February 1947 Radio News
[Table of Contents]
Wax nostalgic about and learn from the history of early
electronics. See articles from
Radio & Television News, published 19191959. All copyrights hereby
acknowledged.

It is amazing to me how many
times I read an article, whether in a vintage magazine like this 1947 issue of
Radio News, or a current edition of QST, how when discussing maximum
power transfer from a source to a load, the author states merely that the load impedance
must equal the source impedance. The fact of the matter is that the source and load
impedances must be the
complex conjugates of each other in order for maximum power
transfer to occur. That is to say that if the source has a complex impedance of
R + jX, then the load must have a complex impedance of R  jX (and vice versa) in order for maximum
power transfer to occur. If the source and load are purely resistive, meaning there
is no reactive component (X = 0) to the impedance, technically that does
not render the complex conjugate rule void, merely not of consequence in that case
since j0 = j0.
Transmission Line Systems for FM & Television Home Receivers
By C. Spear
Conventional antenna systems with which most
servicemen are acquainted in standard broadcast work will not suffice in FM and
television installations. Each antenna system for these higher frequency bands must
be individually "engineered."
The trend toward the use of higher frequency bands for FM and television has
accentuated the importance of an efficient transmission line system between antenna
and receiver. For as the frequency goes up it becomes increasingly difficult to
feed an adequate signal from the antenna to the receiver and every effort must be
made to conserve the comparatively little energy that is available. For this reason
high gain directive antennas become necessary in many localities, and by the same
logic highly efficient transmission line systems must be installed.
Fig. 1  Power loss that occurs when a mismatch of antenna
to receiver exists.
Fig. 2  Semipictorial representation of what an electrical
wave experiences at end of transmission line. (A) Perfect match and (B) when mismatch
occurs.
Fortunately, due to the advances made during the war in the high frequency cable
field, lowloss transmission lines are available at low cost and if used properly
will transmit the energy picked up by the antenna to the receiver without undue
loss. However, the word "properly" has a great deal of significance, for another
adverse effect of the increase in frequency is to make mismatching more critical
and unless transmission lines are installed with a complete understanding of this
phenomenon they may be useless.
This latter statement is intended only to emphasize the importance of the problem,
and not in any way to indicate a difficult or hopeless condition, for the remedy
is both simple to perform and understand.
It is the objective of the author to unveil the mystery of matching and indicate
the necessary calculations  requiring only a knowledge of fundamental multiplication
and division, a straight edge, and some rule of the thumb procedures  with which
the serviceman can solve virtually any of his transmission line problems.
Included in these h.f. cable line problems that can easily be solved are; how
to match any antenna to any receiver whether it be FM, television, radar, instrument
landing, Army, Navy or any other electronic device; the effect of mismatches in
terms of power or signal lost and how they can be corrected; how to intelligently
select the appropriate transmission line; the "net" gain of directive antennas.
In addition to a discussion of these questions some of the terms frequently used
in the field will be clearly defined and converted into simpler expressions.
"Decibels," one of the terms that will be used very frequently throughout this
article, should be carefully defined. The decibel, abbreviated dB, is a numerical
means of expressing the ratio of two compared powers or voltages. The following
formula shows the relation between dB and power: dB = 10 log P_{1}/P_{2},
where P_{1} and P_{2} are the two powers compared; or in terms of
voltages where E_{1} and E_{2} are the two voltages compared, dB = 20 log
E_{1}/E_{2} assuming that the two voltages are measured across equal
impedances.
For example, if a dipole antenna normally picks up 1 microvolt of signal, and,
after adding directive arrays, it picks up 10 microvolts, then the gain of the antenna
in dB due to the array is: 20 log 10 = 20 dB.
Likewise, if a transmission line receives 10 milliwatts from an antenna, but
delivers only 5 milliwatts to the receiver then the power lost in the cable is:
10 log 2 = 3 dB.
Table 1. Decibel conversion table. Power or voltage ratios can
be converted to dB (or vice versa) without the need of logarithm tables or slide
rule.
In order to simplify the calculation of the decibels gained or lost see the conversion
table (Table 1). From this table the reader can convert dB into power or voltage
ratios or vice versa without the need of logarithm tables or a slide rule.
There are three sources of power loss between antenna and receiver; mismatch
between antenna and transmission line, attenuation or power loss in the transmission
line, mismatch between transmission line and receiver.
Antenna Mismatch
One of the fundamental concepts of power transmission is that to obtain maximum
power transfer, the output impedance of the generator (in this case the antenna)
must be equal to the input impedance of the load (in this case receiver). Thus if
the antenna resistance is 70 ohms, the receiver input should be 70 ohms, otherwise
some of the power is lost. This is shown in Fig. 1, which is a graphic presentation
of the signal voltage lost due to mismatch.
At the present time consideration of the antenna impedance is very important
for two reasons. In the first place receiver input and antenna impedances may vary
to a great extent due to the lack of standardization amongst the various manufacturers,
and due to the fact that many surplus Army and Navy receivers, designed for use
with special antennas, may be circulated for general use. Secondly the addition
of directive arrays changes the antenna impedance, and therefore it is necessary
to calculate the power loss due to mismatch in order to determine the net or effective
gain of the antenna. For example a typical problem of this type might be:
Fig. 3. Graph shows increment of attenuation as a function of the standing
wave ratio (SWR) and normal line attenuation. Note in particular that the power
loss due to transmission line mismatch does not become serious until the standing
wave ratio is about 3:1.
Fig. 4. Method of matching antenna to receiver via a quarterwave
transformer.
Intelin type K200 antenna leadin wire. The characteristic impedance
of this wire is 200 ohms, while the attenuation at 30 mc. is .4 dB per 100 feet.
Given: An antenna array which gives a 5 dB gain but changes the impedance
from 300 ohms to 100 ohms. The original antenna was matched to the receiver  calculate
the net gain.
Solution: From Fig. 1 we note that a 3:1 impedance mismatch ratio results
in signal which is 25 percent or 1.2 dB less. The net gain is therefore only
3.8 dB It then becomes a matter of mathematics whether the extra expense is
worth the resultant gain. Of course as the mismatch becomes greater, the effective
gain decreases, and the array becomes useless unless a matching network is utilized.
However the matching can be performed rather simply, and the details will be discussed
later in the article.
Attenuation of the Cable
The limiting factor on the minimum amount of power loss possible in any transmission
line system is the attenuation or power loss of the cable; for any power lost due
to mismatch can be corrected by means of matching circuits, but there is no remedy
for the power lost due to the attenuation of the cable. Though there is no fixed
standard, cable attenuation is usually rated in dB per 100 feet by most manufacturers.
However, the power loss is proportional to the length of the cable. That is, 100
times more power is dissipated in a 100 foot cable than in a one foot cable. Therefore
cable is sometimes rated in dB per foot instead of per 100 feet so that it will
sound more efficient. For example, a h.f. cable whose attenuation is 20 dB
per 100 foot (a very high value) could be rated at 0.2 dB per foot or 0.016 dB
per inch.
Another factor that affects the attenuation is the frequency at which it is used;
for the power loss of any h.f. line increases approximately as the square of the
frequency. This is an a essential fact particularly at the present time, since many
of the cables are rated at the old FM frequency range of about 45 mc., and
many manufacturers have not had a chance to reevaluate their cables so as to rate
them at the new FM frequency band centering around 100 mc. Thus a 4dBper100foot
cable rated at 30 mc., would be rated at approximately 6.8 dB per 100 feet
at 100 mc.
Matching the Transmission Line to Load
All the sources of power loss discussed heretofore are not limited to high frequency
receiver equipment, but apply equally as well to all types.
Posted March 7, 2023 (updated from original post
on 2/11/2016)
