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#112




W5DXP wrote: Jim Kelley wrote: W5DXP wrote: I don't think there's anything to argue about. From _Optics_, by Hecht: "We define the reflectance R to be the ratio of the reflected power to the incident power." He certainly wasn't including Max Born and Emil Wolf when he said "We". They define reflectance in terms of indices of refraction i.e. (n1n2)/(n1+n2). The Reflectance is equal to the square of the amplitude reflection coefficient. R = Ir/Ii = [(n1n2)/(n1+n2)]^2 Again, Born and Wolf disagree with Hecht. They define Reflectivity as being the square of the reflection coefficient. Hecht says the definition "leads to" the last term above. Certainly he didn't feel that some relative amounts of power are what determine the indices of refraction of the system. That would be ridiculous. 73, ac6xg 
#113




"Dr. Slick" wrote in message om... "David Robbins" wrote in message ... Incorrect. You need the conjugate in the numerator if the Zo is complex. If it is purely real, WHICH MOST TEXTS ASSUME, then you can use the normal equation. sorry, the derivation for the table in the book i sent before is for the general case of a complex Zo. they then go on to simplify for an ideal line and for a nearly ideal line... nowhere does a conjugate show up. Please post this derivation again. sorry, i don't have time for this. its really quite simple, just apply kirchoff's and ohm's laws at the connection point and it falls right out. When they say "ideal line" do they mean purely real? yes, purely real with no loss terms. and that reference you give is not for a load on a transmission line, it is talking about a generator supplying power to a load... a completely different animal. Not at all really. The impedance seen by the load can be from either a source or a source hooked up with a transmission line. It doesn't matter with this equation. the reference you gave is looking at a generator connected to a load. true, it doesn't matter if there is a transmission line in between the generator and the 'load' but the impedance being used is the one transformed back to the generator end of the line, not the one at the far end of the line... so basically that equation is not a transmission line equation, it is a generator to load reflection calculation done to maximize power not to satisfy kirchoff. 
#114




On Tue, 26 Aug 2003 22:35:29 0000, "David Robbins"
wrote: the reference you gave is looking at a generator connected to a load. true, it doesn't matter if there is a transmission line in between the generator and the 'load' but the impedance being used is the one transformed back to the generator end of the line, not the one at the far end of the line... so basically that equation is not a transmission line equation, it is a generator to load reflection calculation done to maximize power not to satisfy kirchoff. Hi David, If it is time invariant (linear), it doesn't matter. 73's Richard Clark, KB7QHC 
#115




Richard Clark wrote in message . ..
The scenario begins: "A 50Ohm line is terminated with a load of 200+j0 ohms. The normal attenuation of the line is 2.00 decibels. What is the loss of the line?" Having stated no more, the implication is that the source is matched to the line (source Z = 50+j0 Ohms). This is a half step towards the full blown implementation such that those who are comfortable to this point (and is in fact common experience) will observe their answer and this answer a "A = 1.27 + 2.00 = 3.27dB" Interesting. I'd first have asked if the line was really 50 ohms, completely nonreactive. If so, L/C=R/G and I'd have said A=3.266dB. If the line was just 50 ohms nominal, then I can think of at least one scenario in which A=0.60dB. And I can think of another in which A= 5.2dB. The definition I have used for loss in those cases is A=10*log10(P1/P2), where P2 is the power delivered to the (line+load) and P1 is the power delivered to the load, with steadystate excitation. The answer, given that definition, never depends on source impedance of the driving source. Of course it could with a different definition, for example involving the maximum available power from the source, but that just confuses the issue by lumping "(source) mismatch loss" with acutal line loss, as has been pointed out before. Cheers, Tom 
#116




Roy:
[snip] "Roy Lewallen" wrote in message ... In transmission line analysis, we're not free to rescale the forward and reverse voltage waves, unless we also scale all the voltages, currents and powers accordingly. The forward and reverse waves have to add to the total voltage in the line and at its ends, and the ratio of each component to the corresponding current component has to equal the Z0 of the line. [snip] I agree, that's why I say the definition of rho with Zo and not the conjugate is actually Mother Natures definition. Simply because that's the way the solution to the wave equation [The Telegraphists Equation] turns out. [snip] It's quite apparent that in S parameter analysis you're quite free to scale them as you wish, as you have. Vendelin et al didn't just scale them, but chose a set of V+ and V which aren't even related to a and b by the same constant. [snip] Actually you are free! Just define the waves a and b as any linear combination of i and v and as long as the linear combination is nonsingular you will be just fine! You can Engineer systems to your hearts content and get all the right answers. [It's sort of like the assumption of current flow in conductors from + to , even though we "know" electrons flow the other way, it always gives us the correct Engineering answers, so who cares!] [snip] basic principles. And from it or other methods, we can conclude that when a transmission line is terminated in its characteristic impedance, there is no reflection of the voltage (or current) wave. When it's terminated in the complex conjugate of its characteristic impedance, or any other impedance except its characteristic impedance, there is a reflection. Roy Lewallen, W7EL [snip] Roy my friend we are in violent agreement!  Peter K1PO Indialantic BytheSea, FL. 
#117




Cecil:
[snip] The scaling is defined by the sparameter specification. Nobody is free "to scale them as you wish". For instance, a1 is defined as: (V1+I1*Z0)/2*Sqrt(Z0)  73, Cecil http://www.qsl.net/w5dxp [snip] I like that definition best of all in a theoretical setting... but be prepared... there are many others to be found in the literature. Even though I like the definition you have shown above, I find the definitions... a = v + Zo*i and b = v  Zo*i To be very convenient in practice since they correspond to a very easy to understand, visualize and manipulate single Operational Amplifier reflectometer circuit. As long as the relationship between v and i and a and b are simple linear combinations without singularities, i.e. the transformation matrix M which allows you to transform between the [a, b] vectors and the [i, v] vectors is nonsingular then you are just fine, as long as you remain consistent with your initial definition. You can perform reliable and accurate Engineering with any definition of the "waves" [a, b] that are a suitable linear combination of the "electricals" [i, v].  Peter K1PO Indialantic BytheSea, FL. 
#118




Richard:
[snip] I know you eschew academic references in favor of "first principles," but others may want more material than the simple puzzle aspect. They can consult "Transmission Lines & Networks," Walter C. Johnson, Chapter 13, "Insertion Loss and Reflection Factors." But lest those who go there for the answer, I will state it is from another reference, Johnson simply is offered as yet another reference to balance the commonly unstated inference of SWR mechanics being conducted with a Z matched source. "Transmission Lines," Robert Chipman is another (and not the source of the puzzle either). 73's Richard Clark, KB7QHC [snip] I hear you... I don't eschew academic references, but when it comes to systems Engineering, I do try to follow what our great President Regan once said, "Trust, but Verify!"  Peter K1PO Indialantic BytheSea, FL. 
#119




Roy:
[snip] You didn't show differently in your analysis, and no one has stepped forward with a contrary proof, derivation from known principles, or numerical example that shows otherwise. Roy Lewallen, W7EL [snip] Yes I did. I guess that you missed that post. I'll paste a little bit of that posting here below so that you can see it again. [begin paste] We are discussing *very* fine points here, but... [snip] ratio of the reflected to incident voltage as rho = b/a would yeild the usual formula: rho = b/a = (Z  R)i/(Z + R)i = (Z  R)/(Z+ R). In which no conjugates appear! Now if we take the internal/reference impedance R to be complex as R = r + jx then for a "conjugate match" the unknown Z would be the conjugate of the internal/reference impedance and so that would be: Z = r  jx Thus the total driving point impedance faced by the incident voltage a would be 2r: R + Z = r + jx + r  jx = 2r and the current i through Z would be i = a/2r with the voltage v across Z being v = a/2. Now the reflected voltage under this conjugate match would not be zero, rather it would be: b = (Z  R)i = ((r  jx)  (r + jx))i = (r  r jx jx)i = 2jxi = 2jxa/2r = jax/r and the reflection coefficient value under this conjugate match would be simply: b/a = rho =  jx/r Thus I conclude that, under the classical definitions, when one has a "conjugate match" [i.e. maximum power transfer] the reflected voltage and the reflection coefficient are not zero. : : In summary: Under the classical definition of rho = (Z  R)/(Z + R) rho will be not be zero for a "conjugate match" and in fact there will be a "residual" reflected voltage of jx/r times the incident voltage at a conjugate match. The only time the classical definition of rho and the reflected voltage is null is for an "image match" when the load equals the reference impedance. : : Unless one changes ones definition of the reflected voltage/reflection coefficient to utilize the conjugate of the internal impedance as the "reference" impedance then the reflected voltage is not zero at a conjugate match. End of story. [snip] Regards,  Peter K1PO Indialantic BytheSea, FL. 
#120




Jim Kelley wrote:
Again, Born and Wolf disagree with Hecht. They define Reflectivity as being the square of the reflection coefficient. From the IEEE dictionary: "reflectivity  The reflectance of the surface of a material so thick that the reflectance does not change with increasing thickness" Looks like Born and Wolf are wrong.  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! = 
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