According to Benlo.com:
Figure 1. Hero 2 battery eliminator connection points.
Figure 2. Hardwired Hero 3 battery eliminator.
Using a Battery Eliminator with the Hero 3 Camera
GoPro cameras can be run off a 4 volt power source which replaces the internal battery. The voltage must be no less than 3.75V and no greater than 4.2V. The power supply must be capable of supplying 0 to 1.1 A of current without deviating from the above range. The T-sense pin on the camera is not needed with a battery eliminator power supply.
You can't supply directly from USB 5 V supply. Some form of regulation will be required.
simulate this circuit – Schematic created using CircuitLab
Figure 3. Simple "constant" voltage dropper.
You could try the circuit of Figure 3 to power the camera. The theory of operation is that
- each diode will drop 0.7 of a volt when even a few mA is drawn through them.
- R1 draws the small current so the voltage across the resistor should be about 3.6 V.
- Depending on your exact 5 V voltage from the USB port, the diodes and the camera this might just work. It won't cause any damage as it would be the same as a flat battery.
- If it doesn't work then you could replace one or both diodes with Schottky diodes which have a lower forward voltage drop.
- Connect up the components but not the camera.
- Plug in to USB port and measure voltage across R1.
- If voltage is about right then unplug USB, solder up and test.