TowerTalkians --
I am pleased to let you know that Walt Maxwell, W2DU, has subscribed to
TowerTalk and has posted the following message. He said that he is working on
a new edition of his preeminent book on transmission lines and related topics,
"Reflections".
Welcome, Walt!
In a message dated 98-08-21 13:43:33 EDT, you write:
<< I have just come across some information concerning mismatch loss,
apparently
written by a Mr. Steve Best, that is misleading because it contains incorrect
statements that I'm sure the people in the Towertalk group would appreciate
having corrected.
The quote I have from Mr. Best is as follows:
"Antenna VSWR does reduce antenna gain. No question. If you feed an antenna
with
a 20:1 VSWR you will give up 7.41 dB of radiated power. VSWR results in a
mismatch loss regardless of cable attenuation."
I can't let this incorrect statement go unchallenged, because it shows a
misunderstanding of transmission-line operation and technique. It is one of
the
misunderstandings that I addressed in the 1970's in my series of QST
articles,
"Another Look at Reflections," in which I explained the reason for the
misconception. The same material appears in my book
'Reflections---Transmission
Lines and Antennas'.
So please allow me to explain why Mr. Best's statement is incorrect.
For starters, first assume a matched lossless transmission line, SWR = 1:1.
We
adjust a transmitter to deliver 100 watts into the line, which will all be
absorbed in the matched load. Second we replace the matched load with an
antenna
that produces a 20:1 mismatch, thus reflecting 81.9 watts of the 100 watts
delivered by the transmitter. This leaves 18.1 watts to be absorbed and
radiated
by the antenna. This is a reflection loss of 7.41 dB, just as Mr. Best
indicated. The reason that only 18.1 watts is delivered to the antenna is
that,
when the 81.9 watts of reflected power reaches the transmitter, that
reflected
power tells the transmitter to reduce its output by 81.9 watts. Unless
something
is done to change this situation the transmitter will continue delivering
only
18.1 watts, the power delivered to the antenna and radiated. And yes, this
power
is 7.41 dB lower than the original 100 watts delivered to the matched load.
HOWEVER, we do not operate in this manner---we either readjust the
transmitter
to again feed 100 watts into the new line-input impedance resulting from the
reflected power, or insert a matching network (antenna tuner) between the
transmitter and line input. In this particular case a tube transmitter with a
pi-network output will not be able to match into a complex input impedance
resulting from a 20:1 SWR, so the correct choice is to use an antenna tuner.
With open wire or ladder line a 20:1 SWR is in the normal working range when
matched with a tuner.
So what exactly does the tuner do? In another quotation from Mr. Best it is
clear that he doesn't understand that the tuner re-reflects ALL of the 81.9
watts back to the antenna, and since we're talking lossless line to
appreciate
the principles, all of the reflected power does reach the antenna. I will
explain how this happens. You should also be aware that the real loss in a
well
designed tuner ranges from only 0.1 to 0.5 dB---insignificant.
So what does the tuner do? It totally compensates for the reflection LOSS by
introducing an equal amount of reflection GAIN, which re-reflects the 81.9
watts
of reflected power back to the antenna, thus preventing it from reaching the
transmitter, prohibiting it from reducing its delivery of power from the
original 100 watts.
The power reflection coefficient resulting from a 20:1 mismatch at the
antenna
is 0.819, which is why 81.9 watts are reflected. Because 81.9 percent of any
amount of forward power will be reflected, no matter what we do at the line
input, a much higher level of forward power than the 100 watts delivered by
the
transmitter must reach the 20:1 mismatched antenna for the 100 watts to be
absorbed and radiated by the antenna. After several cycles of RF have
traversed
the line the steady-state condition is reached, in which the level of the
total
forward power has increased by a factor of 1/0.181 which equals 5.513. This
means that the accumulated forward power in the mismatched lossless feedline
has
increased to 551.3 watts in order for 89.1% (7.41 dB) to be reflected, and
continuously re-reflected, because the 7.41 dB of REFLECTED POWER IS NOT LOST
POWER, but circulates in the line.
The factor 0.181 above is the power transmission coefficient, which is (1 -
the
power reflection coefficient). The derivation and verification of the 1/0.181
power-increase factor may be found on page 99 in "Transmission Lines and
Networks," by Walter Johnson, McGraw-Hill, 1950.
I hope this explanation clarifies the misunderstanding that may have resulted
from the incorrect statement of Mr. Best.
73, Walt Maxwell, W2DU
>>
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