Which of these transmission line impedances would be suitable for constructing a quarter-wave Q-section for matching a 100-ohm feed point impedance to a 50-ohm transmission line?

A quarter-wave Q-section is a matching transformer made from a quarter-wavelength piece of transmission line. It is used to match a feed line to an antenna when their impedances differ. The required characteristic impedance of this matching section is found by calculating the geometric mean of the two impedances you are trying to match. The formula is Z_match = square root of (Z_1 * Z_2). In this scenario, you are matching a 100-ohm antenna (Z_1) to a 50-ohm feed line (Z_2). Multiplying 100 by 50 gives 5000. The square root of 5000 is approximately 70.7 ohms. Since 70.7-ohm cable is not a standard manufactured size, we use the closest widely available transmission line impedance. Standard 75-ohm coaxial cable (such as RG-11 or RG-59) is an excellent substitute and provides a highly effective match for this system.