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Cecil Moore wrote: Tom Donaly wrote: Give it up, Cecil. You don't even have a coherent notion of the meaning of the term "phase." Selectively quoting, and re-interpreting Bibles in order to make it seem as if the Gods agree with you won't cut it, either. All the simple-minded rural sophistry in the world won't make you right, or the rest of us wrong. When you lose the technical argument, Tom, you always respond with ad hominem attacks devoid of any technical content. Cecil, I don't understand why you complain about Tom D. You do exactly the same thing all through any discussion. On the QRZ forum you have post after post edited by moderators, that's something that almost never happens! It's all on QRZ for people to see. The list moderator even made a very rare public appearance to directly warn you about your style. It's pretty tough to have a non-personal technical discussion with you because you distort facts and resort to the very same ad hominem attacks you dislike from others. Why not set a good example rather than yelling about Tom D.? 73 Tom |
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Cecil Moore wrote:
Gene Fuller wrote: Sorry, I missed the comments that Kraus made about the phase of a standing wave. Quoting: "Figure 14-2 Relative current amplitude AND PHASE along a center-fed 1/2WL cylindrical antenna." Emphasis mine so you can't miss it this time. I thought you were knowledgable enough to convert Kraus's independent variable of wavelength to degrees in his graph on page 464 of the 3rd edition of "Antennas For All Applications". Allow me to assist you in that task. The 'X' axis is "Distance from center of antenna in WL" X in X in wavelength degrees 0.00 0 0.05 18 0.10 36 0.15 54 0.20 72 0.25 90 Hope that helps you to understand Kraus's graph better. Using the degree column, the standing wave current, Itot, on that graph equals cos(X). The standing wave current also equals Ifor*cos(-X) + Iref*cos(X) where 'X' is the phase angle of the forward traveling current wave and the rearward traveling current wave. A phasor diagram at 0.02WL = 72 degrees would look something like this: / Iref / / +----- Itot = Ifor*cos(-X) + Iref*cos(X) \ \ \ Ifor Incidentally, from the above phasor diagram, it is easy to see why the phase angle of the standing wave current is always zero (or 180 deg) since Ifor and Iref are rotating in opposite directions at the same phase velocity. Cecil, I don't know why you go through all of these gyrations. The phase shown by Kraus is durn close to zero. Everyone else who has joined in on this thread agrees; there is no meaningful phase characteristic for a standing wave. Your last sentence above says the same thing. It seems you simply like to argue, even when there is no disagreement. Perhaps you need a dog to go with your hog. 8-) 73, Gene W4SZ |
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Cecil Moore wrote:
When you lose the technical argument, Tom, you always respond with ad hominem attacks devoid of any technical content. Chuckle. A perfect example of an ad hominem attack devoid of any technical content. Roy Lewallen, W7EL |
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yeah, i know, you guys are so busy fighting with each other that you can't
see the forest for the trees. keep going, its still raining here and may be for a few more days yet! "Cecil Moore" wrote in message t... Dave wrote: you guys are just fighting over your own statements since there was no initial technical question or statement that started this thread... Doesn't have to be. This is a continuation of earlier threads. And I'm not fighting - I'm simply stating the laws of physics as asserted by Balanis, Kraus, and Hecht. -- 73, Cecil http://www.qsl.net/w5dxp |
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Cecil Moore wrote:
Tom Donaly wrote: Give it up, Cecil. You don't even have a coherent notion of the meaning of the term "phase." Selectively quoting, and re-interpreting Bibles in order to make it seem as if the Gods agree with you won't cut it, either. All the simple-minded rural sophistry in the world won't make you right, or the rest of us wrong. When you lose the technical argument, Tom, you always respond with ad hominem attacks devoid of any technical content. Fact is, the phase of the forward traveling current referenced to the source current is equal to the distance from the source expressed in degrees. The laws of physics will not stand for anything else. That same number of degrees *IS* the phase angle of the traveling wave(s). Every competent engineer knows that as it is obvious from the equations in any good textbook. I was just giving you some good advice, Cecil. If I wanted to give you an ad hominem attack I'd just call you a rat and have done with it. No, make that a dirty rat. But, for a blobberlipped quodlibetarian like yourself, whose gothamist blatteration attaminates the pure newsgroup aether with low defoedation of the worst kind, perhaps stronger words are in order. 73, Tom Donaly, KA6RUH |
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Gene Fuller wrote:
I don't know why you go through all of these gyrations. The phase shown by Kraus is durn close to zero. That's the phase of the standing wave current which W7EL used to make meaningless measurements. Everyone else who has joined in on this thread agrees; there is no meaningful phase characteristic for a standing wave. Are you retracting your earlier statement just because its technical accuracy disagrees with your friend's misconceptions? Gene Fuller wrote: The only "phase" remaining is the cos (kz) term, which is really an amplitude description, not a phase. If you retract your statement then you contradict his other statement that nothing is lost during superposition. You guys simply cannot have it both ways. Why not stick with technical accuracy? -- 73, Cecil http://www.qsl.net/w5dxp |
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Roy Lewallen wrote:
Cecil Moore wrote: When you lose the technical argument, Tom, you always respond with ad hominem attacks devoid of any technical content. Chuckle. A perfect example of an ad hominem attack devoid of any technical content. Chuckle. The truth is not an ad hominem attack. Incidentally, Tom didn't lose the argument to me - he lost it to Balanis. -- 73, Cecil http://www.qsl.net/w5dxp |
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Tom Donaly wrote:
I was just giving you some good advice, Cecil. If I wanted to give you an ad hominem attack I'd just call you a rat and have done with it. No, make that a dirty rat. But, for a blobberlipped quodlibetarian like yourself, whose gothamist blatteration attaminates the pure newsgroup aether with low defoedation of the worst kind, perhaps stronger words are in order. The technical content of your posting is, once again, conspicuous by its absence. How about a reference for the standing wave current not being a sinusoid? -- 73, Cecil http://www.qsl.net/w5dxp |
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Cecil Moore wrote:
Gene Fuller wrote: I don't know why you go through all of these gyrations. The phase shown by Kraus is durn close to zero. That's the phase of the standing wave current which W7EL used to make meaningless measurements. Everyone else who has joined in on this thread agrees; there is no meaningful phase characteristic for a standing wave. Are you retracting your earlier statement just because its technical accuracy disagrees with your friend's misconceptions? Gene Fuller wrote: The only "phase" remaining is the cos (kz) term, which is really an amplitude description, not a phase. If you retract your statement then you contradict his other statement that nothing is lost during superposition. You guys simply cannot have it both ways. Why not stick with technical accuracy? Cecil, I am really puzzled. I cannot see even one inconsistency in my statements, including those you quote. What is the problem? What is there to "retract"? 73, Gene W4SZ |
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Roy Lewallen wrote:
As I pointed out some time ago, the envelope of a standing wave isn't in general sinusoidally shaped. Assuming the source signal is sinusoidal, your above assertion would require non-linearity in the antenna. Since antennas are generally considered to be linear systems, would you please explain where the nonlinearity is coming from? -- 73, Cecil http://www.qsl.net/w5dxp |
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Gene Fuller wrote:
I am really puzzled. I cannot see even one inconsistency in my statements, including those you quote. What is the problem? You said there is phase remaining in the cos(kz) term which is contained in the amplitude. Then you said there is no phase information. Those statements contradict each other. In any case, the graph at http://www.qsl.net/w5dxp/travstnd.GIF proves that there is phase information contained in the standing wave current magnitude. The arc-cosine of the standing wave current magnitude is identical to the phase of the traveling wave referenced to the source current. Please note that the "experts" have been strangely silent on the contents of that graph. -- 73, Cecil http://www.qsl.net/w5dxp |
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Cecil Moore wrote:
Roy Lewallen wrote: As I pointed out some time ago, the envelope of a standing wave isn't in general sinusoidally shaped. Assuming the source signal is sinusoidal, your above assertion would require non-linearity in the antenna. Since antennas are generally considered to be linear systems, would you please explain where the nonlinearity is coming from? Additional thought: Assuming the source signal is a pure sine wave, if the standing wave current "isn't in general sinusoidally shaped", then the antenna would have to be introducing harmonic radiation that doesn't exist in the source signal. That fact is easily proved with a Fourier analysis. I wasn't aware that standing wave antennas cause radiation on harmonic frequencies. Any standing wave current waveform that deviates very far from a sinusoid would be illegal. -- 73, Cecil http://www.qsl.net/w5dxp |
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Cecil Moore wrote:
Gene Fuller wrote: I am really puzzled. I cannot see even one inconsistency in my statements, including those you quote. What is the problem? You said there is phase remaining in the cos(kz) term which is contained in the amplitude. Then you said there is no phase information. Those statements contradict each other. Cecil, My exact words, which you quoted, were, The only "phase" remaining is the cos (kz) term, which is really an amplitude description, not a phase. If you interpreted that comment as supporting the existence of a phase in this situation, then I cannot offer any help except to suggest you go back and review the meaning of "not". This has become sillier than I ever imagined possible. I am done with this FIGHT! 73, Gene W4SZ |
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Cecil Moore wrote:
Roy Lewallen wrote: As I pointed out some time ago, the envelope of a standing wave isn't in general sinusoidally shaped. Assuming the source signal is sinusoidal, your above assertion would require non-linearity in the antenna. Since antennas are generally considered to be linear systems, would you please explain where the nonlinearity is coming from? No it wouldn't, Cecil. Even you know better than that. For those who believe Cecil, consider a lossy transmission line terminated in a short, or open. The signal is attenuated as it goes down the line, and also attenuated as it comes back up the line, in an exponential fashion. The envelope is thus not sinusoidal. The signal may be sinusoidal, but the envelope can't possibly be. Cecil's antennas may be lossless, but most of us want our antennas to radiate energy, hopefully, as efficiently as possible, so we have to put up with current distributions that aren't easy either to envision or to calculate. That's why even Cecil uses EZNEC. 73, Tom Donaly, KA6RUH |
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Cecil, W5DXP wrote:
"Assuming the source signal is a pure sine wave, if the standing wave current "isn`t in general sinusoidally shaped (as Roy said)", then the antenna would have to be introducing harmonic radiation that doesn`t exist in the source signal." Standing waves are produced by forward and reflected traveling soinusoidal waves produced by the same generator. Coherent signals on a transmission line and antenna of the same frequency are correctly represented by phasors. The term phasor is preferred over vector for an arrow which indicates phase separation and magnitude of an electrical unit. Phasors are used to represent sinusoidal voltages and currents. They are also used to represent reactances and impedances. Like vectors, phasors can be "added" by the head-to-tail method or by the component method. If a phasor represents an alternating current: I = Io cos omega t, then the sum of the two phasors representing forward and reflected sinusoidal components is another sinusoid of the same frequency. Point is the components are amenable to phasor representation. All the old authors do it. This amenability is proof the standing wave is a sinusoid too. Best regards, Richard Harrison, KB5WZI |
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Gene Fuller wrote:
The only "phase" remaining is the cos (kz) term, which is really an amplitude description, not a phase. Yes, there it is again, you said there is phase information in the amplitude description and you were right. -- 73, Cecil http://www.qsl.net/w5dxp |
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On Wed, 17 May 2006 16:19:17 GMT, "Tom Donaly"
wrote: Cecil's antennas may be lossless, Hi Tom, Even more amazing is that they are linear transmission lines. 73's Richard Clark, KB7QHC |
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Tom Donaly wrote:
Cecil Moore wrote: Assuming the source signal is sinusoidal, your above assertion would require non-linearity in the antenna. Since antennas are generally considered to be linear systems, would you please explain where the nonlinearity is coming from? No it wouldn't, Cecil. Even you know better than that. For those who believe Cecil, consider a lossy transmission line terminated in a short, or open. The signal is attenuated as it goes down the line, and also attenuated as it comes back up the line, in an exponential fashion. The envelope is thus not sinusoidal. An attenuated (damped) sinusoidal signal is still sinusoidal, Tom. The fact that such a signal doesn't generate harmonics proves that it is sinusoidal. If it were not sinusoidal, it would by definition, be generating harmonics. Are you really asserting that a damped sinusoidal signal generates harmonics? That's the only way to prove it has gone nonsinusoidal. All non-sinusoidal waveforms contain harmonics of the fundamental frequency. Every competent engineer in the world is aware of that technical fact. If the source signal to an antenna is a pure single- frequency sine wave, and if the standing wave current is non- sinusoidal, then the antenna has necessarily introduced harmonics, i.e. the antenna is non-linear. W7EL is simply mistaken when he says the standing wave current waveform is not sinusoidal. If the standing wave current waveform ever was nonsinusoidal, the antenna would, by definition, be non-linear and be generating harmonics not present in the source waveform. Seems you guys need to review your Math 202 course covering Fourier transforms. -- 73, Cecil http://www.qsl.net/w5dxp |
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Richard Harrison wrote:
If a phasor represents an alternating current: I = Io cos omega t, then the sum of the two phasors representing forward and reflected sinusoidal components is another sinusoid of the same frequency. Point is the components are amenable to phasor representation. All the old authors do it. This amenability is proof the standing wave is a sinusoid too. The absence of harmonic frequencies generated by the antenna is also proof that the standing wave is a sinusoid. All nonsinusoidal waveforms contain harmonics. -- 73, Cecil http://www.qsl.net/w5dxp |
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Richard Clark wrote:
wrote: Cecil's antennas may be lossless, Even more amazing is that they are linear transmission lines. In spite of W7EL's assertions that antennas generate nonsinusoidal waveforms, they indeed are linear and bear a striking resemblence to a lossy transmission line. Why do you think they are called standing wave antennas? Take a look at page 18 of Balanis' "Antenna Theory", 2nd edition, Figure 1.15. He shows how to turn a transmission line into an dipole with exactly the same standing wave current distribution before and after. -- 73, Cecil http://www.qsl.net/w5dxp |
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On Wed, 17 May 2006 17:45:08 GMT, Cecil Moore
wrote: Even more amazing is that they are linear transmission lines. they indeed are linear What is distinctly NOT amazing, is to see foolishness repeated. |
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Richard Clark, KB7QHC wrote:
"Even morte amazing is that they (antennas) are linear transmission lines." Antennas and transmission lines are linear, passive, and carry incident and reflected waves in much the same manner. Look at "Current Distribution in Wire Antennas" on page 866 of Terman`s 1955 edition of "Electronic and Radio Engineering": "A wire antenna is a circuit with distributed constants; hence the current distribution in a wire antenna that results from the application of a localized voltage follows the principles discussed in Chapt. 4---." Chapt.4 is entitled "Transmission Lines". Best regards, Richard Harrison, KB5WZI |
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Cecil Moore wrote:
Tom Donaly wrote: Cecil Moore wrote: Assuming the source signal is sinusoidal, your above assertion would require non-linearity in the antenna. Since antennas are generally considered to be linear systems, would you please explain where the nonlinearity is coming from? No it wouldn't, Cecil. Even you know better than that. For those who believe Cecil, consider a lossy transmission line terminated in a short, or open. The signal is attenuated as it goes down the line, and also attenuated as it comes back up the line, in an exponential fashion. The envelope is thus not sinusoidal. An attenuated (damped) sinusoidal signal is still sinusoidal, Tom. The fact that such a signal doesn't generate harmonics proves that it is sinusoidal. If it were not sinusoidal, it would by definition, be generating harmonics. Are you really asserting that a damped sinusoidal signal generates harmonics? That's the only way to prove it has gone nonsinusoidal. All non-sinusoidal waveforms contain harmonics of the fundamental frequency. Every competent engineer in the world is aware of that technical fact. If the source signal to an antenna is a pure single- frequency sine wave, and if the standing wave current is non- sinusoidal, then the antenna has necessarily introduced harmonics, i.e. the antenna is non-linear. W7EL is simply mistaken when he says the standing wave current waveform is not sinusoidal. If the standing wave current waveform ever was nonsinusoidal, the antenna would, by definition, be non-linear and be generating harmonics not present in the source waveform. Seems you guys need to review your Math 202 course covering Fourier transforms. We're talking about the envelope, Cecil, what are you talking about? Since you've become so enamored of math all of a sudden, go ahead and plot the current envelope on a length of very lossy transmission line and tell me, with a straight face, that it follows a sine function. On the other hand, don't bother. I know it's too hard on your head, but it's an interesting exercise for everyone else. 73, Tom Donaly, KA6RUH |
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Richard Clark wrote:
Cecil Moore wrote: Even more amazing is that they are linear transmission lines. they indeed are linear What is distinctly NOT amazing, is to see foolishness repeated. Either transmission lines are linear or they are not linear. The only way for them to generate nonsinusoidal signals is for them to be nonlinear. The same goes for antennas. -- 73, Cecil http://www.qsl.net/w5dxp |
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On Wed, 17 May 2006 20:11:55 GMT, Cecil Moore
wrote: Richard Clark wrote: Cecil Moore wrote: Even more amazing is that they are linear transmission lines. they indeed are linear What is distinctly NOT amazing, is to see foolishness repeated. Either transmission lines are linear or they are not linear. Now there's a motto to live by. The only way for them to generate nonsinusoidal signals is Oh this is going to be good... for them to be nonlinear. Transmission lines generate signals? What a guffaw! The same goes for antennas. Double chuckle. Talk about linear thinking woops Binary thinking, nothing linear from you this round. |
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Richard Clark wrote:
I note you do NOT say "in exactly the same manner," which is unsupportable in the literature. "Exactly" is one of the buzz words like "perfect", "always", "never", "infinite", "lossless", etc. that invariably make any statement using them false. Nobody, except some "experts" on this newsgroup, is ignorant enough to use those words in a supposedly technical valid sentence. -- 73, Cecil http://www.qsl.net/w5dxp |
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Tom Donaly wrote:
We're talking about the envelope, Cecil, what are you talking about? Since you've become so enamored of math all of a sudden, go ahead and plot the current envelope on a length of very lossy transmission line and tell me, with a straight face, that it follows a sine function. On the other hand, don't bother. I know it's too hard on your head, but it's an interesting exercise for everyone else. The envelope of an unattenuated sine wave is a straight line, Tom. Is a straight line sinusoidal? Give us an everloving break! You can fool half the people half the time but please stop trying to fool all the people all the time. Here is an example that should put an end to your foolishness. 100W-----50 ohm coax------50 ohm load dissipating 50 watts Please explain how the 3dB attenuation in the coax causes nonsinusoidal signals in the system. Proof of nonsinusoidal signals would be the generation of harmonics. We are all awaiting your reinvention of the laws of physics. -- 73, Cecil http://www.qsl.net/w5dxp |
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Richard Clark wrote:
Transmission lines generate signals? What a guffaw! Put a diode in a transmission line and it will definitely generate a signal on a frequency that didn't exist before. I'm really surprised that you don't know that fact of physics. -- 73, Cecil http://www.qsl.net/w5dxp |
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"Gene Fuller" wrote in message ... Cecil Moore wrote: Gene Fuller wrote: I am really puzzled. I cannot see even one inconsistency in my statements, including those you quote. What is the problem? You said there is phase remaining in the cos(kz) term which is contained in the amplitude. Then you said there is no phase information. Those statements contradict each other. Cecil, My exact words, which you quoted, were, The only "phase" remaining is the cos (kz) term, which is really an amplitude description, not a phase. If you interpreted that comment as supporting the existence of a phase in this situation, then I cannot offer any help except to suggest you go back and review the meaning of "not". This has become sillier than I ever imagined possible. I am done with this FIGHT! you haven't been around this group long have you? if you think its silly now, check back next week and see how its still going on! |
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"Cecil Moore" wrote in message . com... Richard Harrison wrote: If a phasor represents an alternating current: I = Io cos omega t, then the sum of the two phasors representing forward and reflected sinusoidal components is another sinusoid of the same frequency. Point is the components are amenable to phasor representation. All the old authors do it. This amenability is proof the standing wave is a sinusoid too. The absence of harmonic frequencies generated by the antenna is also proof that the standing wave is a sinusoid. All nonsinusoidal waveforms contain harmonics. -- i found a way for just a piece of hardline to generate harmonics... and even stranger, it generated sub-harmonics, dividing the frequency in half to be exact... now have fun with that one! |
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Cecil Moore wrote:
Tom Donaly wrote: We're talking about the envelope, Cecil, what are you talking about? Since you've become so enamored of math all of a sudden, go ahead and plot the current envelope on a length of very lossy transmission line and tell me, with a straight face, that it follows a sine function. On the other hand, don't bother. I know it's too hard on your head, but it's an interesting exercise for everyone else. The envelope of an unattenuated sine wave is a straight line, Tom. Is a straight line sinusoidal? Give us an everloving break! You can fool half the people half the time but please stop trying to fool all the people all the time. Here is an example that should put an end to your foolishness. 100W-----50 ohm coax------50 ohm load dissipating 50 watts Please explain how the 3dB attenuation in the coax causes nonsinusoidal signals in the system. Proof of nonsinusoidal signals would be the generation of harmonics. We are all awaiting your reinvention of the laws of physics. Nice try, but you still keep conflating time with distance. If any of the lurkers on this newsgroup want, they can consider a dipole somewhat shorter than 1/2 wavelength. According to one of Cecil's sources, Balanis, the current distribution on such a wire resembles a triangle. Now, it's true you can do a Fourier analysis on this triangle, but you won't come up with frequencies. You will come up with an infinite group of sine and cosine waves with units of cycles/meter (as opposed to cycles/second). What earthly use are units of cycles/meter? Does Cecil have a radio that can tune in cycles/meter? On the other hand, if you could measure the current and turn it into a voltage so an oscilloscope could show it, you would see a nice sine wave everywhere except at the ends of your antenna. And the units would be in cycles per second. Cycles per meter, phaseless phasors... you sure have a vivid imagination, Cecil. 73, Tom Donaly, KA6RUH |
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On Wed, 17 May 2006 20:46:12 GMT, Cecil Moore
wrote: Put a diode in a transmission line and it will definitely generate a signal on a frequency that didn't exist before. Third generation joke, or the Texas philospher's theory of a Free Lunch. I'm really surprised that you don't know that fact of physics. You have a limitless capacity for being surprised, certainly. What is more amusing is your capacity to make unrelated correlations to it. Antennas as non-linear transmission lines have already been covered and have been part of the literature for quite some time. You simply need to invest more effort in reading rather than more dimes for Xerox toner. |
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On Wed, 17 May 2006 20:36:41 GMT, Cecil Moore
wrote: Richard Clark wrote: I note you do NOT say "in exactly the same manner," which is unsupportable in the literature. "Exactly" is one of the buzz words like "perfect", "always", "never", "infinite", "lossless", etc. that invariably make any statement using them false. Another motto we can all live by, except maybe its author who in so many words: On Fri, 10 Mar 2006 13:35:14 GMT, in rec.radio.amateur.antenna you wrote: Exactly On Mon, 27 Mar 2006 13:42:12 GMT, in rec.radio.amateur.antenna you wrote: Exactly exactly On Tue, 14 Mar 2006 05:13:52 GMT, Cecil Moore wrote: Exactly On Thu, 20 Apr 2006 17:45:39 GMT, "Cecil Moore" wrote: Exactly On Thu, 09 Mar 2006 21:40:40 GMT, "Cecil Moore" wrote: always On Thu, 16 Mar 2006 17:34:51 GMT, "Cecil Moore" wrote: always always always On Sun, 30 Apr 2006 12:20:10 GMT, Cecil Moore wrote: always On Wed, 08 Mar 2006 19:04:02 GMT, Cecil Moore wrote: never On Tue, 07 Mar 2006 18:01:18 GMT, Cecil Moore wrote: never On Fri, 10 Mar 2006 13:35:14 GMT, Cecil Moore wrote: never On Thu, 16 Mar 2006 18:20:19 GMT, "Cecil Moore" wrote: never On Tue, 14 Mar 2006 14:28:35 GMT, Cecil Moore wrote: never and on and on and on (luckily I only pick up 1/4 of all the effluent) so much that I'm not inspired to quote the rest of these 5 forbidden words when 3 peg the irony meter. Nobody, except some "experts" on this newsgroup, is ignorant enough to use those words in a supposedly technical valid sentence. You know why cowboys wear their jeans inside their boots? [hint is found above] |
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Gene Fuller wrote:
Cecil, I don't know why you go through all of these gyrations. The phase shown by Kraus is durn close to zero. Everyone else who has joined in on this thread agrees; there is no meaningful phase characteristic for a standing wave. Your last sentence above says the same thing. It seems you simply like to argue, even when there is no disagreement. Perhaps you need a dog to go with your hog. 8-) 73, Gene W4SZ That's why I don't pay any attention to anything Cecil posts. I do, however, pay attention to the responses. Therein lies the gold. tom K0TAR |
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Tom Donaly wrote:
According to one of Cecil's sources, Balanis, the current distribution on such a wire resembles a triangle. It only resembles a triangle. It is actually part of a cosine waveform. From cos(80) to cos(90), the cosine function is close to a straight line but it is *NOT* a straight line. Assuming the current distribution is a triangular is only an approximation with a known error. The current distribution acutally remains a cosine function but assuming a straight line simplifies the math and doesn't cause an unacceptably large error. It is akin to the approximation that A = sin(A) when A is very small. It is *ONLY* an approximation with limited accuracy. cos(80)=0.17365, cos(85)=0.08716, cos(90)=0 0.17365/2 = 0.08682 which is an error of 0.4% when one assumes a triangular function. -- 73, Cecil http://www.qsl.net/w5dxp |
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Dave wrote:
yeah, i know, you guys are so busy fighting with each other that you can't see the forest for the trees. keep going, its still raining here and may be for a few more days yet! Dave You obviously haven't figured out who is "fighting" and who is "amused". I'll give you a clue, the ones fighting are "C" and "Y" hihi. tom K0TAR |
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Richard Clark wrote:
Antennas as non-linear transmission lines have already been covered and have been part of the literature for quite some time. Antennas are linear systems. -- 73, Cecil http://www.qsl.net/w5dxp |
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On Thu, 18 May 2006 03:32:49 GMT, Cecil Moore
wrote: Antennas are linear systems. another list game, hmm? Antennas are wires in the sky; Antennas are fun; Antennas are this, ....that, ....and, ....another. |
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