Some Coaxial Cable Facts and Trivia

A little data from Wiki.  The 1/4 wave antenna impedance is ~ 36 ohms
resistive (at resonance), and a 1/2 wave dipole cut-and-fed in the middle
(1/4 wave to each side) as a nominal 73 ohms of Radiation Resistance (left
as the "impedance" where XL and XC cancel each other out), where as the 1/2
wavelength antenna, fed at the end, is a very high (>3,000 ohms) impedance
antenna and seldom used for that reason (exception:  thru-the-glass
antennas and their special and unique conditions*).  From there, I have
mentioned about why we use 50 ohm coax, and how happily it makes a good
match to which ever 1/4 wave (mobile) or 1/2 wave (center fed) dipole
antenna we happen to be using without having to keep two kinds of coax (and
never enough of the 'right one' we need more of) around!  30 ohms handles
the most power for its size, and 76 ohm has the least loss for its size.
Below from Wiki are some of those facts from a source other than off the
top of my head.  Enjoy!

     *Feeding an end-fed antenna can be very difficult, and even more so
when the end-fed is indeed 1/2 wavelength long.  The end point is a very
high impedance, between 1,000 and 10,000 ohms.  The end of a 1/2 wavelength
whip is attaches to a 'plate' which is glued to the outside of the glass.
The inside coupler has a coil and a capacitor in parallel, which makes a
high impedance circuit to feed 'the third plate' on the outside of the
glass in this "high impedance, voltage feed, low current" end of the 1/2
wave whip, through the glass, which itself makes for a great capacitor
insulator - provided it does not have passivating or tinting in it which
contains metal, in which case, all bets are off!.  On the inside, the 50
ohm coax feeds at tap on the parallel coil perhaps only a turn or two up
from where the shield connects 'at the bottom of the coil.'

     Read the following about coax impedances for fun and pleasure.  Did I
say there would be a quiz Saturday morning?

     They did not mention in the text, but did in the notes on the tables
(not cut 'n pasted here, see link) that RG-62 cable at 93 ohms is what is
used in car radios for the AM Band:  "cable has the lowest capacitance per
unit-length when compared to other coaxial cables of similar size.
Capacitance is the enemy of "...among other things, loading a very short
whip antenna for the hundreds of meters long wavelengths on the AM Band
(31" = 1/4 wave at FM Band).  That very low capacitance cable (and a short
length of it at that) helps to keep from "loading down" ("killing") the AM
Band signals in the coax from such a short "voltage probe" of an antenna on
the AM Band.  Since the antenna system is more critical to performance on
the AM Band, and the FM Band signal reception at least gets a much better
start with a full 1/4 wave, 31" tall, antenna, they use the RG-62 to help
the AM Band performance most.  The low capacitance doesn't hurt the FM Band

     First question:  What is the "geometric mean" impedance of the factors
cited below?  Hint:  Why do we use what impedance cable for radio
transmission systems today?

     What is this all about:  "Installations which need exact matching will
use some kind of matching circuit at the base of the antenna,"?  Hint:
That little metal cap on a Motorola NMO mount 1/4 wave whip.... or an
automatic antenna tuner in my trunk!

Choice of impedance

The best coaxial cable impedances in high-power, high-voltage, and
low-attenuation applications were experimentally determined at Bell
Laboratories in 1929 to be 30, 60, and 77 Ω, respectively. For a coaxial
cable with air dielectric and a shield of a given inner diameter, the
attenuation is minimized by choosing the diameter of the inner conductor to
give a characteristic impedance of 76.7 Ω.[12] When more common dielectrics
are considered, the best-loss impedance drops down to a value between
52–64 Ω. Maximum power handling is achieved at 30 Ω.[13]

The approximate impedance required to match a centre-fed dipole antenna in
free space (i.e., a dipole without ground reflections) is 73 Ω, so 75 Ω
coax was commonly used for connecting shortwave antennas to receivers.
These typically involve such low levels of RF power that power-handling and
high-voltage breakdown characteristics are unimportant when compared to
attenuation. Likewise with CATV, although many broadcast TV installations
and CATV headends use 300 Ω folded dipole antennas to receive off-the-air
signals, 75 Ω coax makes a convenient 4:1 balun transformer for these as
well as possessing low attenuation.

The arithmetic mean between 30 Ω and 77 Ω is 53.5 Ω; the geometric mean is
48 Ω. The selection of 50 Ω as a compromise between power-handling
capability and attenuation is in general cited as the reason for the
number.[14] 50 Ω also works out tolerably well because it corresponds
approximately to the drive impedance (ideally 36 ohms) of a quarter-wave
monopole, mounted on a less than optimum ground plane such as a vehicle
roof. The match is better at low frequencies, such as for CB Radio around
27 MHz, where the roof dimensions are much less than a quarter wavelength,
and relatively poor at higher frequencies, VHF and UHF, where the roof
dimensions may be several wavelengths. The match is at best poor, because
the antenna drive impedance, due to the imperfect ground plane, is reactive
rather than purely resistive, and so a 36 ohm coaxial cable would not match
properly either. Installations which need exact matching will use some kind
of matching circuit at the base of the antenna, or elsewhere, in
conjunction with a carefully chosen (in terms of wavelength) length of
coaxial, such that a proper match is achieved, which will be only over a
fairly narrow frequency range.

RG-62 is a 93 Ω coaxial cable originally used in mainframe computer
networks in the 1970s and early 1980s (it was the cable used to connect IBM
3270 terminals to IBM 3274/3174 terminal cluster controllers). Later, some
manufacturers of LAN equipment, such as Datapoint for ARCNET, adopted RG-62
as their coaxial cable standard. The cable has the lowest capacitance per
unit-length when compared to other coaxial cables of similar size.
Capacitance is the enemy of square-wave data transmission (in particular,
it slows down edge transitions), and this is a much more important factor
for baseband digital data transmission than power handling or attenuation.