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Analyzing Stub Matching with Reflection Coefficients
I have to agree with what Richard and some others have said.
First, that you've done a tremendous job of sharing your extensive knowledge and experience, and explaining transmission line phenomena in such a clear and understandable manner. We all owe you a great debt for this. But second, that there's something which you do state that I and some others can't accept. And that is that a "virtual" short (or open) circuit causes reflections, or that waves reflect from it. I maintain that for either to happen requires that traveling waves interact with each other. The "virtual" short or open is only the result of the sum -- superposition -- of traveling waves. Those traveling waves, and hence their sum, cannot cause a reflection of other waves, or alter those other waves in any way. Only a physical change in the (assumed linear) propagating medium can alter the fields in a traveling wave and cause a reflection. A real short circuit is in this category; a virtual short circuit is not. It doesn't matter if the waves are coherent or not, or even what their waveshapes are or whether or not they're periodic -- as long as the medium is linear, the waves cannot interact. You have clearly shown, and there is no doubt, that waves behave *just as though* a virtual short or open circuit were a real one, and this is certainly a valuable insight and very useful analysis tool, just like the "virtual ground" at the summing junction of an op amp. But I feel it's very important to separate analytical tools and concepts from physical reality. If we don't, we're led deeper and deeper into the virtual world. Sooner or later, we reach conclusions which are plainly wrong. There are many other examples of useful alternative ways of looking at things, for example differential and common mode currents in place of the reality of two individual currents, or replacing the actual exponentially depth-decaying RF current in a conductor with an imaginary one which is uniform down to the skin depth and zero below. But we have to always keep in mind that these are merely mathematical tools and that they don't really correspond to the physical reality. Unless I've incorrectly read what you've written, you're saying that you've proved that virtual shorts and opens reflect waves. But in every example you can present, it can be shown that all waves and reflections in the system can be explained solely by reflections from real impedance changes, and without considering or even noticing those points at which the waves superpose to become virtual short or open circuits. That, I believe, would disprove the conjecture that virtual shorts or opens cause reflections. Can you present any example which does require virtual shorts or opens to explain the wave behavior in either a transient or steady state condition? If I've misinterpreted what you've said, I share that misinterpretation with some of the others who have commented here. And if that's the case, I respectfully suggest that you review what you've written and see how it could be reworded to reduce the misunderstanding. Once again, we all owe you a great deal of thanks for all you've done. And personally, I owe you thanks for many other things, including setting such an example of courtesy, civility and professionalism here in this group (as well in everything else you touch). It's one I strive for, but continually fall far short of. Roy Lewallen, W7EL |
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Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 15:01:19 -0700, Roy Lewallen wrote:
I have to agree with what Richard and some others have said. First, that you've done a tremendous job of sharing your extensive knowledge and experience, and explaining transmission line phenomena in such a clear and understandable manner. We all owe you a great debt for this. But second, that there's something which you do state that I and some others can't accept. And that is that a "virtual" short (or open) circuit causes reflections, or that waves reflect from it. I maintain that for either to happen requires that traveling waves interact with each other. The "virtual" short or open is only the result of the sum -- superposition -- of traveling waves. Those traveling waves, and hence their sum, cannot cause a reflection of other waves, or alter those other waves in any way. Only a physical change in the (assumed linear) propagating medium can alter the fields in a traveling wave and cause a reflection. A real short circuit is in this category; a virtual short circuit is not. It doesn't matter if the waves are coherent or not, or even what their waveshapes are or whether or not they're periodic -- as long as the medium is linear, the waves cannot interact. You have clearly shown, and there is no doubt, that waves behave *just as though* a virtual short or open circuit were a real one, and this is certainly a valuable insight and very useful analysis tool, just like it's very important to separate analytical tools and concepts from physical reality. If we don't, we're led deeper and deeper into the virtual world. Sooner or later, we reach conclusions which are plainly the "virtual ground" at the summing junction of an op amp. But I feel wrong. There are many other examples of useful alternative ways of looking at things, for example differential and common mode currents in place of the reality of two individual currents, or replacing the actual exponentially depth-decaying RF current in a conductor with an imaginary one which is uniform down to the skin depth and zero below. But we have to always keep in mind that these are merely mathematical tools and that they don't really correspond to the physical reality. Unless I've incorrectly read what you've written, you're saying that you've proved that virtual shorts and opens reflect waves. But in every example you can present, it can be shown that all waves and reflections in the system can be explained solely by reflections from real impedance changes, and without considering or even noticing those points at which the waves superpose to become virtual short or open circuits. That, I believe, would disprove the conjecture that virtual shorts or opens cause reflections. Can you present any example which does require virtual shorts or opens to explain the wave behavior in either a transient or steady state condition? If I've misinterpreted what you've said, I share that misinterpretation with some of the others who have commented here. And if that's the case, I respectfully suggest that you review what you've written and see how it could be reworded to reduce the misunderstanding. Once again, we all owe you a great deal of thanks for all you've done. And personally, I owe you thanks for many other things, including setting such an example of courtesy, civility and professionalism here in this group (as well in everything else you touch). It's one I strive for, but continually fall far short of. Roy Lewallen, W7EL Thank you, Roy, I appreciate your comments, as always. However, I knew that you have always considered that virtual opens and shorts cannot cause reflections, and I was hoping my discussion would have persuaded you otherwise. So I ask you this: What then causes the total re-reflection at the stub point if not a virtual short circuit? The re-reflection is real, but there is no physical short circuit at the re-reflection point. The resultant of the reflection coefficients of both the forward and reflected waves of voltage and current possess the exact reflection coefficients, 0.5 at 180° for voltage and 0.5 at 0° for current, that are present when the short is a physical short, except that the magnitude would be 1.0 instead of 0.5. The only operational difference is that a physical short on the line prevents wave propagation in both directions, while the virtual short is transparent in the forward direction, but opaque in the reverse direction. So I repeat the question: If a virtual short circuit cannot cause reflections, then what causes the reflection at the stub point? Incidentally, there has been mention of 'virtual' reflection coefficients. I can't agree with this terminology. Reflection coefficients are real, and for every reflection coefficient there is an equivalent real impedance. As such, it is just as valid to use reflection coefficients in transmission-line analyses as it is to use correspondingly-equal impedances. How now, Roy? Walt Walt |
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Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote:
Thank you, Roy, I appreciate your comments, as always. However, I knew that you have always considered that virtual opens and shorts cannot cause reflections, and I was hoping my discussion would have persuaded you otherwise. So I ask you this: What then causes the total re-reflection at the stub point if not a virtual short circuit? The re-reflection is real, but there is no physical short circuit at the re-reflection point. The resultant of the reflection coefficients of both the forward and reflected waves of voltage and current possess the exact reflection coefficients, 0.5 at 180° for voltage and 0.5 at 0° for current, that are present when the short is a physical short, except that the magnitude would be 1.0 instead of 0.5. The only operational difference is that a physical short on the line prevents wave propagation in both directions, while the virtual short is transparent in the forward direction, but opaque in the reverse direction. I'd think that this diode-like property of virtual shorts would be a major clue that they're not real, but a mathematical convenience. The virtual short is a point where the sum of the voltages of all waves, forward and reflected, add to zero. If this condition causes waves to reflect when struck from one direction, what possible physical explanation could there be for it to do absolutely nothing to waves traveling the other way? So I repeat the question: If a virtual short circuit cannot cause reflections, then what causes the reflection at the stub point? My answer is this: There is no total re-reflection at the stub point. It only looks that way. As you've observed, the waves (traveling in one direction, anyway) behave just as though there was such a re-reflection. But the waves actually are reflecting partially or totally from the end of the stub and other more distant points of impedance discontinuity, not from a "virtual short". The sum of the forward wave and those reflections add up to zero at the stub point to create the "virtual short", and to create waves which look just like they're totally reflecting from the stub point. This has some parallels to a "virtual ground" at an op amp input. From the outside world, the point looks just like ground. But it isn't really. The current you put into that junction isn't going to ground, but back around to the op amp output. Turn off the op amp and the "virtual ground" disappears. Likewise, waves arriving at the virtual short look just like they're reflecting from it. But they aren't. They're going right on by -- from either direction --, not having any idea that there's a "virtual short" there -- that is, not having any idea what the values or sum of other waves are at that point. They go right on by, reflect from more distant discontinuities, and the sum of those reflections arrives at the virtual short with the same phase and amplitude the wave would have if it had actually reflected from the virtual short. Like with the op amp, you can "turn off" the virtual short by altering those distant reflection points such as the stub end. Please let me emphasize again that not I or anyone else who has posted is disputing the validity of your matching methods or the utility of the "virtual short" concept. The only disagreement is in the contention that the "virtual short" actually *effects* reflections rather than being solely a consequence of them. Incidentally, there has been mention of 'virtual' reflection coefficients. I can't agree with this terminology. Reflection coefficients are real, and for every reflection coefficient there is an equivalent real impedance. As such, it is just as valid to use reflection coefficients in transmission-line analyses as it is to use correspondingly-equal impedances. I don't use "virtual reflection coefficient" by name or in concept, although it might have some utility in the same vein as "virtual short". However, great care would have to be used, as it must with virtual shorts, to separate analytical conveniences from reality. But I'll leave that discussion to others, and don't want it to divert us from the important point at hand. How now, Roy? A question: Do you think you can present an example where a "virtual short" is necessary to explain the impedances, voltages, and currents -- or any other measurable properties -- on a transmission line? Where a person who assumes that *no* reflection takes place at "virtual shorts" but only at physical discontinuities would be unable to arrive at the correct result? If reflections really do occur at "virtual shorts", I would think that this phenomenon would have a profound effect on transmission line operation, to the extent that a valid solution couldn't be obtained if it were totally ignored. I maintain that such an example can't be found, because in fact reflection takes place only at physical discontinuities and not at "virtual shorts". Waves in a linear medium simply don't reflect from or otherwise affect each other. I'm not saying that you can't apply the analytical concept of "virtual shorts" to arrive at the same, valid, result. Or that the "virtual short" approach won't be easier. But I am saying that it's not necessary in order to fully analyze any transmission line problem, simply because it's not real. Can you come up with such an example? Roy |
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Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen wrote:
Please let me emphasize again that not I or anyone else who has posted is disputing the validity of your matching methods or the utility of the "virtual short" concept. The only disagreement is in the contention that the "virtual short" actually *effects* reflections rather than being solely a consequence of them. The key word there is "utility" - the virtual short/open concept is *useful* as a short-cut in our thinking. But concepts are only useful if they help us to think more clearly about physical reality; and short-cuts are dangerous if they don't reliably bring us back onto the main track. We know that in reality both the forward and the reflected waves take a side-trip off the main line into the stub, and from the far end of the stub they are reflected back to rejoin the main line at the junction. Since an open- or short-circuited stub has a predictable effect at the junction where it is connected, then we could save a little time by noting that a stub is present, and simply assuming what its effect will be. Within those limitations, I don't have any particular problem about calling the effect a "virtual short" or "virtual open". As Richard said, it is only a metaphor. We are using the word "virtual" as a label to remind ourselves that the effect at the junction is not the same as a genuine physical short or open circuit on the main line. Where the concept goes off track is if anyone forgets about the limitations, and begins to believe that a metaphor has physical properties of its own. (It doesn't, of course - all of the physical effects on the main line are caused by the stub, and the stub is the only place where the root causes can be found.) If there is any problem in using a short-cut, then simply forget it - step back and analyse the complete physical system including the stub. Walt said: Incidentally, there has been mention of 'virtual' reflection coefficients. I can't agree with this terminology. Roy replied: I don't use "virtual reflection coefficient" by name or in concept, although it might have some utility in the same vein as "virtual short". Agreed. It all comes back to "usefulness" or "utility" again. As I said, concepts are only useful if they help us to think more clearly about physical reality - and "virtual reflection coefficient" has exactly the opposite effect. -- 73 from Ian GM3SEK |
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Analyzing Stub Matching with Reflection Coefficients
Ian White GM3SEK wrote:
Agreed. It all comes back to "usefulness" or "utility" again. As I said, concepts are only useful if they help us to think more clearly about physical reality - and "virtual reflection coefficient" has exactly the opposite effect. Also, please note that in an S-Parameter analysis, all reflection coefficients are physical, not virtual. Since I may have used the term first here, let me explain what I meant by it. a1, b1, a2, and b2 are the S-Parameter normalized voltages. Below, a1=10, b1=0, b2=14.14, and a2=10. s11 is the physical reflection coefficient encountered by forward wave a1. s11 is (291.4-50)/(291.4+50) = 0.707. In an S-Parameter, the reflection coefficient is NOT the ratio of b1/a1. a1-- b2-- --b1 --a2 100w---50 ohm line---+---1/2WL 291.4 ohm line---50 ohm load Vfor1=100V-- Vfor2=241.4V-- --Vref1=0V --Vref2=170.7V Given the actual voltages, someone might say the reflection coefficient is Vref1/Vfor1 = 0. That is a virtual reflection coefficient. The physical reflection coefficient at point '+' remains at 0.707. Vfor1 sees a virtual impedance of 50 ohms at point '+' during steady-state because of the wave cancellation that results in a net Vref1=0. But the physical reflection coefficient doesn't change from power-up through steady-state. One has to be careful to specify whether the physical rho, (Z02-Z01)/(Z02+Z01), is being used or whether the virtual rho, Vref1/Vfor1, is being used. One advantage of an S- Parameter analysis is that virtual reflection coefficients are not used and all reflection coefficients are physical. -- 73, Cecil http://www.w5dxp.com |
#6
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Analyzing Stub Matching with Reflection Coefficients
On Apr 13, 11:49 pm, Ian White GM3SEK wrote:
Roy Lewallen wrote: Please let me emphasize again that not I or anyone else who has posted is disputing the validity of your matching methods or the utility of the "virtual short" concept. The only disagreement is in the contention that the "virtual short" actually *effects* reflections rather than being solely a consequence of them. The key word there is "utility" - the virtual short/open concept is *useful* as a short-cut in our thinking. But concepts are only useful if they help us to think more clearly about physical reality; and short-cuts are dangerous if they don't reliably bring us back onto the main track. .... Indeed. I was thinking about this in terms of short-cuts before reading Ian's post. What if you take a short-cut and it just takes you off into the woods? I'm not sure my posting about this made it into the thread in an intelligible way. (I fear Google may have sent it off on a "short-cut.") The gist of it was that, although there are examples where considering points an even number of half-waves from a short as being shorts themselves work fine, there are plenty of counter examples too. I fear that people new to the use of stubs will be lulled into a false sense of security using that concept, when indeed it fails miserably at times. Especially in this age of computers and readily available programs to deal with lines, INCLUDING their loss, why would I use a concept that may take me on a short-cut that turns out to be the long way around? What IS useful to me about the concept is NOT the calculation of the performance of a particular network of stubs, but rather in coming up with the trial design to test with full calculations. My example was the use of two stubs to give me a null on one frequency and pass another frequency; I can get a null by putting a "virtual short" at that frequency, and that's a line that's a half wave long on that frequency, shorted at the other end. But on a slightly lower frequency, it looks capacitive, so I can put another stub that's inductive in parallel with it to create an open circuit at the frequency I want to let pass. THEN I pull out the calculations with line attenuation included, and discover that in some situations it works fine, and in others, the performance is terrible. It's a useful visualization tool and design aid; it's a poor analysis tool at best. At worst, it will lull you into building something that just won't work, wasting time and resources. Cheers, Tom |
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Analyzing Stub Matching with Reflection Coefficients
K7ITM wrote:
. . . It's a useful visualization tool and design aid; it's a poor analysis tool at best. At worst, it will lull you into building something that just won't work, wasting time and resources. In my opinion, the potential harm can be much worse. If it causes you to buy into the notion that traveling waves interact in a linear medium, that opens the door to a whole universe of invalid conclusions. We've seen some of those promoted very vigorously in this newsgroup. Roy Lewallen, W7EL |
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Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen wrote:
K7ITM wrote: . . . It's a useful visualization tool and design aid; it's a poor analysis tool at best. At worst, it will lull you into building something that just won't work, wasting time and resources. In my opinion, the potential harm can be much worse. If it causes you to buy into the notion that traveling waves interact in a linear medium, that opens the door to a whole universe of invalid conclusions. Here is how Hecht described interference in "Optics": "... interference corresponds to the *interaction* of two or more lightwaves yielding a resultant irradiance that deviates from the sum of the component irradiances." If traveling waves cannot interact in a linear medium, why does Hecht say they do indeed interact? To deny the body of laws of physics regarding EM waves from the field of optics is an example of extreme ignorance. -- 73, Cecil http://www.w5dxp.com |
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Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen wrote:
If it causes you to buy into the notion that traveling waves interact in a linear medium, that opens the door to a whole universe of invalid conclusions. Roy, seems you are the one with the invalid conclusions. Here is a java-script of "traveling wave interaction in a linear medium". http://micro.magnet.fsu.edu/primer/j...ons/index.html "... when two waves of equal amplitude and wavelength that are 180-degrees ... out of phase with each other meet, they are not actually annihilated, ... All of the photon energy present in these waves must somehow be recovered or redistributed in a new direction, according to the law of energy conservation ... Instead, upon meeting, the photons are redistributed to regions that permit constructive interference, so the effect should be considered as a redistribution of light waves and photon energy rather than the spontaneous construction or destruction of light." Does energy being redistributed in new directions really look like a lack of interaction to you? -- 73, Cecil http://www.w5dxp.com |
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Analyzing Stub Matching with Reflection Coefficients
On Apr 14, 6:06 pm, Roy Lewallen wrote:
K7ITM wrote: . . . It's a useful visualization tool and design aid; it's a poor analysis tool at best. At worst, it will lull you into building something that just won't work, wasting time and resources. In my opinion, the potential harm can be much worse. If it causes you to buy into the notion that traveling waves interact in a linear medium, that opens the door to a whole universe of invalid conclusions. We've seen some of those promoted very vigorously in this newsgroup. Roy Lewallen, W7EL Yes, you're right, Roy. I guess I didn't consider that because I'm not very likely to buy into it, but from the point of view of someone just learning about linear systems, it's a danger. The analogy may not be prefect, but I think it's a lot like the usefulness of the idea of a "virtual ground" at the inverting input of an op amp. But it's a virtual ground only under specific conditions: strong negative feedback is active, and the non-inverting input is at (AC, at least) ground potential. For it to be a useful concept without too many pitfalls, the person using it has to be aware that the conditions that make it a good approximation don't always hold. Similarly for a "virtual short" on a line. Again, though, it IS useful to me to think along these lines, when looking to do something useful with stubs: I want to kill frequency W, so I can put a stub across my line that's half a wave long at W, shorted at the far end. At the same time I want to pass V, and the stub I just put there to kill W has reactance X at frequency V. If I put another stub with reactance -X at freq V across the line there, it will let V through with minimum effect. Now go calculate how well it will perform with particular lines. So, to come up with a design to try, I do think about how stubs behave, in a general sense, including things like "a half-wave line shorted at the far end echos a short", but with the programs I have readily available, it's silly to rely on approximations that drop the line attenuation, when I want to know how my idea will actually work when I build it. Cheers, Tom |
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