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.

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).