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#51




Dan wrote:
So Chipman states quite clearly that zero reflected voltage wave magnitude does _not_ mean maximum power transfer. On the contrary, maximum power is transferred only when there is a nonzero voltage wave reflection (assuming a complex Zo line). Counter arguments along the lines of "Well that doesn't seem right to me so therefore Chipman must be wrong" don't carry much weight given Chipman's credentials. Thanks for that posting, Dan, and for what looks like a very clear summary. Just one point, about that very last word: what are Chipman's "credentials", really? They are not that he is a wellknown[*] textbook author, college professor, PhD, or anything like that. This discussion is already way overloaded with personal "credentials" of that kind! Chipman's true credentials are that he has thought about this subject, noticed the apparent problem, worked it out, and presented clear, correct conclusions in a way that other people can follow. Those are the only credentials that really count. [*] Wellknown to some college students in the USA, perhaps? I'd never heard of him, but Dan's summary suggests this book might be worth looking for.  73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB) Editor, 'The VHF/UHF DX Book' http://www.ifwtech.co.uk/g3sek 
#52




Roy Lewallen wrote:
Although it's not really relevant to the discussion at hand, I believe a valid argument could be made that if a2 isn't equal to zero, then S11 isn't a reflection coefficient at all. It surely isn't the reflection coefficient at port 1, anyway. Actually, it is, Roy. s11 is the *physical* reflection coefficient. For instance, in the following twoport network: source50 ohm feedline+1/2WL 150 ohm feedline50 ohm load s11 is *defined* as the input reflection coefficient with the output port terminated by a matched load (ZL=150 ohms sets a2=0). s11 continues to be *defined* as 0.5 even when a2 is not zero. s11 = (15050)/(150+50) = 0.5 Since a Z0match exists at '+', the reflection coefficient on the 50 ohm feedline is zero. rho = Sqrt(Pref/Pfwd) For a twoport network with a2 not equal to zero, the reflection coefficient 's11' is NOT equal to the reflection coefficient 'rho'. The energy analysis on my web page deals only with physical reflection coefficients. If 'rho' is not a physical reflection coefficient, then it is the END RESULT of a mathematical calculation and is not the CAUSE of anything. If a source doesn't "see" a physical impedance discontinuity, it doesn't "see" anything except forward and reflected waves. Coherent waves traveling in opposite directions are "unaware" of each other. Coherent waves traveling in the same direction merge, lose their separate identies, and become indistinguishable from one another.  73, Cecil http://www.qsl.net/w5dxp = Posted via Newsfeeds.Com, Uncensored Usenet News = http://www.newsfeeds.com  The #1 Newsgroup Service in the World! == Over 100,000 Newsgroups  19 Different Servers! = 
#53




Dan wrote:
Now that the various typo mistakes have been corrected, and putting aside for the moment the name calling and ad hominem arguments, could it be that _both_ sides in this discussion are correct? Camp 'A' says that the reflection coefficient is computed the classical way, without using Zo conjugate, and offers various mathematical proofs and discussions of infinitely long lines. Camp 'B' says the reflection coefficient is computed with Zo* (Zo conjugate) in the numerator, and offers explanations dealing with the conservation of energy and maximum transfer of power. Both sides may be correct since they are talking about _two different_ meanings for the term "reflection coefficient." One has to do with voltage (or current) traveling waves and the other has to do with power. If a lossy line is terminated with the complex Z0, there is no reflection from the load, but the maximum possible power is not delivered. If the *load* is made equal to the complex conjugate of Z0 the maximum *forward power* is delivered but there is a reflected power (VSWR is not 1:1). It is difficult to say that the maximum *power* is delivered without knowing the generator impedance, since it is involved in any socalled "conjugate match". For a lossy line, the idea of conjugate match is, at best, very approximate anyway. And generator impedance is a mystery in most, but not all, transmitter PA situations. One possible exception: a large amount of negative feedback helps to determine, to some extent, output impedance, for a signal with timevarying amplitude (e.g. SSB). It seems to me to be clear that the use of Z0* in the reflection coefficient equation has not been corroborated (see Roy's post), but the use of ZL=ZO* has been. The two ideas are not equivalent. After looking at some examples, using the exact complex hyperbolic equations with Mathcad, it is obvious that a line must be very lossy to make a significant difference whether ZL or ZL* is used to terminate the line. Still, it is important to understand the basic principles involved, so this exercise is not foolishness at all. A word about "credentials". We all respect established and competent authors. But I have noticed on several occasions that blind faith has some exceptions. As an experienced author, I am personally familiar with this problem. G. Gonzalez (highly respected) "Microwave Transistor Amplifiers" second edition, has a good discussion of Power Waves, based on Kurokawa (I also have his article). There are no transmission lines, and the term ZS* (ZS=generator impedance) is used. In particular, a power wave reflection coefficient is defined: Gp = (ZLZS*)/(ZL+ZS) which looks quite familiar, with ZS replacing Z0. Also, a voltage reflection coefficient: Gv = [Zs/Zs*] x [(ZLZS*)/(ZL+ZS)] and a current reflection coefficient Gv = Gp. The author also defines twoport scattering parameters in terms of power waves, in which ZS* and ZL* appear. For the purposes of the present topic, involving transmission lines, it seems best to stay away from power waves, without a lot more studying. Bill W0IYH 
#54




Cecil:
[snip] s11 is a reflection coefficient that has the special condition that a2 must be equal zero. When a2 is not equal zero, the s11 reflection coefficient and the apparent reflection coefficient are not the same.  73, Cecil http://www.qsl.net/w5dxp [snip] No! The scattering paramters, e.g for a twoport the s11, s12, s21 and s22 are all parameters fixed by the network and are not dependent upon either the independent or dependent variables! i.e. b1 = s11*a1 + s12*a2, and b2 = s21*a1 + s22* a2.  Peter K1PO Indialantic BytheSea, FL. 
#55




Roy:
[snip] "Roy Lewallen" wrote in message ... This is interesting. But how did it lead you to the equation you determined must be correct? That is, what definition of reflection coefficient did you start with, where did you get it, and how did you get from there to the reflection coefficient equation you presented? I assume that, consistent with the admonition in the last paragraph of your posting, you were "careful to follow through and be consistent with your definitions, measurements, algebra, and arithmetic". It would be very instructive for us to be able to follow the process you did in coming to what you feel is the "right answer". Roy Lewallen, W7EL [snip] I followed up with a complete, and I hope simple and easy to follow, algebraic development in another nearby posting. Have a look and let us know what you think. BTW... I don't necessarily agree with Slick's defintition of the reflection coefficient and for sure, his is not the one I use. But I will defend to the death his right to use the one he defines, as long as all of his subsequent calculations and measurements are consistent with that definition. Slice and I will always end up with the same voltages v and currents i, it's just that our wave variables a and b won't agree! Viewing "waves" is just a viewpoint! One has to view them "through" an instrument called a reflectometer. When viewed through ammeters and voltmeters we will all measure the same things. Only the "electricals" the v and I are "real"! The "waves" the a and b are just different manifestations of v and i as viewed through and instrument [reflectometer] using a, perhaps arbitrary, reference impedance, or matrix transformation. Sorry Cecil. :)  Peter K1PO Indialantic BytheSea, FL. 
#56




Reg:
[snip] "Reg Edwards" wrote in message ... Peter, what an excellent, straightforward, plain English, explanation. And you didn't enlist the aid of a single guru. Not even Terman or the ARRL handbook. ;o)  Reg [snip] Heh, heh... I beleive in working it all out from first principles, can't trust anybody else, except of course you and your wonderful programs. :)  Peter K1PO Indialantic BytheSea, FL. 
#57




William E. Sabin wrote:
Dan wrote: Now that the various typo mistakes have been corrected, and putting aside for the moment the name calling and ad hominem arguments, could it be that _both_ sides in this discussion are correct? Camp 'A' says that the reflection coefficient is computed the classical way, without using Zo conjugate, and offers various mathematical proofs and discussions of infinitely long lines. Camp 'B' says the reflection coefficient is computed with Zo* (Zo conjugate) in the numerator, and offers explanations dealing with the conservation of energy and maximum transfer of power. Both sides may be correct since they are talking about _two different_ meanings for the term "reflection coefficient." One has to do with voltage (or current) traveling waves and the other has to do with power. If a lossy line is terminated with the complex Z0, there is no reflection from the load, but the maximum possible power is not delivered. If the *load* is made equal to the complex conjugate of Z0 the maximum *forward power* is delivered but there is a reflected power (VSWR is not 1:1). It is difficult to say that the maximum *power* is delivered without knowing the generator impedance, since it is involved in any socalled "conjugate match". For a lossy line, the idea of conjugate match is, at best, very approximate anyway. And generator impedance is a mystery in most, but not all, transmitter PA situations. One possible exception: a large amount of negative feedback helps to determine, to some extent, output impedance, for a signal with timevarying amplitude (e.g. SSB). It seems to me to be clear that the use of Z0* in the reflection coefficient equation has not been corroborated (see Roy's post), but the use of ZL=ZO* has been. The two ideas are not equivalent. After looking at some examples, using the exact complex hyperbolic equations with Mathcad, it is obvious that a line must be very lossy to make a significant difference whether ZL or ZL* Correction: Z0 or Z0* is used to terminate the line. Still, it is important to understand the basic principles involved, so this exercise is not foolishness at all. A word about "credentials". We all respect established and competent authors. But I have noticed on several occasions that blind faith has some exceptions. As an experienced author, I am personally familiar with this problem. G. Gonzalez (highly respected) "Microwave Transistor Amplifiers" second edition, has a good discussion of Power Waves, based on Kurokawa (I also have his article). There are no transmission lines, and the term ZS* (ZS=generator impedance) is used. In particular, a power wave reflection coefficient is defined: Gp = (ZLZS*)/(ZL+ZS) which looks quite familiar, with ZS replacing Z0. Also, a voltage reflection coefficient: Gv = [Zs/Zs*] x [(ZLZS*)/(ZL+ZS)] and a current reflection coefficient Gv = Gp. Correction: Gi = Gp The author also defines twoport scattering parameters in terms of power waves, in which ZS* and ZL* appear. For the purposes of the present topic, involving transmission lines, it seems best to stay away from power waves, without a lot more studying. Bill W0IYH 
#58




Slick:
[snip] Correction: rho = (Z  conj(R))/(Z + (R)), the conjugate being only in the denominator. Slick [snip] Well here we have to part company. Not using the same "thing" in both numerator and denominator *is* being inconsistent! See my algebraic development in another posting on this thread.  Peter K1PO Indialantic BytheSea, FL. 
#59




On Sun, 24 Aug 2003 15:27:02 GMT, "Peter O. Brackett"
wrote: See anything wrong with this analysis? Hi Peter, One thing: you are expecting everyone to agree that the source has a characteristic Z. The chasm that separates factions is found in this alone where many who say, no "it is NOT 50 Ohms" (or "it doesn't matter") are loath to come up with an actual value to conjugate (in other words, a sterile position). Such a forced choice leads obviously to the deflation of pet theories. To date their best argument is you cannot possibly know that value (for any of a variety of reasons, unrelated to simply sitting down at the bench and measuring an actual value). In short, institutionalized ignorance, embraced with a mystic missionary zeal, is their crowing logic. But I do enjoy their examples and logic puzzles reminiscent of the necromancer's formulĂ¦ for transmutation of gold into lead. The unrequited dreams would be fulfilled if only the discovery of the Philosopher's Stone could be realized. Hence debate proceeds with the leaps and twirls of zencartwheeling. 73's Richard Clark, KB7QHC 
#60




Richard Clark wrote:
To date their best argument is you cannot possibly know that value (for any of a variety of reasons, unrelated to simply sitting down at the bench and measuring an actual value). In short, institutionalized ignorance, embraced with a mystic missionary zeal, is their crowing logic. The problem lies in the difficulty of measuring or calculating Zs, especially for signals that have large variations in amplitude, such as SSB. There is no institutionalized ignorance, just a lot of skepticism regarding the reliability of the analysis methods and the measurement methods. Bill W0IYH 
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