Antennas, Transmission Lines, and Feed Lines
Resonance and length
A half-wave dipole is about 0.5 wavelength in free space; end effects shorten a practical wire. Classic shortcuts: half-wave length in feet is about 468 divided by frequency in MHz; quarter-wave is about 234 divided by frequency in MHz. A quarter-wave vertical needs a ground plane or counterpoise. Short antennas have low radiation resistance and high loss unless loaded with a coil.
Feed lines
Coaxial cable is unbalanced: shield to ground, center conductor to the antenna. Characteristic impedance (50 ohms for most radio, 75 ohms for video) depends on conductor diameters and dielectric, not on length. Loss rises with frequency and with lossy dielectric; foam cable beats solid polyethylene of the same size. Velocity factor (0.66 to 0.9) slows the wave, so physical length = electrical length x velocity factor.
Matching
VSWR is the ratio of maximum to minimum voltage on the line. 1:1 is perfect; 2:1 reflects roughly 11 percent of the power; higher values stress the transmitter. Return loss in dB states the same condition more cleanly. A balun couples a balanced antenna to unbalanced coax and prevents shield current. Use an antenna tuner at the transmitter end only when the line can withstand the standing waves.
Gain and patterns
Gain is directional: dBi references an isotropic radiator, dBd references a dipole, and dBi = dBd + 2.15. Doubling the number of identical stacked elements adds about 3 dB. ERP is transmitter power times antenna gain, less feed-line loss.
Rule of thumb: 468/f for a half-wave, 234/f for a quarter-wave, and add 2.15 to dBd to get dBi.