (as long as the same units are used for all steps). They're labeled in ms and V for convenience.

When the supply drops, load voltage decays exponentially according to the RC time constant. Hold-up time is a simple exponential ratio. Typical examples include simple loads like resistive heaters, lamps, motors, etc., and some digital logic circuits. Load Resistance RL = Ω Minimum (Nominal) Supply Voltage Vmin = V Load Cutoff Voltage Voff = V Hold-Up Time t = ms Capacitor C = μF

## Constant Current

A constant current load discharges the capacitor linearly. Hold-up time is an even simpler linear ratio. Typical examples are analog circuits, such as op-amps, power amplifiers and linear regulators. Vmin will typically be around the point where the amps/regulators begin to saturate or clip or drop out. Load Current IL = A Minimum (Nominal) Supply Voltage Vmin = V Load Cutoff Voltage Voff = V Hold-Up Time t = ms Capacitor C = μF

## Constant Power

A switching converter makes much better use of the energy storage, but has a negative resistive input characteristic. This accelerates discharge as it goes to zero. Fortunately, the differential equation is solved with a simple quadratic. Load Resistance RL = Ω Nominal Output Voltage Vo = V Typical Converter Efficiency η = % Converter Power Input P = W Minimum (Nominal) Supply Voltage Vmin = V Converter Cutoff Voltage Voff = V Hold-Up Time t = ms Capacitor C = μF

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