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Would adding an impedance matching device at the antenna's feed point make a difference?  I would have to think it would make a difference in the impedance match between the antenna and feed line, wouldn't you?  A good impedance match means that there's a better transfer of energy between feed line and antenna, more signal getting to the antenna to be radiated.  The typical 25 - 35 ohms input impedance of a 1/4 wave antenna would then be closer to 50 ohms which would certainly make the transmitter 'happier'.  (That holds true for any frequency, not just RF.  The typical AC from those power lines for instance.)  Efficient transfer of energy is the whole idea, less losses because of reactance, right?  If the load is the same impedance as the transmission line and the transmitter, there's only resistive losses present because of the length of that transmission line.  (Those resistive losses are nothing compared to the potential losses from an impedance mismatch.)  If the load is reactive, then the amount of loss depends on just how reactive it is, and why.  One of the contributors for that reactance is the feed line if there's a mismatch between it and the antenna, or it and the transmitter.  That means that while the length of feed line can act as an impedance 'transformer', it also has the liability of not being designed or constructed to handle that transformation very efficiently.  In other words it can be 'over-loaded' real easily and destroy it's self.  Coaxial cable is just not made to handle the voltages common to impedance transformation.

So can the length of the feed line make a difference?  Sure.  Is there a better way of doing things?  Sure.  That 'itty-bitty' coil at the feed point of a mobile antenna is just one of those ways to do it 'better'.  So why don't mobile antenna makers include such a coil that can be adjusted?  Because then it wouldn't be 'plug-n-play' anymore.  And it'd cost more.

 - 'Doc