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Analyzing Stub Matching with Reflection Coefficients
In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings
in Reflections concerning the analysis of stub matching procedures using reflection coefficients are applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in what follows I hope to persuade those who agree with Owen's position to reconsider. To assist in understanding why my use of reflection coefficients in analyzing impedance-matching circuitry, I find it useful to include the concept of virtual open- and short-circuit conditions. I realize that some of the posters on this NB deny the existence of virtual open-and short-circuits. Therefore, I hope that my presentation here will also persuade those posters to reconsider their position. While working in an antenna lab for more than 50 years I have analyzed, constructed, and measured hundreds of impedance-matching circuits comprising transmission-line circuitry using reflection coefficients as parameters. For example, in 1958 my assignment was to develop the antenna system for the World's first weather satellite, TIROS 1. The system required an antenna that would radiate efficiently on four different frequencies in two bands that were more than an octave related. It required a coupling circuit that would allow four transmitters to operate simultaneously on all four frequencies without mutual interference. After developing the antenna that also required radiating circular polarization, I then developed the coupling system, which, pardon my English, utilized several virtual open- and short-circuit conditions to accomplish the required isolation between the individual transmitters. The entire coupling system was fabricated in printed-circuit stripline transmission line (not microstrip), with no connectors except for transmitter input ports and output ports feeding the antenna. Remember, this was in 1958. Initially I had only a slotted line for impedance measurements during the development stage, but soon after the PRD-219 Reflectometer became available, invented by my bench mate, Woody Woodward. The PRD-219 measured SWR and the angle of the voltage reflection coefficient. The magnitude rho of the reflection coefficient was obtained from the SWR measurement using the equation rho = (SWR - 1)/(SWR + 1), thus the PRD actually measured the complete complex reflection coefficient. Consequently, all measurements from then on were in terms of reflection coefficient. Keep in mind that I was working with real transmission lines--not lossless lines. There were several stub-matching circuits, several occurrences of virtual open- and short-circuits, and the total loss through the coupler at both the 108 and 235 MHz bands was no greater than 0.2 dB. The input SWR at all four input ports for a run of 12 manufactured units never exceeded 1.05:1 relative to 50 ohms. Please let me now explain my understanding of virtual open- and short-circuits. These circuits are developed by interference between two sets of voltage and current waves having reflection coefficients of equal magnitude and phase differences of 180°, respectively. Consider these two examples of a virtual short circuit: 1: The input impedance of a lossless half-wave (180°) transmission line terminated in a physical short circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short terminating the line. The reflected current wave on return to the input encountered no phase change during its travel, thus the current reflection coefficient is in phase with that of the source current, allowing the short circuit to occur. 2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open circuit terminating the line. The current reflection coefficient occurs in the same manner as with the half-wave line above. These two examples can be confirmed by referring to any reputable text concerning transmission line theory. The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both physical and virtual short or open circuits placed on a transmission line can cause reflections. Proof is in measurements performed at various points in the antenna coupler developed for the TIROS spacecraft in 1958. Now let's examine a specific example of impedance matching with a stub using reflection coefficients, with more details than I used in the previously-mentioned thread. As I said earlier, I have measured hundreds of stub-matching circuitry, but for this discussion, yesterday I set up an experimental stub-matching circuit for the purpose of being able to report directly on the results of current measurements taken on the circuit. The source is an HP-8640A signal generator, an HP-5328A counter to determine the operating frequency, and the combination of an HP-8405 Vector Voltmeter and an HP-778D dual directional coupler to form a precision RF network analyzer. Because using a 3:1 mismatch the resulting numbers are convenient, I paralleled three precision 50-ohm resistors to form a resistance of 16.667 ohms, resulting in a 3:1 mismatch on the line to be stubbed. On a line with a 3:1 mismatch the correct positioning of a parallel matching stub is 30° toward the source from a position of minimum SWR, where the normalized admittance y = 1.0 + 1.1547. Thus, I selected a short piece of RG-53 coax that measured exactly 30° in length at 16.0 MHz, meaning the stub will be placed 30° rearward of the load. All measurements obtained during the experiment were less than 2 percent in error compared to a perfect text-book setup. Consequently, rather than bore you with the exact measured values, I'm going to use the text-book values for easier understanding. At the 16.667 + j0 load the measured voltage reflection coefficient = 0.5 at 180°, current 0.5 at 0°. At the stub point voltage reflection coefficient of the line impedance = 0.5 at +120°, current 0.5 at -60°. Open-circuited stub 49° in length measured separately in parallel with 50 ohms yields voltage reflection coefficient 0.5 at -120°, current 0.5 at +60°. (Keep in mind that in operation the stub is in parallel with the 50-ohm line resistance at the stub point.) With stub connected in parallel with the line the voltage reflection coefficient at the stub point is 0.04 at 0°, current 0.04 at 180°. (Equivalent SWR = 1.083, and impedance = 54.16 + j0 ohms.) Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° Stub coefficients: voltage 0.5 at -120°, current +60° Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° These two resultant reflection coefficients resulting from the interference between the load-reflected wave at the stub point and the reflected wave produced by the stub define a virtual short circuit established at the stub point. Let's now consider what occurs when a wave encounters a short circuit. We know that the voltage wave encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with source current wave. Consequently, the reflected waves add in phase with the source waves, thus increasing the forward power in the line section between the stub and the load. So how do we know that the virtual short circuit resulting from the interference is really performing as a short circuit? First, an insignificant portion of the reflected wave appears on the source side of the stub point, thus, from a practical viewpoint, indicating total re-reflection of the reflected waves at the stub point. Second, the voltage in the line section between the stub and load that has a 3:1 SWR has increased relative to that on the source line by the factor 1.1547, the amount expected on a line having a 3:1 SWR after total re-reflection at an open or short circuit. This increase factor is determined from the equation for the increase in forward power on a line with a specific value of SWR, where rho is the corresponding value of reflection coefficient. The power increase factor equation is power increase = 1/(1 - rho^2). Thus the voltage increase factor is the square root of the power increase factor. With rho = 0.5, as in the case of the above experiment, the power increase factor is 1.3333..., the square root of which is 1.1547. We have thus proved that the virtual short circuit established at the stub point is actually performing as a real short circuit. I believe it is remarkable that the maximum deviation of the measured values obtained during the experiment is less than 2 percent of the text-book values that would appear with lossless elements, and ignoring measurement errors and tolerances of the measuring equipment. The recognized sources of error a 1. Tolerance in readings from the Vector Voltmeter 2. Ripple in the coupling factor in the directional coupler 3. Attenuation in the coax 4. The fact that the nomional Zo of the RG-53 coax is 53.5 ohms, not 50, as used as the reference in the measurements. My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted to lossless or distortionless transmission lines. Walt, W2DU |
Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote: Hi Walt, 1: The input impedance of a lossless half-wave (180°) transmission line There are two parts to the following statement: terminated in a physical short circuit is zero ohms, a short circuit, which is the causal relationship; but a VIRTUAL short circuit because it was achieved only by the interference between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short terminating the line. this is the correlationship. Without the cause, there is no correlation. There is nothing to be disputed beyond that. The reflected current wave on return to the input encountered no phase change during its travel, thus the current reflection coefficient is in phase with that of the source current, allowing the short circuit to occur. Allowing, as a verb, suggests causality. The cause is established in the short. All intermediary apparatus merely maintain the correlation. There is nothing to be disputed beyond that. 2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open circuit which is the causal relationship; is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open circuit terminating the line. this is the correlationship. The current reflection coefficient occurs in the same manner as with the half-wave line above. It is merely the correlation to an existing, physical open without which the VIRTUAL short circuit would disappear. All intermediary apparatus merely maintain the correlation. There is nothing to be disputed beyond that. These two examples can be confirmed by referring to any reputable text concerning transmission line theory. There is nothing to be disputed beyond that. The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both physical and virtual short or open circuits placed on a transmission line can cause reflections. And here we get to the nut of the matter - causality. It is already established that either the physical short, or physical open, whose absence would render any correlation invalid, dominates the action. The proof follows the quality of the physical open or the physical short. A poor physical open or poor physical short will never be improved by ANY transmission line mechanics. On the other hand, poor transmission line mechanics will never deliver the action of the best physical short or the best physical open. We have thus proved that the virtual short circuit established at the stub point is actually performing as a real short circuit. There is nothing to be disputed beyond that. This is not, however, a proof that the VIRTUAL short (or open) is the cause. This may appear to be a criticism of semantics (English to some). However, engineering relies on a far stricter degree of meaning than most endeavors. Correlation is not Causality is one particular admonition that comes to mind from the field of logic. It applies here too. Walt, it seems to me that you have a need to distinguish VIRTUAL from physical for reasons other than the transmission line mechanics of combining loads (or as I distinguished in other threads, routing energies). A VIRTUAL short or open is metaphor, and it is an useful metaphor for describing systems. What I see beyond these examples you have provided are statements (in other discussions) that tend to confer a reality to the VIRTUAL which is obviously a contradiction on the face of it. Other than that, there is absolutely nothing in your published work that is in dispute. 73's Richard Clark, KB7QHC |
Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell
wrote: My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted to lossless or distortionless transmission lines. Hi Walt, You have tackled a job that some would shrug off as being impossible to accomplish. You have performed an admirable job of bench work demonstrating the lessons of the best text books. Few here go to those lengths, or with such precision and accuracy. Your tight writing also reveals a mind that still sees the "big picture" and can describe it with sufficient detail for those who would otherwise dismiss the topic as being too vast and complex to comprehend. 73's Richard Clark, KB7QHC |
Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 12:08:10 -0700, Richard Clark wrote:
On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell wrote: My final comment is that I hope I have assisted in appreciating the practical use of virtual open and short circuits, and that matching procedures can be analyzed using reflection coefficients that are not restricted to lossless or distortionless transmission lines. Hi Walt, You have tackled a job that some would shrug off as being impossible to accomplish. You have performed an admirable job of bench work demonstrating the lessons of the best text books. Few here go to those lengths, or with such precision and accuracy. Your tight writing also reveals a mind that still sees the "big picture" and can describe it with sufficient detail for those who would otherwise dismiss the topic as being too vast and complex to comprehend. 73's Richard Clark, KB7QHC Richard, thank you for your comments and kind words. Coming from you it's hard to express my true appreciation for what you've said. Sincerely, Walt |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote in
: In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings in Reflections concerning the analysis of stub matching procedures using reflection coefficients are applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in what follows I hope to persuade those who agree with Owen's position to reconsider. Hi Walt, I did not say that, or in my view, imply that, it is your own interpretation of what I did say. I did make comment limited to Chapter 3 of Reflections II, and I stand by that comment. Chapter 3 does not discuss stub matching at all, though you may apply principles that you develop in Chapter 3 to your discussion / analysis in later chapters, including to stub matching. Owen |
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 |
Analyzing Stub Matching with Reflection Coefficients
Richard Clark wrote:
On Fri, 13 Apr 2007 16:37:02 GMT, Walter Maxwell wrote: The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both physical and virtual short or open circuits placed on a transmission line can cause reflections. And here we get to the nut of the matter - causality. It is already established that either the physical short, or physical open, whose absence would render any correlation invalid, dominates the action. The proof follows the quality of the physical open or the physical short. A poor physical open or poor physical short will never be improved by ANY transmission line mechanics. On the other hand, poor transmission line mechanics will never deliver the action of the best physical short or the best physical open. I agree that this is the problem in Walt's otherwise brilliant work. Reflections are only caused by the direct interaction between electromagnetic waves and matter. It is nevertheless valid to say that systems behave as though virtual impedances cause reflections. Virtual reflection coefficients are a clever tool and methodology for systems analysis. But it must be remembered that the propagation of electromagnetic waves is effected only by certain physical properties of matter, as described eloquently by James C. Maxwell and others. Those fundamentals of wave behavior are not different in the steady state than at other times. A VIRTUAL short or open is metaphor, and it is an useful metaphor for describing systems. What I see beyond these examples you have provided are statements (in other discussions) that tend to confer a reality to the VIRTUAL which is obviously a contradiction on the face of it. Other than that, there is absolutely nothing in your published work that is in dispute. I completely agree. I think if we got past this one issue, the newsgroup might actually find itself devoted more to discussions of antennas. 73, Jim AC6XG |
Analyzing Stub Matching with Reflection Coefficients
On Apr 13, 9:37 am, Walter Maxwell wrote:
In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings in Reflections concerning the analysis of stub matching procedures using reflection coefficients are applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in what follows I hope to persuade those who agree with Owen's position to reconsider. To assist in understanding why my use of reflection coefficients in analyzing impedance-matching circuitry, I find it useful to include the concept of virtual open- and short-circuit conditions. I realize that some of the posters on this NB deny the existence of virtual open-and short-circuits. Therefore, I hope that my presentation here will also persuade those posters to reconsider their position. While working in an antenna lab for more than 50 years I have analyzed, constructed, and measured hundreds of impedance-matching circuits comprising transmission-line circuitry using reflection coefficients as parameters. For example, in 1958 my assignment was to develop the antenna system for the World's first weather satellite, TIROS 1. The system required an antenna that would radiate efficiently on four different frequencies in two bands that were more than an octave related. It required a coupling circuit that would allow four transmitters to operate simultaneously on all four frequencies without mutual interference. After developing the antenna that also required radiating circular polarization, I then developed the coupling system, which, pardon my English, utilized several virtual open- and short-circuit conditions to accomplish the required isolation between the individual transmitters. The entire coupling system was fabricated in printed-circuit stripline transmission line (not microstrip), with no connectors except for transmitter input ports and output ports feeding the antenna. Remember, this was in 1958. Initially I had only a slotted line for impedance measurements during the development stage, but soon after the PRD-219 Reflectometer became available, invented by my bench mate, Woody Woodward. The PRD-219 measured SWR and the angle of the voltage reflection coefficient. The magnitude rho of the reflection coefficient was obtained from the SWR measurement using the equation rho = (SWR - 1)/(SWR + 1), thus the PRD actually measured the complete complex reflection coefficient. Consequently, all measurements from then on were in terms of reflection coefficient. Keep in mind that I was working with real transmission lines--not lossless lines. There were several stub-matching circuits, several occurrences of virtual open- and short-circuits, and the total loss through the coupler at both the 108 and 235 MHz bands was no greater than 0.2 dB. The input SWR at all four input ports for a run of 12 manufactured units never exceeded 1.05:1 relative to 50 ohms. Please let me now explain my understanding of virtual open- and short-circuits. These circuits are developed by interference between two sets of voltage and current waves having reflection coefficients of equal magnitude and phase differences of 180°, respectively. Consider these two examples of a virtual short circuit: 1: The input impedance of a lossless half-wave (180°) transmission line terminated in a physical short circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference between the source voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 360° of two-way travel on the line and the 180° phase reversal at the physical short terminating the line. The reflected current wave on return to the input encountered no phase change during its travel, thus the current reflection coefficient is in phase with that of the source current, allowing the short circuit to occur. 2: The input impedance of a lossless quarter-wave (90°) transmission line terminated in a physical open circuit is zero ohms, a short circuit, but a VIRTUAL short circuit because it was achieved only by the interference between the voltage wave incident on the input (0°) and the reflected voltage wave (180°) returning to the input after 180° of two-way travel on the line and the 0° phase reversal at the physical open circuit terminating the line. The current reflection coefficient occurs in the same manner as with the half-wave line above. These two examples can be confirmed by referring to any reputable text concerning transmission line theory. The voltage reflection coefficient at the input of these two transmission lines is 1.0 at 180°, and the current reflection coefficient at this point is 1.0 at 0°. These are the reflection coefficients that would be found when measuring at any short circuit, no matter whether it is physical or virtual. Consequently, both physical and virtual short or open circuits placed on a transmission line can cause reflections. Proof is in measurements performed at various points in the antenna coupler developed for the TIROS spacecraft in 1958. Now let's examine a specific example of impedance matching with a stub using reflection coefficients, with more details than I used in the previously-mentioned thread. As I said earlier, I have measured hundreds of stub-matching circuitry, but for this discussion, yesterday I set up an experimental stub-matching circuit for the purpose of being able to report directly on the results of current measurements taken on the circuit. The source is an HP-8640A signal generator, an HP-5328A counter to determine the operating frequency, and the combination of an HP-8405 Vector Voltmeter and an HP-778D dual directional coupler to form a precision RF network analyzer. Because using a 3:1 mismatch the resulting numbers are convenient, I paralleled three precision 50-ohm resistors to form a resistance of 16.667 ohms, resulting in a 3:1 mismatch on the line to be stubbed. On a line with a 3:1 mismatch the correct positioning of a parallel matching stub is 30° toward the source from a position of minimum SWR, where the normalized admittance y = 1.0 + 1.1547. Thus, I selected a short piece of RG-53 coax that measured exactly 30° in length at 16.0 MHz, meaning the stub will be placed 30° rearward of the load. All measurements obtained during the experiment were less than 2 percent in error compared to a perfect text-book setup. Consequently, rather than bore you with the exact measured values, I'm going to use the text-book values for easier understanding. At the 16.667 + j0 load the measured voltage reflection coefficient = 0..5 at 180°, current 0.5 at 0°. At the stub point voltage reflection coefficient of the line impedance = 0.5 at +120°, current 0.5 at -60°. Open-circuited stub 49° in length measured separately in parallel with 50 ohms yields voltage reflection coefficient 0.5 at -120°, current 0.5 at +60°. (Keep in mind that in operation the stub is in parallel with the 50-ohm line resistance at the stub point.) With stub connected in parallel with the line the voltage reflection coefficient at the stub point is 0.04 at 0°, current 0.04 at 180°. (Equivalent SWR = 1.083, and impedance = 54.16 + j0 ohms.) Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° Stub coefficients: voltage 0.5 at -120°, current +60° Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° These two resultant reflection coefficients resulting from the interference between the load-reflected wave at the stub point and the reflected wave produced by the stub define a virtual short circuit established at the stub point. Let's now consider what occurs when a wave encounters a short circuit. We know that the voltage wave encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with source current wave. Consequently, the reflected waves add in phase with the source waves, thus increasing the forward power in the line section between the stub and the load. So how do we know that the virtual short circuit resulting from the interference is really performing as a short circuit? First, an insignificant portion of the reflected wave appears on the source side of the stub point, thus, from a practical viewpoint, indicating total re-reflection of the reflected waves at the stub point. Second, the voltage in the line section between the stub and load that has a 3:1 SWR has increased relative to that on the source line by the factor 1.1547, the amount expected on a line having a 3:1 SWR after total re-reflection at an open or short circuit. This increase factor is determined from the equation for the increase in forward power on a line with a specific value of SWR, where rho is the corresponding value of reflection coefficient. The power increase factor equation is power increase = 1/(1 - rho^2). Thus the voltage increase factor is the square root of the power increase factor. With rho = 0.5, as in the case of the above experiment, the power increase factor is 1.3333..., the square root of which is 1.1547. We have thus proved that the virtual short circuit established at the stub point is actually performing as a real short circuit. I believe it is remarkable that the maximum deviation of the measured values obtained during the experiment is less than 2 percent of the text-book values that would appear with lossless elements, and ignoring measurement errors and tolerances of the measuring equipment. The recognized sources of error a 1. Tolerance in readings... read more » Grrr...thought I had posted a followup but it seems to have not shown up. I'll try to capture the essence of it here... I think the idea of a virtual short and a virtual open is fine. I use similar things all the time in my work with op amps, with AGC controlled levels, and even with ratiometric measurements. However, in all these cases, including the transmission line virtual short and open, it's important to understand that it IS only an approximation to the real thing. There are times when the approximation is fine, as in Walt's posted example. However, there are times when the approximation fails, and it's important to somehow be aware of those times. One way to do that is to simply use the tools that are available on modern computers to keep track of line loss, and then the times when the approximation isn't good become obvious. For example... I want to receive signals on 4.00MHz, but there's a very strong station on 4.30MHz. Knowing a little about transmission lines and stubs, I think, "I can build a resonator from a half wave of line shorted at both ends, and tune it to 4MHz. Then I can tap my 50 ohm through line from the antenna to the receiver onto that resonator, and it won't affect the 4.00MHz signal since it looks like an open circuit. If I position the tap point so that at 4.300MHz it's half a wave away from the short at the end of the line, it will see a 4.300MHz virtual short there, and it will eliminate the strong signal that's giving me trouble." So I figure out that the line, using solid polyethylene dielectric line, needs to be about 81 feet long, and the tap point will be 75.53 feet from one end, 5.67 feet from the other. 81 feet of line could get pretty big, so I'll use RG-174 line. I build the resonator--you can look at it as two shorted stubs--and try it out. It doesn't seem to work very well, and I measure it and discover to my horror that the attenuation at 4.3MHz is only about 12dB, and the attenuation at 4.00MHz is over 8dB. I've gained less than 4dB net on my problem. Realizing now that the problem is that the stubs I assumed were lossless really do have some loss, I try larger coax. Well, I've smartened up a bit by now and I first do some calculations and find that with RG-58 (about 0.6dB/100ft at 4MHz), I can get 18.6dB loss at 4.300MHz and only 4.8dB loss at 4.000MHz. That's better, but still not wonderful by any stretch of the imagination. With RG-8, at only about .19dB/100 feet loss at 4MHz, it improves to 28dB loss at 4.300MHz and only about 1.9dB at 4.00MHz. That wouldn't be bad, except that it's an awfully big pile of coax on the floor. At that point I go off and design a good LC filter to do the job, and find I can get less than a dB loss at 4.00MHz and fully 45dB loss at 4.300MHz, with modest size coils (smaller even than the coil of RG174, and much smaller than the RG8), and I can use a trimmer cap to fine- tune the notch to get the most benefit. (BTW--you can also use trimmer caps to tune stubs...which can save lots of cutting.) You can develop a feel for when approximations like the virtual short and the virtual open actually work, but I think you need to go through several scenarios that show the good, but also the bad and the ugly, before you jump into blindly using an approximation. Given how easy it is for me to just include the loss of line in calculations, I'm unlikely to drop that in favor of the approximation. It's practically as easy for me to put loss into my calculations as it is to leave it off, and putting it in makes it immediately obvious when the approximations fail. Cheers, Tom |
Analyzing Stub Matching with Reflection Coefficients
On Apr 13, 11:40 am, Richard Clark wrote:
[lotsa good stuff snipped] A poor physical open or poor physical short will never be improved by ANY transmission line mechanics. Well, I dunno about that. Try this experiment: Take a "poor" short, say 1 ohm, and transform it through a lossless 1/4 wavelength line of Zo=200 ohm. The result will be 40,000 ohm. Now transform this 40K ohm load through another lossless 1/4 wavelength line of Zo=10 ohm. The result of this transformation will be a "virtual" 0.003 ohm. Is that an improvement? [g] Regards, Wes |
Analyzing Stub Matching with Reflection Coefficients
On 13 Apr 2007 15:56:26 -0700, "Wes" wrote:
On Apr 13, 11:40 am, Richard Clark wrote: [lotsa good stuff snipped] A poor physical open or poor physical short will never be improved by ANY transmission line mechanics. Well, I dunno about that. Try this experiment: Take a "poor" short, say 1 ohm, and transform it through a lossless 1/4 wavelength line of Zo=200 ohm. The result will be 40,000 ohm. Now transform this 40K ohm load through another lossless 1/4 wavelength line of Zo=10 ohm. The result of this transformation will be a "virtual" 0.003 ohm. Is that an improvement? [g] Hi Wes, There is always a rational example to deflate absolutisms. Thanx for the interesting twist of transmission line. However, I wouldn't want to be the wallet that pays for this. 73's Richard Clark, KB7QHC |
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 |
Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 21:39:22 GMT, Owen Duffy wrote:
Walter Maxwell wrote in : In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings in Reflections concerning the analysis of stub matching procedures using reflection coefficients are applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in what follows I hope to persuade those who agree with Owen's position to reconsider. Hi Walt, I did not say that, or in my view, imply that, it is your own interpretation of what I did say. I did make comment limited to Chapter 3 of Reflections II, and I stand by that comment. Chapter 3 does not discuss stub matching at all, though you may apply principles that you develop in Chapter 3 to your discussion / analysis in later chapters, including to stub matching. Owen Hi Owen, I'm afraid we both got off the the wrong foot along the way. I'm sorry if I misinterpreted what you said in the post where we got off track. Quite possibly the misinterpretation arose in your referencing Chapter 3. When I saw that I assumed you had made a typo, either for 4 or 23, both of which contain the stub discussions. And I thought I had earlier referenced Chapter 4. I didn't realize you had actually reviewed Chapter 3 instead of 4. Perhaps also you missed my two responses to your post of 4-7-07 in the earlier thread, in which I accepted your apology (not needed). Anyway, the issue where I felt you were wrong is my interpretation that you believed my statements concerning use of reflection coefficients was wrong because they are applicable for use in analysis only when the transmission lines are either lossless distortionless. I hope we can resume on a new footing. Sincerely, Walt |
Analyzing Stub Matching with Reflection Coefficients
Walter, W2DU wrote:
"The magnitude rho of the reflection coefficient was obtained from SWR measurement using the equation rho = (SWR-1)/(SWR+1), thus the PRD actually measured the compleete complex reflection coefficient." Walter is on solid ground. Slotted or trough lines have been around for a long time. The formula Walter used to calculate a reflection coefficient rho is given by Terman as eqn. 4-22b on page 97 of his 1955 opus. Best regards, Richard Harrison, KB5WZI |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote in
: On Fri, 13 Apr 2007 21:39:22 GMT, Owen Duffy wrote: Walter Maxwell wrote in m: In the thread 'Constructive Interference and Radiowave Propagation', Owen, on 4-8-07 asserted that my writings in Reflections concerning the analysis of stub matching procedures using reflection coefficients are applicable only in cases where the transmission line is either lossless, or distortionless. I disagree, and in what follows I hope to persuade those who agree with Owen's position to reconsider. Hi Walt, I did not say that, or in my view, imply that, it is your own interpretation of what I did say. I did make comment limited to Chapter 3 of Reflections II, and I stand by that comment. Chapter 3 does not discuss stub matching at all, though you may apply principles that you develop in Chapter 3 to your discussion / analysis in later chapters, including to stub matching. Owen Hi Owen, I'm afraid we both got off the the wrong foot along the way. I'm sorry if I misinterpreted what you said in the post where we got off track. Quite possibly the misinterpretation arose in your referencing Chapter 3. When I saw that I assumed you had made a typo, either for 4 or 23, both of which contain the stub discussions. And I thought I had earlier referenced Chapter 4. I didn't realize you had actually reviewed Chapter 3 instead of 4. Perhaps also you missed my two responses to your post of 4-7-07 in the earlier thread, in which I accepted your apology (not needed). Anyway, the issue where I felt you were wrong is my interpretation that you believed my statements concerning use of reflection coefficients was wrong because they are applicable for use in analysis only when the transmission lines are either lossless distortionless. I hope we can resume on a new footing. Walt, the last thing I want to do is to upset you. You have a considerable investment in your publications, and they are a great service to the amateur community, and a credit to you. Much of the discussion isn't so much about what happens in the transmission line, it is about simplified explanations, explanations that are appealling to learners, and the extension of those simplified explanations to the more general case. If you look back over the threads, you and I have both intiated threads where "explanation" was a key word in the subject line. My own view is that whilst analysing a simple case that can be seen as special cases is a good way of introducing the issue that is to be dealt with (eg showing the inconsistency of the Vf/If=Zo constraint in the initial wave that travels along a transmission line, and the V/I ratio a s/c or o/c load), one needs to move on to dealing with the more general load case, even if in a simplified context (eg lossless line). The "rules" that are derived have to be clearly qualified with the applicable limits. To overemphasis the simple / easy cases and downplay the error of approximation is at risk of consigning all problem solving to simplification to a trivial case and applying the solution of that trivial case to the real problem without appreciation of the leap that might entail. Whilst it is no doubt appealing to some to see a virtual s/c or virtual o/c as an explanation for the single stub tuner example, and it might be a suitable model for that purpose, it gives the learner a new analysis tool (without limitations), the virtual s/c or o/c. How perfect does a virtual s/c need to be to be approximately effective? If I have an approximately lossless feedline with a VSWR of 100:1, will the virtual s/c at a current maximum prevent energy propagating in the same way as the virtual s/c in the stub explanation, or could each virtual circuit choke of x% of the energy flow? Can you solve a two stub tuner using only virtual s/c or o/c? It is a challenge to devise simplified explanations that don't contain errors that need to be un-learned to develop further. I hate to say to a learner "throw away what you already know about this, because the explanation you have learned, understood, and trusted is wrong in part, and we need to discard it before we move on to a better understanding... trust me...". Owen |
Analyzing Stub Matching with Reflection Coefficients
Richard Clark, KB7QHC wrote:
"A poor physical open or physical short will never be improved by ANY transmission line mechanics." An open-circuit 1/4-wave stub is an open circuit at both ends, physically. As such, its input is a poor short-circuit until it receives a reflection from its far end. After the reflection reaches the stub`s input, it becomes a virtual short-circuit. This occurs at its "poor physical short" input. This is a dramatic improvement by transmission line mechanics when this is the desired effect. Best regards, Richard Harrison, KB5WZI |
Analyzing Stub Matching with Reflection Coefficients
Richard Harrison wrote:
An open-circuit 1/4-wave stub is an open circuit at both ends, physically. Let's look at a 1/4WL open stub. source ----------------------------------+ | | 1/4WL | | open The transmission line and stub are the same Z0 and both are lossless. The virtual impedance at point '+' is zero but there is no physical impedance discontinuity at point '+'. Are there any reflections originating at point '+'? If we straighten out the line, 1/4WL source-----------------------------------+------------open Are there any reflections originating at point '+'? -- 73, Cecil http://www.w5dxp.com |
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 |
Analyzing Stub Matching with Reflection Coefficients
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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 |
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 |
Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen, W7EL wrote:
"Those traveling waves, and hence their sum, cannot cause a reflection of other waves, or alter those waves in any way." Let`s reason together on the situation in a quarter-wavelength short-circuited transmission line stub. I maintain it has a hard short on its far end and a high impedance on its near end. A high impedance means just what it says. You can put a high voltage on it and the resulting current is small. Reflection from a short-circuit results in a 180-degree voltage phase reversal at the short. A round-trip on a 1/4-wave stub produces an additional 180-degree phase reversal. This means thats volts returning to the open-circuit end of the stub are about of the same phase and magnitude as when they started out. Nearly identical voltages appear at the same pair of terminals from opposite directions. Significant current flows in either direction? I think it does not. Where voltage causes insignificant current flow, we have a high impedance. That is why King, Mimno, and Wing on page 30 of Transmission Lines, Antennas and Wave Guides say: "Since the input impedance of a short-circuited quarter-wavelength section of transmission line is a very high resistance, short-circuited stubs may be used to support the line." Best regards, Richard Harrison, KB5WZI |
Analyzing Stub Matching with Reflection Coefficients
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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 |
Analyzing Stub Matching with Reflection Coefficients
I'm not sure I understand the point you're trying to make. Nothing I've
said disputes in any way that the input impedance of a shorted quarter wave stub is high. I'm quite able to make transmission line calculations and arrive at correct results. You're certainly correct that there's very little net current at the open end of the stub. Yet there are waves traveling in both directions right through that point. Don't believe it? Then check the current anywhere else along the stub. How did it get there without going through the "open" at the input end? Roy Lewallen, W7EL Richard Harrison wrote: Roy Lewallen, W7EL wrote: "Those traveling waves, and hence their sum, cannot cause a reflection of other waves, or alter those waves in any way." Let`s reason together on the situation in a quarter-wavelength short-circuited transmission line stub. I maintain it has a hard short on its far end and a high impedance on its near end. A high impedance means just what it says. You can put a high voltage on it and the resulting current is small. Reflection from a short-circuit results in a 180-degree voltage phase reversal at the short. A round-trip on a 1/4-wave stub produces an additional 180-degree phase reversal. This means thats volts returning to the open-circuit end of the stub are about of the same phase and magnitude as when they started out. Nearly identical voltages appear at the same pair of terminals from opposite directions. Significant current flows in either direction? I think it does not. Where voltage causes insignificant current flow, we have a high impedance. That is why King, Mimno, and Wing on page 30 of Transmission Lines, Antennas and Wave Guides say: "Since the input impedance of a short-circuited quarter-wavelength section of transmission line is a very high resistance, short-circuited stubs may be used to support the line." Best regards, Richard Harrison, KB5WZI |
Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen wrote in
: anywhere else along the stub. How did it get there without going through the "open" at the input end? Ah, a total re-reflector! Owen |
Analyzing Stub Matching with Reflection Coefficients
Richard Clark wrote:
"This conforms to my experience with many plumbing designs on the microwave bench." Good. Then, Richard Clark must also be familiar with the grooved circular flange used in conjunction with a smooth flange to join waveguide segments. This groove isn`t just used to hold a neoprene gasket. It is also used as an electrical choke to keep the microwaves within the pipe. It is approximately a 1/4-wave choke and its high impedance across its open-circuit helps foil the wave escape. If virtual open-circuits didn`t work, the "choke-flange wouldn`t work either. Best regards, Richard Harrison, KB5WZI |
Analyzing Stub Matching with Reflection Coefficients
On Fri, 13 Apr 2007 19:10:18 -0700, Roy Lewallen wrote:
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. snip 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. snip 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 Hi R oy, Consider my two explanations, or definitions of what I consider a virtual short--perhaps it should have a different name, because of course 'virtual' implies non-existence. The short circuit evident at the input of the two line examples I presented---do you agree that short circuits appear at the input of the two lines? If so, what would you call them? Roy, I'd like for you to take another, but perhaps closer look at the summarizing of the reflection coefficients below. I originally typed in the wrong value for the magnitude of the resultant coefficients. With the corrected magnitudes in place, the two paragraphs following the summarization now make more sense, because the short circuit established at the stub point leads correctly to the wave action that occurs there. Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1 + j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y = 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current 1.0 at 0° CORRECT Repeating from my original post for emphasis: These two resultant reflection coefficients resulting from the interference between the load-reflected wave at the stub point and the reflected wave produced by the stub define a virtual short circuit established at the stub point. The following paragraph shows how the phases of the reflected waves become in phase with the source waves so that the reflected waves add directly to the source waves, establishing the forward power, which we know exceed the source power when the reflected power is re-reflected. The same concept applies to antena tuners. Again repeating for emphasis: Let's now consider what occurs when a wave encounters a short circuit. We know that the voltage wave encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with source current wave. Consequently, the reflected waves add in phase with the source waves, thus increasing the forward power in the line section between the stub and the load. Keep in mind that the short at the stub point is a one-way short, diode like, as you say, because in the forward direction the voltage reflection coefficient rho is 0.0 at 0°, while in the reverse direction, rho at the stub point is 1.0 at 180°, which is why it's a one-way short. You say that no total re-reflection occurs at the stub point. However, with a perfect match the power rearward of the stub is zero, and all the source power goes to the load in the forward direction. Is that not total reflection? Using the numbers of my bench experiment, assuming a source power of 1 watt, and with the magnitude rho of 0.04, power going rearward of the stub is 0.0016 w, while the power absorbed by the load is 0.9984 w, the sum of which is 1 w. The SWR seen by the source is 1.083:1, and the return loss in this experiment is 27.96 dB, while the power lost to the load is 0.0070 dB. From a ham's practical viewpoint the reflected power is totally re-reflected. In my example using the 49° stub the capacitive reactance it established at its input is Xc = -57.52 ohms. Thus its inductive susceptance B = 0.0174 mhos, which cancels the capacitive line susceptance B = -0.0174 mhos appearing at the stub point. My point is that the 49° stub can be replaced with a lumped capacitance Xc = -57.52 ohms directly on the line with the same results as with the stub--with the same reflection coefficients. In this case one cannot say that the re-reflection results from the physical open circuit terminating the stub line. Various posters have termed my approach as a 'short cut'. I disagree. I prefer to consider it as the wave analysis to the stub-matching procedure, in contrast to the traditional method of simply saying that the stub reactance cancels the line reactance at the point on the line where the line resistance R = Zo. In my mind the wave analysis presents a more detailed view of what's actually happening to the pertinent waves while the impedance match is being established. Walt |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote in
: Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1 + j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y = 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current 1.0 at 0° CORRECT Walt, Though admittance or impedance at a point on the mismatched line are calculated from the underlying Zo and the reflection coefficient corrected for line loss, they are easier to work in than the raw reflection coefficient. It is easier to explain why the stub is located at a position where Yn'=1 +jB than where Gamma=0.5120 (assuming lossless line). It is relatively obvious that where Yn'=1+jB, a shunt reactance of -jB from a s/c or o/c stub will leave Yn=1 which is the matched condition. Re your worked solution (above), I agree that the normalised admittance looking into 30deg of line with load 16.667+j0 is about 1-j1.1547 (not the different sign). I make the normalised admittance looking into the stub about 0+j1.15 (and the reflection coefficient about 0.5-98, how do you get 1+j1.15? The addition of the two normalised admittances 1-j1.15 + 0+j1.15 gives 1 +j0 which is the matched condition. The design is correct, the stub results in a match at the stub connection point (irrespective of what is connected on the source side of the point), but I can't understand your maths above (allowing for the sign error that I think you have made). Is the reflection coefficient explanation a clearer explanation than using admittances? Owen BTW, my line loss calculator solutions (http://www.vk1od.net/tl/tllc.php) for Belden 8262 RG58 (you said RG53, but you probably meant RG58) a (Note some symbols arent supported by plain ascii and appear as '?'.) Load to Stub connection: Parameters Transmission Line Belden 8262 (RG-58C/U) Code B8262 Data source Belden Frequency 16.000 MHz Length 1.030 metres Zload 16.67+j0.00 ? Yload 0.059999+j0.000000 ? Results Zo 50.00-j0.54 ? Velocity Factor 0.660 Length 29.97 ?, 0.083 ? Line Loss (matched) 0.059 dB Line Loss 0.149 dB Efficiency 96.63% Zin 22.12+j24.55 ? Yin 0.020258-j0.022480 ? Gamma, rho, theta, VSWR (source end) -2.44e-1+j4.29e-1, 0.493, 119.6?, 2.950 Gamma, rho, theta, VSWR (load end) -5.00e-1+j4.03e-3, 0.500, 179.5?, 3.000 ? 6.54e-3+j5.08e-1 k1, k2 1.30e-5, 2.95e-10 Loss model source data lowest frequency 1.000 MHz Correlation coefficient (r) 0.999884 Stub: Parameters Transmission Line Belden 8262 (RG-58C/U) Code B8262 Data source Belden Frequency 16.000 MHz Length 1.685 metres Zload 100000000.00+j0.00 ? Yload 0.000000+j0.000000 ? Results Zo 50.00-j0.54 ? Velocity Factor 0.660 Length 49.02 ?, 0.136 ? Line Loss (matched) 0.096 dB Line Loss 40.574 dB Efficiency 0.01% Zin 0.50-j43.44 ? Yin 0.000265+j0.023019 ? Gamma, rho, theta, VSWR (source end) -1.37e-1-j9.69e-1, 0.978, - 98.0?, 90.720 Gamma, rho, theta, VSWR (load end) 1.00e+0+j1.07e-8, 1.000, 0.0?, inf ? 6.54e-3+j5.08e-1 k1, k2 1.30e-5, 2.95e-10 Loss model source data lowest frequency 1.000 MHz Correlation coefficient (r) 0.999884 |
Analyzing Stub Matching with Reflection Coefficients
Walt, before digging into your recent posting, I'd really like to get
one issue settled. I think it would be helpful in our discussion. The issue is: Can you find even one example of any transmission line problem which cannot be solved, or a complete analysis done, without making the assumption that waves reflect from a "virtual short" or "virtual open"? That is, any example where such an assumption is necessary in order to find the currents, voltages, and impedances, and the magnitude and phase of forward and reverse voltage and current waves? Roy Lewallen, W7EL |
Analyzing Stub Matching with Reflection Coefficients
On Sat, 14 Apr 2007 22:31:37 GMT, Owen Duffy wrote:
Walter Maxwell wrote in : Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1 + j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y = 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current 1.0 at 0° CORRECT Walt, Though admittance or impedance at a point on the mismatched line are calculated from the underlying Zo and the reflection coefficient corrected for line loss, they are easier to work in than the raw reflection coefficient. Depends on the instrumentation available for obtaining the raw data. It is easier to explain why the stub is located at a position where Yn'=1 +jB than where Gamma=0.5120 (assuming lossless line). It is relatively obvious that where Yn'=1+jB, a shunt reactance of -jB from a s/c or o/c stub will leave Yn=1 which is the matched condition. Re your worked solution (above), I agree that the normalised admittance looking into 30deg of line with load 16.667+j0 is about 1-j1.1547 (not the different sign). Yes Owen, you're right. I added the y values at the last moment, and didn't catch the errors. Both the line and stub signs are reversed. Sorry 'bout that. I make the normalised admittance looking into the stub about 0+j1.15 (and the reflection coefficient about 0.5-98, how do you get 1+j1.15? Normalized y looking into the stub directly is y = 0 + 1.1547, but looking at the stub while on the line at the 30° point is y = 1 + 1.1547. To view the stub separately on the line the line is terminated in 50 ohms, because the real component of the line impedance at the match point is 50 ohms. The addition of the two normalised admittances 1-j1.15 + 0+j1.15 gives 1 +j0 which is the matched condition. Of course. The design is correct, the stub results in a match at the stub connection point (irrespective of what is connected on the source side of the point), but I can't understand your maths above (allowing for the sign error that I think you have made). The resultant coefficients are obtained by simply adding the voltage coefficients and the current coefficients, as in the adding of the line and stub admittances. Is the reflection coefficient explanation a clearer explanation than using admittances? Not at all, Owen, but as I said in the original post, the instrument I acquired early in my time with the RCA antenna lab was the PRD-219 reflectometer. At that time I considered it the best instrument for measuring transmission line circuitry at VHF, and because it delivered readings in reflection coefficient I became somewhat more efficient in my thinking process using that mode. Walt Owen BTW, my line loss calculator solutions (http://www.vk1od.net/tl/tllc.php) for Belden 8262 RG58 (you said RG53, but you probably meant RG58) a (Note some symbols arent supported by plain ascii and appear as '?'.) Load to Stub connection: Parameters Transmission Line Belden 8262 (RG-58C/U) Code B8262 Data source Belden Frequency 16.000 MHz Length 1.030 metres Zload 16.67+j0.00 ? Yload 0.059999+j0.000000 ? Results Zo 50.00-j0.54 ? Velocity Factor 0.660 Length 29.97 ?, 0.083 ? Line Loss (matched) 0.059 dB Line Loss 0.149 dB Efficiency 96.63% Zin 22.12+j24.55 ? Yin 0.020258-j0.022480 ? Gamma, rho, theta, VSWR (source end) -2.44e-1+j4.29e-1, 0.493, 119.6?, 2.950 Gamma, rho, theta, VSWR (load end) -5.00e-1+j4.03e-3, 0.500, 179.5?, 3.000 ? 6.54e-3+j5.08e-1 k1, k2 1.30e-5, 2.95e-10 Loss model source data lowest frequency 1.000 MHz Correlation coefficient (r) 0.999884 Stub: Parameters Transmission Line Belden 8262 (RG-58C/U) Code B8262 Data source Belden Frequency 16.000 MHz Length 1.685 metres Zload 100000000.00+j0.00 ? Yload 0.000000+j0.000000 ? Results Zo 50.00-j0.54 ? Velocity Factor 0.660 Length 49.02 ?, 0.136 ? Line Loss (matched) 0.096 dB Line Loss 40.574 dB Efficiency 0.01% Zin 0.50-j43.44 ? Yin 0.000265+j0.023019 ? Gamma, rho, theta, VSWR (source end) -1.37e-1-j9.69e-1, 0.978, - 98.0?, 90.720 Gamma, rho, theta, VSWR (load end) 1.00e+0+j1.07e-8, 1.000, 0.0?, inf ? 6.54e-3+j5.08e-1 k1, k2 1.30e-5, 2.95e-10 Loss model source data lowest frequency 1.000 MHz Correlation coefficient (r) 0.999884 |
Analyzing Stub Matching with Reflection Coefficients
On Sat, 14 Apr 2007 16:04:55 -0700, Roy Lewallen wrote:
Walt, before digging into your recent posting, I'd really like to get one issue settled. I think it would be helpful in our discussion. The issue is: Can you find even one example of any transmission line problem which cannot be solved, or a complete analysis done, without making the assumption that waves reflect from a "virtual short" or "virtual open"? That is, any example where such an assumption is necessary in order to find the currents, voltages, and impedances, and the magnitude and phase of forward and reverse voltage and current waves? Roy Lewallen, W7EL No Roy, of course not. I am not attempting to assert that reflection coefficients should be used in such an analysis. I'm only asserting that it's another way of performing an analysis, one that I believe paints a more visible picture of the how the pertinent waves behave in the circuit. If I still haven't persuaded you that it's a viable way of analyzing the impedance matching function then I'll back off and not pursue the issue any further. Incidentally, you didn't answer my questions. Walt |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote in
: .... Re your worked solution (above), I agree that the normalised admittance looking into 30deg of line with load 16.667+j0 is about 1-j1.1547 (not the different sign). Yes Owen, you're right. I added the y values at the last moment, and didn't catch the errors. Both the line and stub signs are reversed. Sorry 'bout that. Ok. I make the normalised admittance looking into the stub about 0+j1.15 (and the reflection coefficient about 0.5-98, how do you get 1+j1.15? Normalized y looking into the stub directly is y = 0 + 1.1547, but looking at the stub while on the line at the 30° point is y = 1 + 1.1547. To view the stub separately on the line the line is terminated in 50 ohms, because the real component of the line impedance at the match point is 50 ohms. You have a junction where three current paths appear in parallel, we can add the admittances of each of those paths. We are agreed that admittance of the load+30deg line is 1-j1.15, and that of the stub is 0+j1.15, so the only place the additional 1+j0 can come from is the source+line branch. If that is the case, then your explanation of the stub (which I assume to be a steady state explanation because you are talking about frequency domain admittances), depends on the source admittance (or impedance). If the equivalent source impedance at the junction figures in the calcs, you are saying that the VSWR on the line from source to junction depends on the source impedance... I thought we got over that error. My view is that the stub in shunt with the 30deg line+load results in an equivalent impedance of approximately 50+j0 at the junction, irrespective of what is on the source side of the junction. Owen |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote:
On Sat, 14 Apr 2007 16:04:55 -0700, Roy Lewallen wrote: Walt, before digging into your recent posting, I'd really like to get one issue settled. I think it would be helpful in our discussion. The issue is: Can you find even one example of any transmission line problem which cannot be solved, or a complete analysis done, without making the assumption that waves reflect from a "virtual short" or "virtual open"? That is, any example where such an assumption is necessary in order to find the currents, voltages, and impedances, and the magnitude and phase of forward and reverse voltage and current waves? Roy Lewallen, W7EL No Roy, of course not. I am not attempting to assert that reflection coefficients should be used in such an analysis. I'm only asserting that it's another way of performing an analysis, one that I believe paints a more visible picture of the how the pertinent waves behave in the circuit. We're certainly not communicating well! I have never questioned that the use of "virtual shorts" is another way of performing an analysis, nor that it helps visualize some of the things going on. If I still haven't persuaded you that it's a viable way of analyzing the impedance matching function then I'll back off and not pursue the issue any further. Nor have I questioned that it's a viable way of analyzing the impedance matching function. If you'll read what I've written, you'll hopefully see that my only point of contention is with your claim that waves reflect from a "virtual short". They do not. And the lack of a single example of a system whose analysis requires this to happen is evidence that they do not. If you back off and not pursue the issue any further, you'll continue with your belief that "virtual shorts" cause reflections. And I'm afraid that will detract from the wealth of accurate and useful things you do say. So please continue. But don't waste time arguing that the concept of "virtual shorts" is a useful analytical tool. I've always agreed with that, and haven't seen any postings indicating anyone else doesn't. Incidentally, you didn't answer my questions. I wanted to get an answer to mine, first. Now that I have, I'll answer yours. Roy Lewallen, W7EL |
Analyzing Stub Matching with Reflection Coefficients
Walter Maxwell wrote:
Consider my two explanations, or definitions of what I consider a virtual short--perhaps it should have a different name, because of course 'virtual' implies non-existence. The short circuit evident at the input of the two line examples I presented---do you agree that short circuits appear at the input of the two lines? If so, what would you call them? I'd call them "virtual shorts". If they were short circuits, we should be able to connect a wire across the transmission line at that point with no change in transmission line operation. But we can't. While things will look the same on the generator side, they won't be the same beyond the real short. So they aren't short circuits. Roy, I'd like for you to take another, but perhaps closer look at the summarizing of the reflection coefficients below. I originally typed in the wrong value for the magnitude of the resultant coefficients. With the corrected magnitudes in place, the two paragraphs following the summarization now make more sense, because the short circuit established at the stub point leads correctly to the wave action that occurs there. Summarizing reflection coefficient values at stub point with stub in place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1 + j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y = 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current 0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current 1.0 at 0° CORRECT Repeating from my original post for emphasis: These two resultant reflection coefficients resulting from the interference between the load-reflected wave at the stub point and the reflected wave produced by the stub define a virtual short circuit established at the stub point. There's no need to repeat this. I'm well acquainted with transmission line phenomena, and understand fully what's happening. I have no disagreement with this analysis. I would draw attention to the fact that the "virtual short" is, as you say, simply the superposition (interference) of traveling waves. So there is nothing at that point except the traveling waves which pass through that point. The following paragraph shows how the phases of the reflected waves become in phase with the source waves so that the reflected waves add directly to the source waves, establishing the forward power, which we know exceed the source power when the reflected power is re-reflected. The same concept applies to antena tuners. Sorry, I'm not going to divert onto the topic of propagating power, either instantaneous or average. If that concept is required in order to show that waves interact with each other, then it simply shows that the concept is invalid. Let's stick to voltages and currents. If that's not adequate, then I'll exit at this point, and turn the discussion over to Cecil. That's his domain, not mine. Again repeating for emphasis: Let's now consider what occurs when a wave encounters a short circuit. Ok. We know that the voltage wave encounters a phase change of 180°, while the current wave encounters zero change in phase. Note that the resultant voltage is at 180°, so the voltage phase changes to 0° on reflection at the short circuit, and is now in phase with the source voltage wave. In addition, the resultant current is already at 0°, and because the current phase does not change on reflection at the short circuit, it remains at 0° and in phase with source current wave. Consequently, the reflected waves add in phase with the source waves, Ok so far. . . thus increasing the forward power in the line section between the stub and the load. Again, let's leave power out of it, ok? Keep in mind that the short at the stub point is a one-way short, diode like, as you say, because in the forward direction the voltage reflection coefficient rho is 0.0 at 0°, while in the reverse direction, rho at the stub point is 1.0 at 180°, which is why it's a one-way short. The voltages, currents, waves, and impedances impedances on the line are just the same as if there were a diode-short at that point. Which is why it's a useful analytical tool. But all there really is at that point are some interfering waves, traveling through that point unhindered. You say that no total re-reflection occurs at the stub point. However, with a perfect match the power rearward of the stub is zero, and all the source power goes to the load in the forward direction. Is that not total reflection? Not from the "virtual short" -- it only looks like it. The re-reflection is actually occurring from the end of the stub and from the load, not from the "virtual short". If, for example, you suddenly increased the source voltage, there would be no reflection as that change propagated through that "virtual short". (That is, after a delay equal to the round-trip time to the "virtual short", you'd see no change.) The apparent reflection from that point wouldn't appear until the change propagated to the end of the stub and to the load (going right through the "virtual short" unhindered), reflected from them, and arrived back at the "virtual short" point. This is one of the ways you can tell that a "virtual short" isn't a real short. Under steady state conditions, it looks just like a real one. But it isn't. Waves which seem to be reflecting from it are really reflecting from the end of the stub and from the load -- they're passing right through the "virtual short", in both directions. Using the numbers of my bench experiment, assuming a source power of 1 watt, and with the magnitude rho of 0.04, power going rearward of the stub is 0.0016 w, while the power absorbed by the load is 0.9984 w, the sum of which is 1 w. The SWR seen by the source is 1.083:1, and the return loss in this experiment is 27.96 dB, while the power lost to the load is 0.0070 dB. From a ham's practical viewpoint the reflected power is totally re-reflected. Sorry, you're going to have to do this without propagating waves of average power, or I'm outta here. In my example using the 49° stub the capacitive reactance it established at its input is Xc = -57.52 ohms. Thus its inductive susceptance B = 0.0174 mhos, which cancels the capacitive line susceptance B = -0.0174 mhos appearing at the stub point. My point is that the 49° stub can be replaced with a lumped capacitance Xc = -57.52 ohms directly on the line with the same results as with the stub--with the same reflection coefficients. That's fine, I agree. In this case one cannot say that the re-reflection results from the physical open circuit terminating the stub line. I most certainly can! And do. I don't see how your example furnishes any proof or even evidence of wave interaction. I can come to the same conclusion without any assumption of wave interaction, and you have agreed (in your response to my question about finding an example that requires interaction for analysis) that this can always be done. Various posters have termed my approach as a 'short cut'. I disagree. I prefer to consider it as the wave analysis to the stub-matching procedure, in contrast to the traditional method of simply saying that the stub reactance cancels the line reactance at the point on the line where the line resistance R = Zo. In my mind the wave analysis presents a more detailed view of what's actually happening to the pertinent waves while the impedance match is being established. I'm sorry, I disagree. It's a less detailed view, and it conceals what's really going on. Roy Lewallen, W7EL |
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 |
Analyzing Stub Matching with Reflection Coefficients
|
Analyzing Stub Matching with Reflection Coefficients
Roy Lewallen wrote:
I don't see how your example furnishes any proof or even evidence of wave interaction. Are you saying that wave interaction doesn't exist? -- 73, Cecil http://www.w5dxp.com |
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 |
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 |
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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