I had a matching technique described to me by a professional broadcast engineer. Here's the problem: you have a vertical antenna with a low resonant impedance1, let's say \$38\Omega\$, but you need a better match to a \$50\Omega\$ feedline.
Solution: put a coil between the base of the aerial and ground. Then, you feed off a tap in the coil:
How could this work? I can understand how adding a shunt inductor could improve the match if the antenna presents a capacitive load. But, why feed off a tap in the middle of the coil? If it's working as an autotransformer, wouldn't it be making the antenna impedance appear to be less to the feedline (the opposite of what we are trying to accomplish)? Also, if the antenna is already resonant, wouldn't the addition of shunt inductance make the match worse? Or is this why the feed is off a tap? Please help me understand how this works.
1: in my particular case, the impedance is even lower (I measure \$14\Omega\$) due to shortening of the antenna.