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There's a big difference between a 'loading' coil and an impedance 'matching' coil in both their placement and their size.  A 'loading' coil provides the inductance reactance required to neutralize the over abundance of capacitance reactance of a 'too short' antenna has.  When the combined inductive and capacitive reactances equal zero reactance the antenna is resonant.  Adding length adds inductance, removing length reduces inductance which means increases capacitance.  (Confused up yet?)  Inductive reactance is (+), capacitive reactance is (-).  Add the right amount of '+' to the right amount of '-' and you end up with '0', which is resonance.  The amount of wire used to make that loading coil has absolutely no direct relation to how 'short' the antenna is.  A length of straight wire has a certain amount of inductive reactance.  If you coil up that length of wire, it will have a lot more inductive reactance than it did when it was straight.  The resulting inductance produced has to take into account the diameter of the coil, the space between windings, and the size of the wire used.  There's a formula for that but it is not a simple one.  Look it up, see for your self.

A 'matching' coil is placed at the feed point of the antenna, the other end is connected to ground, or the braid of the coax.  The size of that coil is quite a bit smaller than is a loading coil.  The combination of the antenna in parallel with an inductor to ground adds enough inductive reactance to produce an input impedance of the desired amount (usually 50 ohms).  [The 'tricky' part of that is that -impedance- is composed of resistance and reactance.  Find a good AC electrical text to understand it, I won't even try to explain it.  And that reactance comes in two kinds, '+' and '-'.  Just keeps getting 'better' and 'better', huh?]

Where you find reactance, and how it's used, can make a huge difference.  A loading coil and a matching coil are very nice examples of that.  Clear as mud, right?

 - 'Doc