August 1944 Radio-Craft
People old and young enjoy waxing nostalgic about and learning some of the history of early electronics.
Radio-Craft was published from 1929 through 1953. All copyrights are hereby acknowledged. See all articles
Is there such as thing as too many articles on transmission lines?
I think not, at least for most visitors to RF Cafe. Since the fundamentals
of transmission lines have not changed in the last century, it really
doesn't matter when an article was written. This one covers the
basics of impedance and wavelength, and then delves briefly into
the subjects of antenna feeder transmission lines and using transmission
lines as impedance transformers. As with most topics these days,
there are many software programs available that will calculate parameters
for you, but successful setup and operation requires a solid understanding
of what is happening with your electronic gear, antennas, and the
transmission lines that provide the interfaces.
By M. N. Beitman*
Specimens of coaxial cable, and a line of it on a turnstile
Fig. 1 - A simple transmission line, showing the physical
and electrical characteristics.
increase in the use of higher radio frequencies for television,
frequency modulation, and radio locator-detector apparatus is forcing
radio servicemen to become acquainted with subjects previously considered
outside the servicing field. Transmission lines is one such subject.
Any electrical line which guides power between two points and has
its physical (actual) length in the order of the electrical wave
length being employed, is considered a transmission line. For complete
understanding of the theory of transmission lines and their applications,
a certain amount of college mathematics is essential. However, a
good general idea of the behavior and uses of transmission lines
can be obtained from this non-mathematical explanation.
Transmission lines are used mainly for coupling the antenna to
a transmitter which may be located some distance away. Besides this
primary application, lines are used as impedance matching devices
(like transformers); in place of lumped series or parallel tuned
circuits, as all types of filters; and for high frequency measurements.
To understand how these functions are obtainable from lines which
at lower frequencies (audio or 60-cycle power frequencies) are considered
simply as conductors of electricity possessing only resistance,
some new concepts must be introduced.
Even a straight short piece of wire has both capacitance and
inductance. Focus your attention on a very tiny piece of the wire
at one end and another tiny piece of this same wire a short distance
away. Certainly these metal pieces (parts of the wire), as such,
are separated by the wire between them which in turn may be considered
as a resistor. This wire does have resistance and this resistance
produces a voltage difference (drop) between the two tiny parts
of the wire. The two tiny pieces of wire form also two plates of
a condenser, with the surrounding air acting as the dielectric.
No fixed quantity of air, or any special section of air, serves
as the dielectric, but all air (and all other insulators in the
universe for that matter) serve as the dielectric of this condenser
which we have just described. In a similar fashion, all other tiny
portions of our wire, form condensers with each other.
In a like manner, it can be shown that the magnetic field produced
by any infinitesimally small portion of the wire, cuts other sections
of the wire and the effects of self-inductance are present. We begin
to see that any wire which may ;form a transmission line has, besides
resistance, capacity and inductance. Also the leakage present may
be expressed as conductance.
Let us connect two adjacent, parallel wires to a high frequency
generator (a radio transmitter will do). In a practical experiment,
these parallel wires (or line) could be made by mounting two lengths
of copper wire on supporting insulators, so arranged that the wires
would run parallel, perhaps two inches apart. The line could be
coupled to the transmitter by being connected to a link coil placed
near the final tank coil.
The electrical energy proceeds along the line at a definite rate.
If our transmitter is producing a sine wave shaped voltage, as is
the usual case, sine wave currents and voltages occur at all points
along the line but with the actual instantaneous values at time
displacements which depend on the distance from the generator.
The end of the line may reflect voltage and current waves. These
may reinforce or reduce the original waves. In particular, if the
line is an odd multiple of a quarter wave length (1/4, 3/4, 5/4
of a wave length) and is properly terminated for the purpose, the
reflected energy will be in phase with the new forthcoming waves,
and large standing waves will be developed. These standing voltage
waves can be detected with a neon bulb, while the current standing
waves can be observed with a pilot bulb connected to an exploring
single turn loop. The voltage and current standing waves are 90
electrical degrees out of phase. See Fig. 1.
The fields produced by the two wires of a line oppose each other
and very little radiation takes place. The main losses are the actual
resistance losses of the conductors used. A resonant line, therefore,
has small losses and a high Q. As. the two wires of a resonant line
are spread apart, radiation increases. Radiation resistance (losses
of energy from the system because of radiation) also increases.
Radiation can be prevented by using a coaxial cable. Such a cable
may be flexible or solid and has one small wire conductor completely
surrounded by (but insulated from) a conducting tube serving as
the second conductor. The characteristics of coaxial cables depend
primarily upon the ratio of the inside diameter of the pipe to the
diameter of the center wire, and upon the dielectric.
If the line we used for our explanation were infinitely long
(that is, continued without an end), there would be no reflection
from the far end, since this end would never be reached. There would
be no standing waves on the line for any frequency since there would
be no reflection. In looking into the line, the generator would
see a definite value of impedance which depends on the spacing of
the conductors, size of the wire selected and the dielectric employed.
This impedance is called the surge or characteristic impedance.
Suppose we cut our 'line a short distance from the generator. (A
few feet of wire removed from an infinitely long line, leaves the
line still infinitely long.)
Looking into the infinite line remaining, the short line connected
to the generator will see the characteristic impedance of this infinite
line. See Fig. 2. Let us say that in this case the characteristic
impedance is 100 ohms. If we replace the infinite line with a 100-ohm
resistor, the short line connected to the generator will behave
exactly the same and will not distinguish between a 100-ohm resistor,
or a 100-ohm characteristic-impedance infinite line. In turn, the
radio frequency generator connected to the input of our short line
will see a 100-ohm impedance whether the line is infinite in length
and has a 100-ohm characteristic impedance, or whether it is of
finite size, and is terminated in its characteristic impedance of
100 ohms, as in this case. This is indeed a simple way to increase
the length of a line to infinity, and is of the greatest value in
Fig. 2 - Connecting the right resistor across it makes
the short line seem infinitely long.
Fig. 3 - Different types of antenna transmission lines.
The Zeppelin is at lower right.
A non-resonant parallel wire line radiates a negligible amount
of energy and does not produce standing waves if it is terminated
in its characteristic impedance. The effective voltage and current
vary along an antenna, giving different impedance values between
any two points along the antenna. A non-resonant line may have its
two wires make contact to the antenna, a short distance on each
side of the antenna center. By moving the contact points closer
together or further apart, the impedance needed to match the line
is obtained. Maximum power transfer will also occur when impedances
are correctly matched.
A single wire transmission line may be used. In this case, the
wire is connected to a point of correct impedance. This point is
usually some distance away from the center of the antenna. The return
circuit is completed through the antenna-to-ground capacitance.
The proper adjustment of a non-resonant line can be checked by striving
to obtain absence of current or voltage maximum points along the
line. Fig. 3 shows several methods of connecting a transmission
line to an antenna.
A line a quarter of a wave length long, connected to a radio
frequency generator at one end and left open at the other
end, will behave as a series resonant circuit. For example, using
a frequency of 300 megacycles, which corresponds to a wave length
of one meter, the line will be 1/4 of a meter long. At and near
this frequency this line will behave as a series circuit similar
to one having a condenser and coil of values which would resonate
at 300 MC. At frequencies considerably removed from resonance, the
behavior of the line and the lumped constants resonant circuit will
differ. In a like manner, a quarter wave length line short-circuited
at the far end will behave as a parallel resonant circuit. Lines
of a quarter wave length dimension are usually employed in practical
circuits. Lines of longer physical length may be employed, but they
produce larger losses, are bulky, and require more material.
A short-circuited quarter wave length line is often used as the
tank circuit of a high frequency transmitter. Such a line is easier
to adjust than a circuit made up of a coil and condenser and, further,
has a much higher Q (smaller losses) at the frequencies employed.
The short circuit at the far end need not be made; in practice,
a condenser of about .0005 mfd. may be used. This capacity serves
as a practical short circuit for the R.F. employed.
At the short-circuited end, the current is maximum, since a direct
path exists between the wires of the line; while the voltage is
minimum (zero) because of the short. At the generator side these
conditions are exactly reversed; the voltage is maximum and the
current is minimum. See the illustration of the current and voltage
Lines As Transformers
The voltage varies along a short-circuited quarter-wavelength
line, being maximum at the generator end and zero at the short circuit.
The current ,variations are in reverse to the voltage changes. If
the generator is left connected at one end, any voltage from maximum
to zero may be obtained by placing a suitable resistive load at
a suitable point along the line. This action corresponds, to that
of a' step-down transformer.
Should the load be connected to the open end instead of the generator,
while the generator is connected to some intermediate point of the
short-circuited quarter wave length line, a voltage step up will
result. Transformers which step voltages up and down also match
impedances. This is a more useful application of the line.
Special short-circuited lines, known as stubs, may be used to tune
out the unwanted reactive component of antennas or other elements,
leaving only the resistive .component to which power can be delivered
at far greater efficiency. This is a very important application
and is used extensively with antennas for high frequency work.
Radio servicemen are accustomed to visualizing radio filters
as being made up of condensers and inductances. Since we now know
that lines can be made to act as series and parallel circuits, they
may be employed instead. Because lines have much smaller losses,
they form filters with much sharper characteristics.
It is very difficult to make tests and measurements at very high
frequencies. Usually these measurements must be made indirectly
or by means of a comparison. Because the physical dimensions of
a transmission line are easily measured and because these dimensions
are related to electrical properties such as frequency, impedance,
etc., transmission lines serve a useful purpose for making measurements
in the radio laboratory.
The value of an unknown high frequency can be determined by connecting
the source of energy to a line and detecting the distance between
successive voltage maximums. Under proper adjustments, this distance
will be equal to one-half the wave length of the signal being considered.
*Supreme Publications, Chicago
Posted October 7, 2014