Aloha,
Well, Dr. Steve Best, VE9SRB, of Cushcraft has tried again,
and, in my view, erred again in his 16 page(!) article in the
Winter, 1999 edition of CQ's Communications Quarterly. I
feel justified in this, my reply, as he names me as one of the
commenters about his work earlier on (see the last sentence
of his text material, just before the 5 pages of tortuously
complex math, including complex algebra calculus, but that
is what Ph.d's do, isn't it.) I was not alone in trying to help
Steve understand Walt Maxwell's work which he published
nearly 25 years ago, particularly in the Dec. 1974 issue
of QST.
In his 16 page piece he attempts to prove that conjugately
matching the antenna system at the shack end of the
transmission line results in great signal losses.
He uses a rather absurd mathematical and experimental
antenna model; one with a feed point complex impedance
of 6.2+j14.4 ohms, or an antenna which will present a
VSWR of 8.743 to a 50 ohm characteristic impedance
transmission line! (Note: three 3 decimal place calculation
is used consistently through out his complex analysis!).
I cannot imagine any amateur setting out to use such an antenna
on the HF bands, but who knows. Anyway, after verbiage, he
concludes that this antenna, when conjugately matched to
the "output impedance" of the tuner/matching network will
have a total loss of 4.448 dB of the power launched onto the
line at the output of the tuner. And of course, he is absolutely
correct, because in his mathematical analysis he does not
bother to set up a 1:1 VSWR match between the transmitter
and the input terminals of the tuner network!! In fact he leaves
that VSWR as being a value of 3.393!!(Note again, all this
3 decimal place exactitude is Steve's work).
Yes, it is a chore to attempt to read and follow his work, as he
scatters the parameters with which he is working all through
the piece; you really have to dig around to find out how
he gets places at times. And I am not sure he did his
conversion of the line alpha attenuation for dB to nepers
per meter correctly, se the 12th page of his piece. Here
he divides the alpha dB value by 868.59; per what one
learns in engineering school, you convert alpha in dB to
nepers by dividing by 20 times the log of the base of the
natural logarithm, or divide by 8.6859. Seems to be a
factor of 100 here that I did not follow in Steve's math, but
perhaps he is correct.
If you dig deep enough into the article, you find, in addition
to the impedance of the antenna Steve is using, that his
work is being done at 21.2 MHz, and the line he is using
is 156.19 feet of RG213 coax.
Of course his value for the total loss of 4.44 dB is absolutely
correct. And you could learn this for yourself from Maxwell's
published info of long ago. Walt updated all in the 1990
publication of this early material in his ARRL published
book, "Reflections." In fact Maxwell's figure 6.1 in his book,
to which Steve was long ago referred ( even Ed Sleight
loaned Steve a copy of Walt's book, as Steve was not
aware of his work!) shows precisely this same value
of total loss when the antenna system is NOT correctly
and conjugately matched. If you have access to Walt's
book, have a look at the lower right hand corner of
his Fig. 6.1, page 68 of the book. There it is, in
very black ink: 4.44 dB loss when there is a VSWR on
the line of 8.7, and when NO conjugate match exists.
If I am reading Maxwell's book correctly, and using his
Fig. 6.1 as he intends, then with reasonably low loss
line, and even a VSWR of 8 or 9, the total loss, when
the line is conjugately matched would include, say for 175
feet of RG213 with about 1.3 dB loss per 100 feet at
21 MHz, added loss of only about 0.5 dB caused by
the operating VSWR of 8 or 9 because of the odd
antenna impedance of 6.2 + j14.4 ohms.
I cannot imagine any HF amateur putting up with that
high a VSWR on any antenna line, and attempting to
match it away using a tuner in the shack. Such an
antenna impedance might be presented by a short
whip on a mobile set up, but then base loading at
the antenna is used to result in a much lower line
VSWR. However, in a short vertical whip,
the proper loading is to use an inductor coil,
as the antenna appears to be a series RC circuit,
so the complex reactance is capacitive, or a
negative value, rather than positive as in Steve's
example. Guess Steve was modeling a long wire
antenna, though he never describes it beyond
giving the impedance numbers.
I believe it is wise to try to get within around 3 or 4
to 1 VSWR's, then use the tuner to get all the power
from the transmitter up to, and radiated by the antenna.
As I wrote at the beginning, I have written this because
Steve mentioned me in his piece. I argued with Steve
long ago, and as he seems to acknowledge in his
reference to those who had commented earlier on his
work, I do not support nor endorse his work. Perhpas
I am completely wrong. I have given my views above. I
firmly believe that Walt Maxwell made the issues very
clear, and very succinctly in his writings over the past
25 years, and it is not clear to me, in any case, what
Steve is hoping to achieve in his complex work.
He clearly points out the problem of great transmitter
power loss, and a very hot transmission line, if
an antenna of great difference from the transmitter's
output impedance is not somehow compensated
by a proper impedance matching network. Of course,
with tube output rigs/amplifiers using either the old
swinging link coupling, or the modern PiL circuits
in use in most of today's linear amps, you can
dispense with the separate tuner unit, and just
use the output plate circuit to do the impedance
matching to whatever impedance the transmitter
"sees" at the input to the transmission line running
on out and up to the antenna.
Now, I am sure if I am wrong in criticizing Steve's
work, it will be brought to my attention by many,
and I will indeed be chagrined and humbled!!
Copies of this are sent to all parties interested in
this discussion in the past, I hope.
73, Jim, KH7M
On the Garden Island of Kauai

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