The formula for Decible Gain is 10Log(10)(In ÷ Out). For loss, 10Log(10)(Out ÷ In). That's Log base ten (Log), not the Natural Log (Ln).
An "S-Unit" is 6 decibles or 4× the signal.
S-Meters work on AM and SSB receivers. On FM, they're at best an approximation.
A Transmission Line or Feedline is the name for whatever wires you're using to connect a radio to an antenna. It requires 2 wires (a complete circuit) and is generally made of one of these types of premade cable:
Coaxiaal Cable is round and composed of an inner insulated wire with an outter braded shield around it and an outter insulation outside of that. It is considred to be unbalanced but you can place next to an unlimited number of other coax lines and even run them underground or inside metal conduit or through metal window frames or pipes and it won't affect the signal. Coax does degrade the signal depending on what type of coax it is (mainly, how thick and how high quality) and what the frequency is. If you're transmitting a signal below 30 MHz (10 meters or longer) then it almost doesn't matter -- the cheap stuff works fine. But above 30 Mhz, particularly 2m (144 MHz) you need higher quality and/or thicker coax cable. If you're using it to receive TV broadcasts, you'll need an RF Preamplifier at the antenna to overcome the loss, typically measured in decibles per hundred feet at different frequencies.
Ladder Line is composed of two wires, of equal size held apart from one another by plastic standoffs, usually every few inches or every foot or two. The two wires are parallel to one another and maybe three-quarters of an inch to 3 inches apart, so the signal doesn't degrade, as with coax. However, when you run ladder line (or twinlead, see below) you must add a twist (1 turn every few feet) or make big loops (3 ft diameter or greater) and it must not come into contact or even come close to metal objects such as a window frame or metal fence. Coax is perfectly okay doing that. Ladder Line is considered to be a balanced feedline because both wires are (relatively) equal. Typically 450 Ohms.
Twinlead is like ladder line in all ways but all enclosed in plastic, the whole way and the wires are maybe one quarter inch apart from one another. It has only 300 ohms typically. It is used primarily for FM and Television broadcast receiving antennas.
Type of Coaxial Cables
RG-174 -- Skinny. Has a lot of loss but fine for very short < 1 ft distance.
RG-58, RG-59 -- RG-58 is the old standard for HF radio. (below 30 MHz). If you go less than 50 feet, no problem. It is about a quarter inch in diameter. RG-59 is slightly thicker and is used by the Cable TV industry. It is 75 ohms so we don't use it much as hams.
RG-8, RG-8X -- RG-8 is a half inch in diameter. RG-8X is the same but a quarter inch in diameter. It is better than RG-58 so you can use it for an HF antenna that needs to be 150 ft away and for very short VHF or UHF runs.
LMR-240, LMR-400, LMR-600 -- LMR400 has become standard for HF and VHF and UHF when you have to go a couple hundered feet.
Types of Connectors for Coax
Type F -- used for RG-59 75 ohm television coax
BNC -- used for test equpment and low power applications
SO-239 and PL-259 -- used for most ham radios. Not as good as type-N
Type N -- the best (that we use) for VHF and UHF applications
Type GR, TNC, etc. -- there are many other coax connectors out there
Introduction to Antennas
The simplest real antenna is a half-wave Dipole. It is composed of a center point where the feedline meets the antenna (usually using a balun, to adapt unbalanced coax feedline to the balanced antenna). One side of the feedline connects to a peice of wire one quarter wavelength long, going one way and the other side connects to a peice of wire, one quarter wavelength long, going in the opposite direction. At the opposite ends of those wires are usually insulators tied to ropes, holding it up. The half wave dipole works best when it is placed at least one quarter wavelength above the ground.
The simplest not-necessarily-real antenna contemplated in textbooks is an "Isotropic" antenna, a theoretical antenna that puts out exactly what you put into it in all directions equally. This doesn't perform as well as a dipole but manufacturers often compare their antennas to it anyway, because it makes them look better. For example, an antenna with 14.9 db of gain over a dipole has 17 db of gain over an isotropic antenna. Hence the terms, "dbd" and "dbi". Usually, if a company is comparing their antenna to dbi, they're trying to misslead you into thinking their antenna is better than it actually is.
So, for instance, the rubber duckie antenna on the top of a handi-talkie (3 to 8 inches long thick rubberized antenna on a portable hand-held radio) is -6 dbd. That means that a normal dipole antenna for the specific frequency on which the radio operates, (1 and a half feet long on 2 meters) works 4 times better than the rubber duckie. (That is, -6db = performance ÷ 4).
To calculate the length of the legs of a dipole antenna, just divide the wavelength by four and convert from meters to feet. For example, the optimal length for a dipole antenna to work on 7 MHz (the Ham 40 meter band; 300 ÷ 7 = 42.857 meters) is 20 meters total length, 10 meters per side. 10 Meters is 32.8084 feet or approximately 32 feet and 9 and three quarters inches.
There is a Shortcut: To calculate the length of the legs of a dipole antenna in feet:
234 ÷ frequency in MHz = each dipole side length in feet
Vertical and Ground Planes -- A verticle antenna can either be a stick pointing up and another (metal) stick pointing down or a stick pointing up and a surface (such as a car) or a bunch of radials, wires going out from the center in every direction to form the other half of the antenna.
Polarization of antennas. If an antenna is oriented horizontally, it will transmit a signal 20 decibles lower to a receiving antennas which is oriented vertically and visa-versa. Always try to orient the receive antenna (horizontal or verticle) in the same polarization as the transmitting antenna.
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