It's fairly simple, but can get complicated in a hurry. A balun is used to match a 'balanced' antenna with an 'unbalanced' feed line. For a typical balun, the balanced/unbalanced thingy is looking from the antenna to the feed line. The balanced part is typically the output of a balun, the unbalanced part is typically the input of the balun.
The impedance ratio is looked at from the other direction. The feed line is the '1'. The impedance of the antenna is the other side of that ratio thingy (2 or 4 or 76, whatever). If the feed line is 50 ohms and the antenna input impedance is 100 ohms, then use a 2:1. If feed line = 50 ohms and the antenna's input is 200 ohms, use a 4:1. And 1:1 if the antenna's input impedance is 50 ohms.
Close counts to some degree. If a balun's transformation ratio is such that it gets the impedance match close to about 1.5:1, then it's probably going to work well. If it won't get sort of that close, it just ain't gonna work too well. Try something else. Probably a closer to reality number is like 2:1 for SWR, sort of.
Then there's the really 'different' solution, use two of the things. If the correct combination of impedance ratios is picked, you can match almost anything, sort of.
And then there's the 'other' side of using baluns. They are typically just another 'point of failure' is one is used that doesn't exceed the voltage/current/power ratings necessary for the particular application. Which basically means use a much larger balun than you think is necessary in terms of voltage/current/power capacity. Having a capacity of two or three times what you think you'll ever feed the thing ain't unreasonable at all.
Baluns do not always stop the feed line from radiating. They do not always cure RFI. And they are not the answer to most problems of that nature. They can certainly help though, if the problem arises from a balanced to unbalanced condition, or a hugely mismatched impedance ratio.
There, that ought'a get it started...
- 'Doc