Capacitor hold-up and backup
Constant-power backup time and required capacitance with efficiency and series ESR.
Development preview. Check the assumptions below before relying on a result. Calculations run in your browser.
How it calculates
Model: I=(Vcap−√(Vcap²−4ESR·Pin))/(2ESR); t=C∫dV/I(V); Pin=Pload/η
Assumptions
- Constant delivered power, constant efficiency and ESR; stable low-current branch. Cutoff includes ESR drop. Numerical integration uses 256-interval Simpson quadrature. No leakage or voltage-dependent capacitance.
Worked example
These are the calculator's default inputs. Change any input above to recalculate.
Inputs
- Installed capacitance
- 1 F
- Initial open-circuit capacitor voltage
- 5 V
- Minimum converter input terminal voltage
- 3 V
- Delivered load power
- 1 W
- Converter efficiency
- 90 %
- Capacitor ESR
- 0.1 Ω
- Required backup duration
- 5 s
Results
- Estimated backup time
- 7.04914 s
- Required capacitance
- 0.709306 F
- Usable capacitor energy
- 7.8882 J
- Initial capacitor current
- 0.223219 A
- Current at cutoff
- 0.37037 A