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## [TowerTalk] Best vs. Maxwell -- Again??( LONG !!)

 To: [TowerTalk] Best vs. Maxwell -- Again??( LONG !!) jreid@aloha.net (Jim Reid) Tue, 16 Mar 1999 11:23:21 -1000
 ```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 6-8 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 Pi-L 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 -- FAQ on WWW: http://www.contesting.com/towertalkfaq.html Submissions: towertalk@contesting.com Administrative requests: towertalk-REQUEST@contesting.com Problems: owner-towertalk@contesting.com Search: http://www.contesting.com/km9p/search.htm ```
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