Square Wave Amplifier - 5VDC -> 13VDC
One way is to essentially build a couple of stages of digital inverter from discrete parts:







simulate this circuit &ndash; Schematic created using CircuitLab

U4 is a linear regulator programmed for 13 V output or a bit higher. Keeping the input power voltage close (but not too close) to 13 V will minimize power lost in the regulator.

The value of R1 can be varied to balance power consumption against switching speed.

Choosing actual part numbers for the FETs is left as an excercise for the reader. M2 needs to have low enough threshold voltage to be turned hard on by a 5 V input. M1 and M3 need to withstand ~15 V Vgs, and need to be able to carry your load current when "on".