Electronic – Why do rubber duck antennas have this metal part, while other antennas do not

The big question is: what distance do you want to cover? The data sheet of the transmitter quotes a maximum range of 50 metres [about 150 ft]. Will you use that, or will the receiver be closer?

Any oscillating signal will radiate: the whole point of the USA's FCC is to limit the amount of annoying [or dangerous] EM radiation coming from devices. Depending on the range, and the presence of bulky metallic objects between transmit and receive, Your Mileage May Vary.

Antenna theory and design can be taught in depth by amateur radio enthusiasts, or groups like ARRL. For starters, a simple piece of wire about 20cm long can act like a "whip" antenna: keep it clear of grounded cases, and it should be enough to get you started. A second piece the same length can act as your receive antenna. Start with the circuits next to each other, make sure they work, then seperate them. If they stop working before reaching the seperation you want, THEN [and only then!] consider delving into antenna theory...

If you need more, I'd suggest TI's Application Note #AN058: http://www.ti.com/lit/an/swra161b/swra161b.pdf

And: http://www.picaxe.orconhosting.net.nz/yagi433.jpg

All antennas have two connections, although sometimes one of the connections may not be obvious. Take a look at a basic dipole antenna. That clearly has two connections, which should be symmetrically driven.

Some "whip" antennas and others may appear to have only one connection, but that is because they use a ground plane. Typical commercial AM transmitters are common examples of that. The antenna is a single conductor (usually some kind of tower) sticking up from the ground. The tower is insulated from the ground. One side of the RF feed connects to the base of the tower, and the other to ground right under the tower.

A ground plane is basically a mirror for radio waves. The AM tower is really only half of a antenna. If you could see at radio wavelengths, from a distance you would see a whole antenna because the top half would be reflected by the ground plane to make a apparent complete antenna. Half of this apparent antenna would be above ground and the other half below ground. The whole acts pretty much like a dipole. One difference between a real dipole and a apparent one made with a mirror is that the second type only works in the half-space above the mirror. However, if you're in that half space, there is little to distinguish the mirrored antenna from the real thing at a distance.

Another way to look at this is that the laws of physic don't go on vacation just because the frequencies get higher than what you are used to. To have a circuit with current flowing thru it still requires a closed path somehow. If you only connected one side of the transmitter output to a antenna, there would be no current coming out of the transmitter, hence no power and no signal gets sent anywhere.

A properly tuned antenna looks like a resistor electrically. That means it absorbs real power from the circuit. However, unlike a resistor that turns the power into heat, the antenna sends it into space as radio waves. If everything is tuned right, your transmitter can't tell the difference between a common dipole at the end of the RF feed line and a 75 Ω resistor.