Home |
Search |
Today's Posts |
#26
![]() |
|||
|
|||
![]()
On Sat, 05 Jun 2004 19:11:32 -0500, Cecil Moore wrote:
Walter Maxwell wrote: Sorry, Cecil, in spite of their similarity with Hecht's, these equations are totally invalid. Before we go any farther, Walt, please reference a copy of _Optics_, by Hecht. Dr. Best's equations are valid. He just didn't understand what he was dealing with and presented them improperly. Hecht presents them properly. Dr. Best's equations are the classical physics equations for the destructive interference and constructive interference. I'm trying to locate my Hecht paper, but can't at the moment. Let's make sure we're talking about the same set of of equations. The ones I'm saying are invalid as stated in his article appear on Page 46, Col 2. These equations are all being used invalidly as a result of his Eq 9, Part 3 being invalid for use with reflected power with only one source. This a concept you're just going to have to learn to accept. This equation is valid ONLY when there are two separate sources--the rearward traveling reflected wave is NOT a second source, and it will NOT work on power contained in the reflected wave. You must understand why the invalidity of his Eq 6 in Part 1is responsible for the entire problem. Once you understand this point you'll understand why the equations on Page 46 are invalid. Cecil, Steve's Eq 9 is valid only if there is more than one source. In this case there is only one, the transceiver. This a concept that you apparentely aren't getting, and Steve didn't either. Because Steve derived his Eqs 10 thru 15 from an invalid premise concerning Eq 6 those equations are invalid. Just plug his values for P1 and P2 into any of those equations and you'll get invalid answers. With the transmission line system Steve's voltage V2 comes from the same source as V1. Yes, V1 comes from the generator and V2 comes from reflections from the load which come originally from the generator. But Cecil, you CAN'T add V1 and V2 in any manner to obtain forward power, because adding V1 and V2 does not yield forward voltage. This is the first place Steve erred in Part 1. Go back and review my previous msg where I explain why his Eq 6 in Part 1 is invalid. Dr. Best didn't understand the S-parameter analysis and presented his material in an invalid way. But even though he didn't understand what he was saying, his equations are valid. He was completely off base in his explanations. It was like Einstein coming up with E = MC^2 and then completely blowing the explanation. In an S-parameter analysis, b2 = s21(a1) + s22(a2) In Dr. Best's analysis, VFtotal = V1 + V2 whe V1 = V1F*(transmission coefficient) + V2R*(reflection coefficient) How many times do I have to explain that V1 + V2 does NOT equal VF total? This concept cannot be fudged into the S- parameter analysis, because V1 + V2 = VF total is an invalid premise. V1F is the voltage incident upon the impedance discontinuity from the left. (port1) V2R is the voltage incident upon the impedance discontinuity from the right. (port2) I repeat, Cecil, V1 + V2 yields only the swr, not VF total forward voltage. There's a one-to-one correspondence above. If the S-parameter analysis is valid, then Dr. Best's equations are valid. He just didn't present them in a valid manner. The S-parameter analysis would be valid if the premise that V1 + V2 = VF were valid, which it is not. Please review my explanation why his Eq 6 in Part 1 is invalid. This is the crux of the entire case, which has made the Eqs that I say are invalid, invalid. Because Steve used Eq 9 in an invalid way to derive Eqs 10 through 15, all of these derived equations are also invalid. Try Eq 13 for example. It says 75 w plus 8.33 w = 133.33 w, as you well know. This is absurd! His equations are valid. His knowledge is what was invalid. It is true that 75w + 8.33W + 2*SQRT(75W*8.33W) = 133.33W This is Steve's Eq 12, which appears to be correct when theta = zero, but he qualifies this equation, saying tghat when V1 and V2 are in phase the total power can be determined by Eq 13. NOT SO. The ironic part of this is that when the system is matched V1 and V2 are always in phase on lossless lines. P1 + P2 + interference power = PFtotal This fact is precisely what Steve emphatically denies, I presented this to Dr. Best 9 months before his Part 3 was published. He simply didn't pay any attention. From a voltage standpoint where ci means constructive interference: I don't understand the ci term--please explain. V1^2/Z02 + V2^2/Z02 + Vci^2/Z02 = VFtotal^2/Z02 V1^2/Zo + V2^2/ Zo = total forward power. The left -hand terms of the above equation are power terms that do not equal VFtotal^2/Zo, because V1 + V2 does not equal VFtotal. For a Z02 equal to 150 ohms (if I remember correctly) 106.07v^2 + 35.35v^2 + 86.6v^2 = 141.42v^2 So V1^2 + V2^2 + Vci^2 = VFtotal^2 Again, if V1 + V2 does not equal VFtotal, then the sum of the squares of V1 and V2 cannot equal the square of VFtotal, unless Vci^2 is a large negative number. This is exactly what you have been saying all along, something that Dr. Best simply didn't understand. He completely ignored the interference term without which the voltage equation cannot balance. 2*SQRT(75W*8.33W) is the constructive interference term supplied by the destructive interference event on the other side of the match point which Dr. Best completely ignored in his article. In addition, because the powers don't add up correctly using V1 and V2 at zero phase relationship, he concocted the ruse that they must add vectorially, and he goes through several values of phase relationships to show what the forward power would be with the various phases. This is poppycock, because the phase relationship between the source (V1) and re-reflected voltage (V2) is ALWAYS ZERO on lossless lines. Only if the system is perfectly matched. If the system is not matched, V1 and V2 can have any phase relationship. Yeah, but if V1 and V2 have any relationship other than zero the system is NOT perfectly matched. Dr. Best's equations are valid but he just didn't comprehend their meaning. When I called him on it, he seemed never to have heard of destructive/constructive interference. That's what set me to researching But Cecil, why would we be considering any condition other than perfectly matched? All of his equations from 9 thru 15 specifiy the route to obtain either PF or VF. This means conditions are for a matched system. EM waves in the arena of optics. I looked at the situation assuming that you two guys are both knowledgeable and intelligent and I arrived at the conclusion that the two of you are only two inches apart. But (IMO) neither one of you is willing to move that one inch to bridge the gap. (I have said this before in private email to Walt.) Sorry, Cecil, we're miles apart, and will be until the erroneous Eq 6 in Part 1 is corrected. I know I've rambled all over the place with redundancies, but I tried to respond to each of your paragraph statements as they occurred. Walt |