I have a receiver board that reads inputs from a key fob like you use to unlock your car. The Rx board has a single coiled wire which seems to be the antenna (first pic). I would like to add a magnetic base antenna (second pic) to extend the range of the system. My problem is that I don't know how to connect the Rx single wire to the SMA connector. Does the center wire of the coax connect to the Rx coiled wire? What about the outer jacket of the coax? Do I connect it to system ground?
Be sure, that antenna designed for specific freq. band, otherwise it 'd be useless. Central pin of SMA goes to onboard RF out, exterior to ground.
Thanks. They are both 433 MHz.
You may want to try with both the wire antenna and the external antenna. The wire antenna may perform better unless you board is in a metal box. Coax loss could become an issue at the frequency.
You'll get far better range with a straight 1/4 wave antenna than the coiled wire one usually... Tuning an antenna by guess-work is
rather hit-and-miss. 1/4 wave at 433MHz is 17.3cm in free air, but nearby objects will detune it somewhat. You ideally have this
at right-angles to a continuous groundplane for best performance. The SMA antenna looks like an inductively loaded 1/4 wave
(the coil allows the antenna to tune when somewhat shorter than ideal). As mentioned the length of coax will have noticeable
losses at UHF frequencies, simple straight 1/4 wave is possibly better.
It's actually a base loaded 3 DB gain antenna. Good Co-axial cable at that frequency should loose about 1 - 1.5 DB for a 3 meter piece of co-ax.
@ 2.4 GHz the best quality miniature cable would loose about 10 DB, So 1/10th of the power received would be available at the other end. IHTH..
Doc
Assuming its a decent piece of coax (polythene or teflon dielectric)... But anything will be better than the coiled wire 
You can get cheap SMA jacks that you can integrate into project by just putting a few small rectangular pads on your PCB and run traces to it. All the pins are ground except the center one. So you typically run a trace to a ground pin, a trace to the signal pin, and solder down all five pins if you are doing this on the edge. Or you can use it through-hole as well. Looking at your PCB above, I bet you could even integrate one of these on the edge of that PCB.
