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1997-02-01
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170 lines
COMPUTER PROGRAM LINELOSS
The program LINELOSS is a versatile program capable of doing
a variety of calculations related to power, VSWR, and
transmission line losses. The program, and the following
explanatory and tutorial information, is excerpted from The
Meteor Burst Communications Handbook, by Jacob Z. Schanker. This
handbook was prepared under U.S. Air Force Funding. It is
expected that it will be available through the N.T.I.S. late in
1988.
TRANSMISSION LINES
Losses in coaxial transmission lines can have a significant
effect on system performance. The losses negatively affect system
performance in several ways. Therefore, reducing coax loss
provides multiple benefits. In fact, reducing coax loss is one of
the easiest, and least expensive, ways to improve communications
system performance. These are the factors involved:
1) Loss in the transmission line between transmitter and
the antenna reduce the power delivered to the antenna,
thus reducing the effective radiated power.
2) Loss in the transmission line between receiving antenna
and receiver increase the effective noise figure of the
receiver, reducing receiver sensitivity.
3) Any standing waves on the transmission line will
increase the losses on the line. That is, the actual
transmission line loss will be higher than the rated line
loss. This point is of particular significance since it
further aggravates the negative effects of the first two
factors.
It's easy to understand how line loss reduces the power
delivered at the end of a transmission line, but the effect of
standing waves in increasing the loss requires some explanation.
Whenever the load at the end of a transmission line is not
perfectly matched to the line, that is when ZL is not purely
resistive and equal in magnitude to the characteristic impedance
of the line Zo, standing waves will exist. The impedance
inequality at the load will cause power to be reflected back down
the transmission line towards the source. This reflected wave
undergoes the same amount of attenuation (in dB.) that the
forward wave experienced intitially in travelling towards the
load. This attenuation increases the overall, actual,
attenuation. The actual attenuation is always greater than the
rated line attenuation, except when a line is perfectly
"flat" (no standing waves).
The load in a communications system is either the antenna,
or the receiver input. In either case, it is unlikely to be
perfectly matched to the line, which will normally be coaxial
cable with 50 ohm nominal characteristic impedance. A multi-
element Yagi beam antenna carefully tuned to the frequency of
operation may have a relatively low VSWR, typically less than
1.5, and possible as low as 1.1. On the other hand, a wideband
log-periodic beam antenna may have a VSWR above 2.0. The input
impedance of a typical receiver is only nominally 50 ohms. The
actual impedance will vary quite a bit from the nominal, and the
VSWR is often between 1.5 and 2.0.
The rated attenuation for coaxial cable is normally
expressed in terms of dB. per 100 feet or dB. per 100 meters. The
attenuation is a function of frequency of operation, so the
rating must specify the frequency at which the attenuation is
given. Manufacturer's literature, handbooks, or MIL specs are
possible sources of this information. Often the rated attenuation
will be given at 10 MHz. and at 100 MHz. Unfortunately, important
communications frequencies lie between these two frequencies, and
attenuation ratings are unlikely to be specified at the specific
frequencies of operation. Since the attenuation of coaxial cable
varies approximately as the square-root of the frequency ratio,
it is possible to make a useful estimate of rated attenuation at
specific frequencies from the rated attenuation at other
frequencies.
Module 7 of the MBC Programs, LINELOSS, may be used to
calculate the rated line loss at a particular frequency, given
rated line loss at some other frequency. Once the rated line loss
is known, the actual line loss can be calculated for whatever
value of VSWR exists on the line. The program also expresses true
line loss as an operating efficiency figure. Additional
calculations provided in LINELOSS are conversion between forward
and reflected power and VSWR.
It's useful to plug some numbers into LINELOSS and play
around a bit. The importance of low transmission line loss should
soon be apparent. Low VSWR is also helpful, but often is not as
easily controllable. As an example of the considerations
discussed above, and of the use of the program, consider the
following:
A meteor burst system operates at 40 MHz. The remote site
operates in half-duplex with the meteor burst terminal
(transmitter/receiver) connected to a 5 element Yagi antenna
through 150 feet of RG8A/U type coaxial cable. The VSWR of the
antenna is 1.30. Use Module 7 to find the true loss in the line,
the line operating efficiency, and the apparent VSWR at the
terminal end of the line.
The rated attenuation of RG8A/U, from manufacturer's data,
is 0.56 dB. per 100 feet at 10 MHz. From the Main Menu, choose
selection 2, "FIND RATED LINE LOSS AT OPERATING FREQUENCY FROM
RATED VALUE AT ANOTHER FREQUENCY." The rated line loss, 0.56 dB.
is entered first. The actual line length, 150 (feet) is then
entered in response to the prompt. Next, the frequency at which
the rating was given, 10 (MHz.) is entered, followed by the
actual operating frequency of 40 (MHz.). The program then
calculates the rated attenuation for 150 feet at 40 MHz. using
the approximation that attenuation is proportional to the square
root of the actual frequency divided by the rating frequency.
This is accurate enough for most purposes. Note that the value
obtained from the program is 1.7 dB. Choose selection 2 to return
to the Main Menu, we then choose selection 4 "CALCULATIONS, USING
CONDITIONS AT ANTENNA END", since we know the VSWR at the antenna
end. The rated line loss for the length of line being used, which
we just found to be 1.7 dB. is entered first. The program then
asks us to enter any additional losses in the transmission path.
These could be due to filters, diplexers, or other accessories
which exhibit some insertion loss. In this case, we assume there
is no additional loss and so enter 0. Finally, we enter the known
VSWR at the antenna, 1.3, in response to the prompt.
The program then calculates that the VSWR at the transmitter
end is 1.19. This points up the fact that for a lossy
transmission line, the VSWR at the transmitter (source) end will
always be less than the VSWR at the antenna (load) end. This is a
result of: (1) the forward power delivered to the antenna is
reduced by the line attenuation, and, (2) the resulting reflected
power caused by the antenna mismatch is further attenuated on its
return trip to the transmitter end. Since VSWR is proportional to
the ratio of reflected power/forward power, the transmitter end
sees a lower reflected power and a higher forward power than the
antenna end, hence a lower VSWR.
Then program the calculates that the true overall loss in
the line (accounting for the effect of VSWR on the rated line
loss) is 1.74 dB., and that the overall transmission line
operating efficiency is 67.0%. Note that, in this example, the
VSWR on the line contributed negligible (.04 dB.) additional
loss. Since the VSWR was relatively low (1.3) this is not too
surprising. But what if the antenna VSWR was 2.5? This is a value
which might be seen with a log-periodic type antenna, or with a
field expedient antenna. It is suggested that the reader go
through the calculations for this case. The result is that the
true line loss is 2.20 dB., an increase of 0.5 dB. over the rated
line loss which would be exhibited for unity VSWR.
As another example, consider that in the previous example we
did not know the VSWR of the antenna. However, using a BIRD
wattmeter or similar instrument, the forward power at the
transmitter end was measured as 300 watts, and the reflected
power as 20 watts. This may seem pretty good, but it isn't.
Choose selection 1 "CONVERT BETWEEN VSWR AND REFLECTED POWER",
from the Main Menu. Entering our values, we find that the VSWR is
1.70. Returning to the Main Menu and choosing selection 3
"CALCULATIONS, USING CONDITIONS AT TRANSMITTER END", the program
calculates that the true VSWR at the antenna end is 2.24, and
that the true overall loss is 2.09 dB. This is 0.39 dB greater
loss than the rated line loss of 1.7 dB. The calculated operating
efficiency is 61.8%. This means that the actual power delivered
to the antenna to be radiated is 0.618 X (Forward Power -
Reflected Power) or 0.618 X (300 - 20) = 173 watts.
Additional reference:
1 "Program Finds True Transmission Line Loss" EDN, February 18, 1981