Creating a backup power supply circuit for a dc battery

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engineerstdent
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I am trying to create a backup dc power supply that is charged by a battery which ranges between 10 and 21Vdc. The backup supply needs to output 20W (10V, 2A) of power for 5 seconds when the battery is disconnected. I have performed some research into how long the capacitor in the backup supply will take to charge and has been determined to be negligible. I was thinking of using a simple RC circuit if possible. Additionally, the backup circuit should only be active when the battery is disconnected. Any suggestions on how to tackle this is appreciated. I was thinking of using a sensor to determine when the battery voltage is zero, meaning the battery is disconnected and then "turn on" the backup circuit.

Mainly, I am looking for any suggestions towards the circuit design of the backup circuitry and any suggestions about how to turn the backup circuit on only when the battery is disconnected.
 
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engineeringstudent, Welcome to Physics Forums!

You have asked two questions:

1. How to sense the battery disconnect?
Normally this is accomplished by an “under voltage sensor”. You may Google that and find lots of choices.

Here is a common device, very inexpensive, you set the "trip voltage level", and the data sheet here shows many applications diagrams:
http://www.mct.net/download/on/mc34064.pdf

2. Backup supply, capacity 20Watts (10V, 2A) for 5 seconds.
Supercapacitors seem the logical choice for your rechargeable backup supply. To gauge the capacity needed for your application see the section labeled “Energy density and power density.
See the section labeled “Electrical parameters of supercapacitor series of different manufacturers” for a wide selection.
https://www.google.com/#q=supercapacitor
 
How big of capacitor do you think you will need?
How will you charge your capacitor?
What will the initial voltage be before you start discharging it and what will the final voltage be after 5 seconds of discharge at 2 amps?