Transmission Lines for Dummies
Robert Lay
Celebrating my 50th anniversary in Ham Radio
Myths and Basic Truths
Myth #1 - 450 ohm Ladder Line requires a 9:1 balun in order to match to a 50 ohm line.
Basic Truth #1 - The Zo of the line is seen only if the line is matched
with its characteristic impedance. Otherwise, the impedance seen is a
complicated formula based on terminating impedance, length and
frequency. (See "Characteristic Impedance" below)
Myth #2 - I don't need a balun, because my antenna (or dipole) is resonant.
Basic Truth #2 - A balun is recommended in connecting coax lines to
balanced lines or balanced antennas - otherwise there will be an RF
conduction path on the outside surface of the coax shield. (See "Baluns
and RF on the Coax Shield" below)
Myth #3 - The SWR should be 1:1 because the antenna is resonant.
Basic Truth #3 - There is no antenna that is inherently matched to any
particular transmission line. The resistive or real component of the
antenna's impedance is a function of its physical dimensions, its
orientation with respect to surroundings and its frequency. (See
"Antenna Impedance" below)
Myth #4 - A quarter wave transformer can always be used to match the antenna to the transmission line.
Basic Truth #4 - A quarter wave transformer has no magical properties.
It can be used between two impedances for which the characteristic
impedance of the transformer is the geometric mean. For example, a
quarter wave, 75 ohm line will match a 112 ohm antenna to a 50 ohm line.
Great! However, if you are familiar with the Smith Chart or other
techniques for designing matching sections, you can use lengths of
transmission line, both open and shorted, to obtain transformations or
to make impedance corrections. (See "Quarter Wave Transformers" below)
Myth #5 - The G5RV anenna will not tune up on the 30 Meter Band.
Basic Truth #5 - The G5RV is not easily tuned to 30 Meters, but the
problem is not really any different than the problems with the center
fed Zepp. It so happens that the distance from the end of the G5RV to
its center and thence to the end of the balanced line section is
approximately 82'. Due to the velocity of propagation of the balanced
line section, the electrical length may approach 90 or 95 feet. A
simple calculation shows this to be approximately one wavelength at 30
meters, which means that there is a very high impedance point at the
transition from balanced line to the coax. In other words the coax will
have almost infinite SWR. Whether or not this can be tuned is a
critical function of exactly how long the balanced line section is in
relation to its velocity of propagation and the ability of the tuner to
deal with high impedances. (See "Tuners" below)
Myth #6 - A heavy gauge wire or strap connected to an earth rod is a "ground".
Basic Truth #6 - Any conductor connected to an earth rod, or any other
solid connection to the earth or a buried conductor, can act like an
antenna all by itself. In fact, such wires can be better antennas than
"grounds". The impedance of a wire or strap changes as a function of
frequency and the length of the wire or strap to the point where it is
earthed. If the length approaches one quarter wavelength or an odd
multiple thereof, the impedance will be extremely high. Therefore,
so-called ground wires can often be very poor grounds indeed. If the
ground wire is getting too long to be a good ground, it may improve
things to make it a half wave long, in which case it begins to act like a
good ground again. However, the RF current flowing in such a ground
wire may be equal to the RF current in the antenna proper. It depends on
the type of antenna - whether it's balanced or unbalanced against
ground. An end fed antenna system is actually comprised of a part that
you normally think of as the antenna itself and also a part that you
think of as the ground wire. The "ground" wires in house wiring are
earthed at, or close to, the service entrance panel, but from there out
to the extremities of each branch you have a veritable Christmas tree of
antenna branches. Each such branch is effectively an antenna resonant
at some frequency. The ends of those branches can be very hot with RF
voltage if they happen to be a quarter wave at or near your frequency of
operation.
Frequently Asked Questions (FAQ)
FAQ#1 - Why is it so difficult to get a center fed Zepp tuned up on certain frequencies?
Apparently, the mythology associated with open wire feed lines leads
people to believe that the open wire feedline automatically avoids the
problems of tuning very high or very low impedances. There is a voltage
loop (high impedance) at the end of an antenna and every half wavelength
thereafter. Therefore, as the distance from the tip to the feed point
and thence down the transmission line to the tuner approaches a half
wavelength (or a multiple thereof), the impedance gets so high as to
make it difficult to tune. (See "Tuners" below)
FAQ #2 - Why does the SWR seem to be different with different lengths of coax?
This is usually a symptom of RF flowing on the outside surface of the
coax. There doesn't seem to be any general agreement as to why an SWR
meter would be sensitive to RF on the shield, but there does seem to be a
correlation. (See "Baluns and RF on the Coax Shield" below)
Technical Topics
Characteristic Impedance:
The characteristic impedance of a
transmission line, Zo, is the impedance with which it must be terminated
at the load end in order to be flat - i.e., not have any standing waves
(SWR = 1:1). If a transmission line is not terminated in its
characteristic impedance, there will be a reflection of energy at that
mismatch which will in turn be responsible for a buildup of standing
waves. The formulae for reflection coefficient and SWR are all found on
p 24-18 of the ARRL Antenna Book, 17th Edition.
Tuners:
The tuners available commercially will generally include a
toroid wound balun, typically 4:1. The tuners will be capable of
transforming the impedance seen looking into the transmission line to a
50 ohm impedance (50 + j 0) - but only if the impedance to be
transformed lies within certain limits. It is impractical with most
tuners to deal with impedances that lie outside the range 10 to 500
ohms. Once the impedance gets above or below that range, the tuner is no
longer able to transform the impedance to 50 + j 0 ohms. Note that the
tuner does not affect the SWR on the line between the tuner and the
load in any case. It only affects the SWR on the coax from the
transmitter to the tuner. The purpose of the tuner is to present a 50
ohm load to the transmitter. The tuner would have to be installed at
the antenna in order to make the entire transmission line flat.
Baluns and RF on the Coax Shield:
From ARRL Antenna Book, 17th Ed.,
p25-14. "A center-fed antenna with open ends, of which the half-wave
dipole is an example, is inherently a balanced radiator. ... If the
antenna is fed at the center through a coaxial line, this balance is
upset because one side of the radiator is connected to the shield while
the other is connected to the inner conductor. On the side connected to
the shield, a current can flow down over the outside of the coaxial
line. .... these "antenna currents" flowing on the outside of the line
will be responsible for radiation."
A Balun is one of the ways in which antenna currents on the outside of the coax can be reduced or eliminated.
Quarter Wave Transformers:
The quarter wave transmission line has
the interesting property that the input impedance, Zi, the
characteristic impedance, Zo, and the terminating impedance, Zt, are
related as follows:
Zi = Zo^2 / Zt.
This property is useful when you have a piece
of transmission line having Zo equal to the geometric mean of a load
impedance and the impedance to which you want to convert.
Antenna Impedance:
While it is true that a resonant dipole has an
impedance very close to 50 + j 0 (50 ohms resistive), antennas in
general can have quite a range of impedance. In fact, the radiation
resistance of the resonant dipole is very dependant upon the height over
ground, as can be seen in the curve on p 3-11 of the ARRL Antenna Book,
17 Edition. The radiation resistances over realistic earth will vary
from 45 to 100 ohms. There are probably more antennas being used off
resonance or at harmonics of the resonant frequency than there are being
operated at resonance. For example, the G5RV is almost never operated
at its resonant frequency, which would be between 4 and 5 MHz.
Folded Dipoles can have impedances of several hundred ohms at resonance, depending on wire diameter and spacing (See p2-33).
Verticals can have impedances at resonance from about 35 ohms and up, depending upon ground impedance (See pp 2-34, 2-35).