Half-Wave Dipole Aerial & Making a Balun

The Half Wave Dipole is an Antenna that is robust, handles high power and has 0dB gain. In real fact it does have some gain. And it will usually outperform 5/8 wave verticals. For a dipole aerial to work properly, it must be resonant at the frequency you are using. It has a fairly wide bandwidth though, so you will be able to use it about 4 MHz above and below the centre frequency without re-tuning, in practice.
The Half Wave Dipole Antenna requires a Pawsey Stub Balun, otherwise you will probably get radiation from the coax. Take a look at the picture below, it's all there! The Pawsey Stub Balun actually converts the Dipole balanced terminals to an unbalanced termination. Another way of looking at it is that the 1/4 wave stub acts as a very high impedance to rf currents wanting to flow back down the outside of the feeder, and radiate.