This seems to be more of a topic of debate that I anticipated. A post on Ham Radio Forum about the subject was posted by a user named "pallen" in 2007.

If the half-wave dipole is installed less than 1/2 wavelength above earth, it probably has a radiation resistance less than 75 ohms and may match 50-ohm feed-line reasonably well without any type of impedance matching device. How high is it above ground and what is its approximate resonant frequency?

Assuming the dipole radiation resistance actually is 75 ohms:

1) If the feed-line has reasonably low loss per wavelength and will be less than a wavelength or so in length, there probably would be no practical difference in reported signal strengths with and without impedance matching, because the difference in radiated field strengths would be a small fraction of an S-unit and would be masked by the normal signal fading that occurs with ionospheric propagation.

2) There are issues other than radiated field strength to consider. One is transmitter loading. Most transmitters with 50-ohm outputs can be tuned, or will self-tune, to match a 75-ohm resistive load. So, if the dipole antenna is perfectly resonant at the operating frequency, so its feed impedance has no reactive component, your transmitter probably will load fine at that frequency if you use 75-ohm transmission line. However, the range of frequencies over which it will load correctly will be less than if the transmitter was working into a 50-ohm center-frequency termination. If you use 50-ohm transmission line without impedance matching, transmitter loading will depend critically on transmission line length.

3) As to the question of whether it is more important to match impedances at the antenna or in the shack, it depends on whether you are transmitting or receiving. A given transmission line has its least possible RF loss per unit length when it is terminated in its characteristic impedance. Many people falsely assume that "terminated" means both ends, but the "terminating" end is the far end. Therefore, when transmitting, a transmission line's characteristic impedance should match the impedance of antenna that terminates it. However, when receiving, the receiver antenna input impedance should match the transmission line impedance. Given that most receivers have plenty of excess RF gain, transmission line loss when receiving tends to be far less important than transmission line loss when transmitting and the distant received signal must compete with noise and/or other signals. So, if only one end of a transmission line is to be matched, the antenna-end tends to be most important.

3) Dipole antenna feed balance generally tends to be more important than transmission line impedance matching throughout the HF spectrum (except where transmission lines are unusually long). If the antenna feed impedance is truly 75-ohms, an ideal solution would be to use 50-ohm coax transmission line and a 50 to 75 ohm balun between the transmission line and the antenna. The impedance matching would make the antenna useful over a wider range of frequencies and the balanced antenna feed would result in a much more symmetrical antenna radiation pattern.

Most baluns have 1 to 4 impedance transformation ratios, such as from 75 to 300 ohms. However, a simple 50 to 75-ohm impedance transforming balun can be made by winding separate primary and secondary windings on a toroidial core. The impedance ratio of a transformer is equal to the square of its turns ratio, so a primary to secondary turns ratio of 1 to 1.225 will transform from 50 to 75 ohms. That exact ratio can't be achieved without using more turns than an HF transformer with a toroidial core should have, but a 1 to 1.2 turns ratio is practical and will transform 50 ohms to 72 ohms, which is plenty close enough.

The complete post can be found here: http://www.smeter.net/ham-radio/issues-f30/50-75-ohm-tx-mis-match-t605.html

An interesting solution is found here: http://www.kx4om.com/TechSolutions/12th-WaveMatching/12th-wave.html

This DIY matching transformer uses twelvth wave coax pieces to achieve an acceptable SWR.

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