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#151




Peter O. Brackett wrote:
In summary, I believe that we agree completely, and that we were typing at "cross purposes". If this newsgroup had its own logo, it would surely be two crossed porpoises.  73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB) Editor, 'The VHF/UHF DX Book' http://www.ifwtech.co.uk/g3sek 
#152




It's often noted in texts that SWR is really a meaningless measure when
applied to lossy lines. So I wouldn't unduly worry about strange SWR numbers for very lossy lines. Take a look at the analysis I just posted on another thread, which gives voltages, currents, impedances, and powers for an example case, and see if you can find anything wrong with it. The calculation used for reflection coefficient is based on its definition, namely reflected voltage divided by forward voltage. That agrees with all the transmission line and electromagnetics texts I have, which is getting to be quite a number now. Roy Lewallen, W7EL William E. Sabin wrote: In simulation programs, transmission lines are solved for their twoport parameters, and are then treated as lumped circuits in the actual simulation, just like any lumpedelement circuit. Which is a good way to do it. I notice that in the ARRL Antenna Book, 19th edition , on page 247, it is stated with definite finality that the reflection coefficient formula uses the complex conjugate of Zo in the numerator. I also understand that this has been established by a "welltrusted authority". I have used Mathcad to calculate rho and VSWR for Reg's example, for many values of X0 (imaginary part of Z0) from 0 to 250 ohms. The data follows: Note: rho1* is conjugated rho1, SWR1 is for rho1*, rho2 is not conjugated and SWR2 applies to rho2 X0.......rho1*..SWR1.....rho2..SWR2 250..... 0.935...30.0.....1.865...3.30 200..... 0.937...30.8.....1.705...3.80 150..... 0.942...33.3.....1.517...4.87 100..... 0.948...37.5.....1.320...7.25 050..... 0.955...43.3.....1.131...16.3 020..... 0.959...47.6.....1.030...76.5 015..... 0.960...48.4.....1.010...204 012..... 0.960...48.9.....0.997....+/ infinity 010..... 0.960...49.2.....0.990....+305 004..... 0.961...76.3.....0.974....+76.3 0000..... 0.961...50.9.....0.961....+50.9 The numbers for notconjugate rho are all over the place and lead to ridiculous numbers for SWR. It is also obvious that for a lowloss line it doesn't matter much. But values of rho greater than 1.0, on a Smith chart correspond to negative values of resistance (see the data). Something is wrong here that we are overlooking. The use of conjugate rho is so much better behaved that I have some real doubts about some of our conclusions on this matter. What about it folks? How can we get to the bottom of this? Bill W0IYH 
#153




"Roy Lewallen" wrote
It's often noted in texts that SWR is really a meaningless measure when applied to lossy lines. ============================= In amateur SWR meter applications even the line is just a figment of the imagination. But that problem is easily solved  change the name of the meter!  Reg 
#154




The equation in the ARRL Antenna Book is identical to the equation for rho that is in the Power Wave literature (see Gonzalez and also see Kurokawa). Also, numerous literature sources describe how an opencircuit generator with internal impedance Z0, connected directly to load ZL, is actually a power wave setup that leads to a rho formula that is identical to the formula in the ARRL Antenna Book. When calculating rho, it is not necessary to fool around with the wave equations, because frequency is constant and everything is steadystate. Bill W0IYH Also the same conjugate formula in Les Besser's RF Fundamentals I, and Kurokawa, and the 1992 ARRL general Handbook, which has NO term for Zo reactance, so it assumes a purely real Zo. This page also has the correct general formula: http://www.zzmatch.com/lcn.html Slick 
#155




A few days ago I posted a derviation of the (nonconjugate) formula for
voltage reflection coefficient on a transmission line. It required only a few assumptions: 1. That the voltage reflection coefficient is the ratio of reverse to forward voltage. 2. That the voltage at any point along the line, including the ends, is the sum of the forward and reverse voltages, and that the current is the sum of forward and reverse currents. 3. That the ratio of forward voltage to forward current, and the ratio of reverse voltage to reverse current, equal the characteristic impedance of the transmission line. Given these assumptions, the derivation is a matter of straightforward algebra. For those promoting some other formula for voltage reflection coefficient: Which of the above assumptions is false? What substitute assumption is true? And what's *your* dervivation? Remember, we're talking about transmission lines here, not a one or twoport analysis with a "reference impedance" instead of a transmission line, and where there's no restriction that the total voltage and current are simply the sum of the forward and reverse components. Roy Lewallen, W7EL 
#156




Roy Lewallen wrote:
1. That the voltage reflection coefficient is the ratio of reverse to forward voltage. For those promoting some other formula for voltage reflection coefficient: Which of the above assumptions is false? Number 1 is not always true for s11, the sparameter reflection coefficient. What substitute assumption is true? For an sparameter analysis, it's that s11 = b1/a1 when a2=0 Your definition above says that rho = b1/a1 no matter what the value of a2. Some configurations have rho = s11 and some don't. There are differences between your transmission line analysis, an sparameter analysis, an hparameter analysis, a yparameter analysis, or a zparameter analysis. If they were all alike, there would be no need for their separate existences. FYI: s11=[(h111)(h22+1)h12*h21]/[(h11+1)(h22+1)h12*h21] s11=[(1y11)(1+y22)+y12*y21]/[(1+y11)(1+y22)y12*y21] s11=[(z111)(z22+1)z12*z21]/[(z11+1)(z22+1)z12*z21] s11=Vref1/Vfwd1 when Vref2=0, i.e. Pref2=0  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! = 
#157




Roy Lewallen wrote:
I tried really hard to say clearly that I'm speaking of transmission lines and not one or twoport analysis. How could I have phrased that in a way it would be understood? You can speak of anything you want. But a transmission line analysis including a tuner and reflected waves *IS* a twoport analysis at the tuner. It *IS* a oneport analysis at the load. There's just no getting around it. Your transmission line analysis resembles a Zparameter analysis of oneport and twoport systems.  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! = 
#158




"Roy Lewallen" wrote
I tried really hard to say clearly that I'm speaking of transmission lines and not one or twoport analysis. ======================= There's no difference between the two. If you produce the symetrical Smatrix for a length of transmission line, its 4 parameters contain complex hyperbolic functions like (Ro+jXo)*Cosh(A+jB) . . . . . where A is nepers and B is radians. Whichever way you go, matrixalgebra or Heaviside, you perform exactly the same set of calculations and, not surpisingly, you end up with the same answers  provided Zo in one place only is not followed with an askerisk just to obtain another answer which is thought to be more preferable.  Reg, G4FGQ 
#159




Roy:
[snip] "Roy Lewallen" wrote in message ... I tried really hard to say clearly that I'm speaking of transmission lines and not one or twoport analysis. How could I have phrased that in a way it would be understood? [snip] !!! Your phrasing is clear, but it is you that does not understand. Since when has a transmission line NOT been a two port network? A transmission line has two ports, period, end of story! Why are you being so picayune about this issue? Something else must be bothering you here... I just can't figure out where you are coming from. What is your purpose in differentiating between networks and transmission lines? As far as I understand an electrical network may consist of nothing more than a simple transmission line, if so, what's your point?  Peter K1PO Indialantic BytheSea, FL. 
#160




Roy Lewallen wrote:
Someone, I don't even recall who now, noticed that the formula used for calculating transmission line reflection coefficient allows a magnitude greater than one when Z0 is complex. From there, the claim was made that a reflection coefficient greater than one is impossible for a passive network, since (they said) it implies the creation of energy. I suspect the problem probably has something to do with squaring the absolute magnitude of a complex voltage reflection coefficient. Maybe only the real part should be squared to obtain the power reflection coefficient?  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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