Home |
Search |
Today's Posts |
|
#1
|
|||
|
|||
Derivation of Reflection Coefficient vs SWR
On Sat, 26 Jan 2008 19:24:22 -0800 (PST)
Keith Dysart wrote: On Jan 26, 12:15*pm, Roger Sparks wrote: On Fri, 25 Jan 2008 19:13:31 -0800 (PST) Keith Dysart wrote: On Jan 24, 10:33*pm, Roger Sparks wrote: [snip] By examining this derivation, the reader can see that power and energy is reflected when a wave encounters a discontinuity. *The reader can also see that more power is present on the transmission line than is delivered to the load. This is the conventional phraseology for describing the behaviour at the impedance discontinuity. Allow me to offer a specific example for which this phraseology is inappropriate. Consider a 50 V step function generator with an output impedance of 50 ohms driving a 50 ohm line that is 1 second long terminated in an open circuit. Turn on the generator. A 50 V step propagates down the line. The generator is putting 50 J/s into the line. One second later it reaches the open end and begins propagating backwards. After two seconds it reaches the generator. The voltage at the generator is now 100 V and no current is flowing from the generator into the line. In the 2 seconds, the generator put 100 joules into the line which is now stored in the line. The line is at a constant 100 V and the current is zero everywhere. Computing Pf and Pr will yield 50 W forward and 50 W reflected. And yet no current is flowing anywhere. The voltage on the line is completely static. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. Does this seem like a reasonable claim for an open circuited transmission line with constant voltage along its length and no current anywhere? I do not find it so. ...Keith This is a reasonable observation for a static situation where energy is stored on a transmission line. * If the example contained an ongoing consideration, like "Where does the power move to?", then it would be reasonable to consider that the wave continued to move, simply to avoid the complication of what EXACTLY happens when a wave starts and stops. So have you thought about "where does the power go?" Yes, only the model I use substitutes a battery for the signal generator that you are using. The returning wave can recharge the battery, but how does the current stop? Or does it ever stop? From a practical aspect, the current must stop, but I can not explain how except by resistance that absorbs the circulating power. We must keep the limitations of our models in mind. When the generator is matched to the line so that the reflected wave does not encounter an impedance discontinuity when it arrives back at the generator (and therefore is not reflected), where does the reflected power go? Does it enter the generator? Is it dissipated somewhere? Answers to these questions will quickly lead to doubts about the *reality* of "reflected power". ...Keith The reflected wave that does not encounter an impedance at the generator must be on an infinitely long line, and therefore the conditions must have changed between the time of launch and return. It makes more sense to think that the reflected voltage of (using your example) 50v meets 50v of forward voltage, and therefore finds an infinite resistance, coming to a stop. If that happens, doesn't the same condition occur as soon as the reflected wave is first generated at the line end? The current really stops as soon as the end is reached, with the energy contained in the magnetic field converted to electric field energy visible as voltage. If this happened, the reflected wave could be better described as an electric "jump", similar to a hydraulic jump found in open channel flow of liquids, where kinetic energy is converted to potential energy. This idea of an electric "jump" requires not a reflection occuring without a discontinuity, but a moving wave front that absorbs the traveling wave, bringing it to a stop (in this case). -- 73, Roger, W7WKB |
#2
|
|||
|
|||
Derivation of Reflection Coefficient vs SWR
On Jan 27, 10:57 am, Roger Sparks wrote:
On Sat, 26 Jan 2008 19:24:22 -0800 (PST) Keith Dysart wrote: On Jan 26, 12:15 pm, Roger Sparks wrote: On Fri, 25 Jan 2008 19:13:31 -0800 (PST) Keith Dysart wrote: On Jan 24, 10:33 pm, Roger Sparks wrote: [snip] By examining this derivation, the reader can see that power and energy is reflected when a wave encounters a discontinuity. The reader can also see that more power is present on the transmission line than is delivered to the load. This is the conventional phraseology for describing the behaviour at the impedance discontinuity. Allow me to offer a specific example for which this phraseology is inappropriate. Consider a 50 V step function generator with an output impedance of 50 ohms driving a 50 ohm line that is 1 second long terminated in an open circuit. Turn on the generator. A 50 V step propagates down the line. The generator is putting 50 J/s into the line. One second later it reaches the open end and begins propagating backwards. After two seconds it reaches the generator. The voltage at the generator is now 100 V and no current is flowing from the generator into the line. In the 2 seconds, the generator put 100 joules into the line which is now stored in the line. The line is at a constant 100 V and the current is zero everywhere. Computing Pf and Pr will yield 50 W forward and 50 W reflected. And yet no current is flowing anywhere. The voltage on the line is completely static. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. Does this seem like a reasonable claim for an open circuited transmission line with constant voltage along its length and no current anywhere? I do not find it so. ...Keith This is a reasonable observation for a static situation where energy is stored on a transmission line. If the example contained an ongoing consideration, like "Where does the power move to?", then it would be reasonable to consider that the wave continued to move, simply to avoid the complication of what EXACTLY happens when a wave starts and stops. So have you thought about "where does the power go?" Yes, only the model I use substitutes a battery for the signal generator that you are using. A battery is not the same since it has a very low output impedance. A battery in series with a 50 ohm resistor would offer a reasonable match to a 50 ohm transmission line. The returning wave can recharge the battery, but how does the current stop? Or does it ever stop? From a practical aspect, the current must stop, but I can not explain how except by resistance that absorbs the circulating power. That is the challenging part to understand when too much emphasis is placed on the existance of energy being transported with the "reflected power". When I was learning this stuff, I did many examples with matched generators (a battery with a 50 ohm resistor is a good example). With step functions, it is easy to compute the final state because you can just treat it as a DC circuit for analysis. We must keep the limitations of our models in mind. True, but over limiting is not good either. When the generator is matched to the line so that the reflected wave does not encounter an impedance discontinuity when it arrives back at the generator (and therefore is not reflected), where does the reflected power go? Does it enter the generator? Is it dissipated somewhere? Answers to these questions will quickly lead to doubts about the *reality* of "reflected power". ...Keith The reflected wave that does not encounter an impedance at the generator must be on an infinitely long line, and therefore the conditions must have changed between the time of launch and return. I don't follow the association between generator impedance and length of line. For a 50 ohm line, a matched generator has a 50 ohm output impedance. The returning wave does not encounter an impedance discontinuity so is not reflected. It disappears into the the generator. It makes more sense to think that the reflected voltage of (using your example) 50v meets 50v of forward voltage, and therefore finds an infinite resistance, coming to a stop. The current does stop (since it can not flow into the infinite resistance at the end of the line), and a 50 V step propagates back along the line. This 50 V reverse propagating step plus the 50 V already on the line produces a total of 100 V on the line. If the generator was constructed as a 100 V battery in series with a 50 ohm resistor, then when the step arrives back at the generator, there is 100 V on both sides of the source resistor (battery on one side, line on the other) and the current through the source resistor becomes zero. No further current flows into the line. If that happens, doesn't the same condition occur as soon as the reflected wave is first generated at the line end? The current really stops as soon as the end is reached, with the energy contained in the magnetic field converted to electric field energy visible as voltage. If this happened, the reflected wave could be better described as an electric "jump", similar to a hydraulic jump found in open channel flow of liquids, where kinetic energy is converted to potential energy. There do seem to be some similarities, though there is likely trouble if the analogy is carried to far. This idea of an electric "jump" requires not a reflection occuring without a discontinuity, but a moving wave front that absorbs the traveling wave, bringing it to a stop (in this case). The current has stoppped, but has the "wave"? Vf, Vr, If, Ir, Pf, Pr are still computable using the normal formulae. ....Keith |
#3
|
|||
|
|||
Derivation of Reflection Coefficient vs SWR
On Sat, 2 Feb 2008 13:01:22 -0800 (PST)
Keith Dysart wrote: On Jan 27, 10:57 am, Roger Sparks wrote: On Sat, 26 Jan 2008 19:24:22 -0800 (PST) Keith Dysart wrote: On Jan 26, 12:15 pm, Roger Sparks wrote: On Fri, 25 Jan 2008 19:13:31 -0800 (PST) Keith Dysart wrote: On Jan 24, 10:33 pm, Roger Sparks wrote: [snip] By examining this derivation, the reader can see that power and energy is reflected when a wave encounters a discontinuity. The reader can also see that more power is present on the transmission line than is delivered to the load. This is the conventional phraseology for describing the behaviour at the impedance discontinuity. Allow me to offer a specific example for which this phraseology is inappropriate. Consider a 50 V step function generator with an output impedance of 50 ohms driving a 50 ohm line that is 1 second long terminated in an open circuit. Turn on the generator. A 50 V step propagates down the line. The generator is putting 50 J/s into the line. One second later it reaches the open end and begins propagating backwards. After two seconds it reaches the generator. The voltage at the generator is now 100 V and no current is flowing from the generator into the line. In the 2 seconds, the generator put 100 joules into the line which is now stored in the line. The line is at a constant 100 V and the current is zero everywhere. Computing Pf and Pr will yield 50 W forward and 50 W reflected. And yet no current is flowing anywhere. The voltage on the line is completely static. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. Does this seem like a reasonable claim for an open circuited transmission line with constant voltage along its length and no current anywhere? I do not find it so. ...Keith This is a reasonable observation for a static situation where energy is stored on a transmission line. If the example contained an ongoing consideration, like "Where does the power move to?", then it would be reasonable to consider that the wave continued to move, simply to avoid the complication of what EXACTLY happens when a wave starts and stops. So have you thought about "where does the power go?" Yes, only the model I use substitutes a battery for the signal generator that you are using. A battery is not the same since it has a very low output impedance. A battery in series with a 50 ohm resistor would offer a reasonable match to a 50 ohm transmission line. The returning wave can recharge the battery, but how does the current stop? Or does it ever stop? From a practical aspect, the current must stop, but I can not explain how except by resistance that absorbs the circulating power. That is the challenging part to understand when too much emphasis is placed on the existance of energy being transported with the "reflected power". When I was learning this stuff, I did many examples with matched generators (a battery with a 50 ohm resistor is a good example). With step functions, it is easy to compute the final state because you can just treat it as a DC circuit for analysis. We must keep the limitations of our models in mind. True, but over limiting is not good either. When the generator is matched to the line so that the reflected wave does not encounter an impedance discontinuity when it arrives back at the generator (and therefore is not reflected), where does the reflected power go? Does it enter the generator? Is it dissipated somewhere? Answers to these questions will quickly lead to doubts about the *reality* of "reflected power". ...Keith The reflected wave that does not encounter an impedance at the generator must be on an infinitely long line, and therefore the conditions must have changed between the time of launch and return. I don't follow the association between generator impedance and length of line. For a 50 ohm line, a matched generator has a 50 ohm output impedance. The returning wave does not encounter an impedance discontinuity so is not reflected. It disappears into the the generator. OK, I think we are saying the same thing. The return wave DISAPPEARS. It makes more sense to think that the reflected voltage of (using your example) 50v meets 50v of forward voltage, and therefore finds an infinite resistance, coming to a stop. The current does stop (since it can not flow into the infinite resistance at the end of the line), and a 50 V step propagates back along the line. This 50 V reverse propagating step plus the 50 V already on the line produces a total of 100 V on the line. If the generator was constructed as a 100 V battery in series with a 50 ohm resistor, then when the step arrives back at the generator, there is 100 V on both sides of the source resistor (battery on one side, line on the other) and the current through the source resistor becomes zero. No further current flows into the line. If that happens, doesn't the same condition occur as soon as the reflected wave is first generated at the line end? The current really stops as soon as the end is reached, with the energy contained in the magnetic field converted to electric field energy visible as voltage. If this happened, the reflected wave could be better described as an electric "jump", similar to a hydraulic jump found in open channel flow of liquids, where kinetic energy is converted to potential energy. There do seem to be some similarities, though there is likely trouble if the analogy is carried to far. This idea of an electric "jump" requires not a reflection occuring without a discontinuity, but a moving wave front that absorbs the traveling wave, bringing it to a stop (in this case). The current has stoppped, but has the "wave"? Vf, Vr, If, Ir, Pf, Pr are still computable using the normal formulae. ...Keith Here is a link to a web site discussing reflections and more. http://www.ivorcatt.co.uk/em.htm He has some drawings that pertain to this discussion. He shows reflections and crossings, but no one-way transmission lines. -- 73, Roger, W7WKB |
#4
|
|||
|
|||
Derivation of Reflection Coefficient vs SWR
"Roger Sparks" wrote in message ... On Sat, 2 Feb 2008 13:01:22 -0800 (PST) Keith Dysart wrote: On Jan 27, 10:57 am, Roger Sparks wrote: On Sat, 26 Jan 2008 19:24:22 -0800 (PST) Keith Dysart wrote: On Jan 26, 12:15 pm, Roger Sparks wrote: On Fri, 25 Jan 2008 19:13:31 -0800 (PST) Keith Dysart wrote: On Jan 24, 10:33 pm, Roger Sparks wrote: [snip] By examining this derivation, the reader can see that power and energy is reflected when a wave encounters a discontinuity. The reader can also see that more power is present on the transmission line than is delivered to the load. This is the conventional phraseology for describing the behaviour at the impedance discontinuity. Allow me to offer a specific example for which this phraseology is inappropriate. Consider a 50 V step function generator with an output impedance of 50 ohms driving a 50 ohm line that is 1 second long terminated in an open circuit. Turn on the generator. A 50 V step propagates down the line. The generator is putting 50 J/s into the line. One second later it reaches the open end and begins propagating backwards. After two seconds it reaches the generator. The voltage at the generator is now 100 V and no current is flowing from the generator into the line. In the 2 seconds, the generator put 100 joules into the line which is now stored in the line. The line is at a constant 100 V and the current is zero everywhere. Computing Pf and Pr will yield 50 W forward and 50 W reflected. And yet no current is flowing anywhere. The voltage on the line is completely static. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. Does this seem like a reasonable claim for an open circuited transmission line with constant voltage along its length and no current anywhere? I do not find it so. ...Keith This is a reasonable observation for a static situation where energy is stored on a transmission line. If the example contained an ongoing consideration, like "Where does the power move to?", then it would be reasonable to consider that the wave continued to move, simply to avoid the complication of what EXACTLY happens when a wave starts and stops. So have you thought about "where does the power go?" Yes, only the model I use substitutes a battery for the signal generator that you are using. A battery is not the same since it has a very low output impedance. A battery in series with a 50 ohm resistor would offer a reasonable match to a 50 ohm transmission line. The returning wave can recharge the battery, but how does the current stop? Or does it ever stop? From a practical aspect, the current must stop, but I can not explain how except by resistance that absorbs the circulating power. That is the challenging part to understand when too much emphasis is placed on the existance of energy being transported with the "reflected power". When I was learning this stuff, I did many examples with matched generators (a battery with a 50 ohm resistor is a good example). With step functions, it is easy to compute the final state because you can just treat it as a DC circuit for analysis. We must keep the limitations of our models in mind. True, but over limiting is not good either. When the generator is matched to the line so that the reflected wave does not encounter an impedance discontinuity when it arrives back at the generator (and therefore is not reflected), where does the reflected power go? Does it enter the generator? Is it dissipated somewhere? Answers to these questions will quickly lead to doubts about the *reality* of "reflected power". ...Keith The reflected wave that does not encounter an impedance at the generator must be on an infinitely long line, and therefore the conditions must have changed between the time of launch and return. I don't follow the association between generator impedance and length of line. For a 50 ohm line, a matched generator has a 50 ohm output impedance. The returning wave does not encounter an impedance discontinuity so is not reflected. It disappears into the the generator. OK, I think we are saying the same thing. The return wave DISAPPEARS. It makes more sense to think that the reflected voltage of (using your example) 50v meets 50v of forward voltage, and therefore finds an infinite resistance, coming to a stop. The current does stop (since it can not flow into the infinite resistance at the end of the line), and a 50 V step propagates back along the line. This 50 V reverse propagating step plus the 50 V already on the line produces a total of 100 V on the line. If the generator was constructed as a 100 V battery in series with a 50 ohm resistor, then when the step arrives back at the generator, there is 100 V on both sides of the source resistor (battery on one side, line on the other) and the current through the source resistor becomes zero. No further current flows into the line. If that happens, doesn't the same condition occur as soon as the reflected wave is first generated at the line end? The current really stops as soon as the end is reached, with the energy contained in the magnetic field converted to electric field energy visible as voltage. If this happened, the reflected wave could be better described as an electric "jump", similar to a hydraulic jump found in open channel flow of liquids, where kinetic energy is converted to potential energy. There do seem to be some similarities, though there is likely trouble if the analogy is carried to far. This idea of an electric "jump" requires not a reflection occuring without a discontinuity, but a moving wave front that absorbs the traveling wave, bringing it to a stop (in this case). The current has stoppped, but has the "wave"? Vf, Vr, If, Ir, Pf, Pr are still computable using the normal formulae. ...Keith Here is a link to a web site discussing reflections and more. http://www.ivorcatt.co.uk/em.htm He has some drawings that pertain to this discussion. He shows reflections and crossings, but no one-way transmission lines. -- 73, Roger, W7WKB I just love this quote from that material "...Thus do these clapped-out radio men..." Though it's all above my head, I have indeed met some clapped out radio men. |
#5
|
|||
|
|||
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote:
Here is a link to a web site discussing reflections and more. http://www.ivorcatt.co.uk/em.htm Interesting - especially about the inductance (loading coil) acting like a transmission line. -- 73, Cecil http://www.w5dxp.com |
Reply |
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Forum | |||
Convert reflection coefficient to Z | Antenna | |||
Reflection Coefficient | Antenna | |||
Uses of Reflection Coefficient Bridges. | Antenna | |||
Reflection Coefficient Challenge Solved | Antenna | |||
Derivation of the Reflection Coefficient? | Antenna |