switching power redundancy
The easiest way to do it is with diode switching







simulate this circuit &ndash; Schematic created using CircuitLab

D1 and D2 are high-current diodes, preferably Schottky for low voltage drop.

There will be a slight loss of efficiency due to heating of the diodes, but for good Schottkys the loss should be in the range of 2%.

PS2 (your backup supply) is set to just below PS1's normal voltage. I've shown it here as 1 volt less, but the exact amount depends on how stable PS1 is.

I've shown the load as resistor just because I'm lazy.

Note that, if PS1 has a temporary dip in output voltage, PS2 will seamlessly fill in for it - it does not require that PS1 fail completely. This may or may not be a good thing. If you were to make a system which monitors PS1 and switches over in case of failure, it's easy to produce an alarm to let you know that PS1 needs attention. This is not so straightforward for this setup.