Random Walk
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In order to make that work, you'll need to supply a voltage of approximately +3.3 - 5 volts relative to the coaxial ground on the center conductor of the coax to the antenna, without sending it to your dongle. (or it could partially burn out the protection diode) The professional way to do that would be to use a bias tee, or power injector. Alternatively, you can build one yourself in a metal project box. Use a low value (pf range) capacitor to block dc from getting to the receiver. Make sure to mark the crucial connections, to antenna, to receiver, + power, - ground clearly! Also filter the power input connection as best as you can because that is an ideal path for RFI to mess up your reception. Use a good rf choke. Don't use a standard binding post as that looks like an antenna to microwaves. I would recommend using a small coaxial connector of a kind you don't use for other stuff for the power, then put both a choke and capacitor and perhaps a current limiting resistor on that using as short leads as possible. Depending on how careful you are on the outside you also might want to put a diode to prevent inadvertent application of the wrong polarity voltage.
The LNAs in GPS antennas don't require a lot of current, so you can safely limit the current with a variable resistor, experiment a bit to get the appropriate value.