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Derivation of Reflection Coefficient vs SWR
It is not too hard to use the concept of traveling waves and reflections
to derive the familiar reflection coefficient to SWR relationship. SWR is a measurable and useful relationship that most hams are familiar with. A clear path between SWR and traveling waves should make the concepts more understandable and believable. Power placed on a transmission line is placed over time. No matter how small the time span interval we might want to examine, the span will always be wide enough to include some quantity of power or energy. If we desire, we can eliminate the time consideration and just consider energy, but there is no need to do that. In this derivation, the distinction between power and energy will be ignored. We will assume that neither power nor energy can be stored at the discontinuity in amounts greater than the natural storage capacity of the lines. This assumption fixes the impedance of any waves to the impedance of the transmission lines. Begin the derivation by assuming that power is applied to a transmission line with impedance Zo. A traveling wave moves down the transmission line to a discontinuity which is composed of a second transmission line or resistor with impedance Zl. The junction between the two lines is like a window or thin plane, with Zo on one side and Zl on the other. Upon encountering the discontinuity, the lead edge of the wave (and all following energy levels) follow a "conservation of energy" rule that requires energy to be preserved at all times. In other words, the energy that has been conveyed to the junction by some interval of applied power is not lost to heat, radiation, or storage, but will leave the junction as fast as it arrives, and can be located, maintaining time shape. The following equation will be valid, Pf = Pl + Pr where Pf = power forward, Pl = power to load, and Pr = power reflected. Use the voltage equivalent, (Vf^2)/Zo = (Vl^2)/Zl + (Vr^2)/Zo where Vf = forward voltage, Vl = load voltage, and Vr = reflected voltage. The reflected wave will travel back down the main line with impedance Zo. Simplify the equation by rearranging and substitute SWR = Zl/Zo (Vf^2)/Zo - (Vr^2)/Zo = (Vl^2)/Zl SWR(Vf^2 - Vr^2) = (Vl^2) Change the Vl into terms of Vf and Vr. Vl = Vf + Vr. We can do this because at a reflection, traveling waves double back over one another, adding voltage. Substitute Vl = Vf + Vr SWR(Vf^2 - Vr^2) = (Vf + Vr)^2 Factor the polynomial on the left above SWR(Vf - Vr)(Vf + Vr) = (Vf + Vr)^2 Divide both sides by (Vf + Vr) SWR(Vf - Vr) = Vf + Vr Divide both sides by Vf SWR(1 - Vr/Vf) = 1 + Vr/vf Vr/Vf = Reflection coefficient Ro, substitute SWR(1 - Ro) = 1 + Ro Rearrange to put Ro on one side Ro + Ro*SWR = SWR - 1 Factor out Ro and rearrange Ro = (SWR - 1)/(SWR + 1) We have found the familiar relationship for the Reflection Coefficient (Ro) and SWR using traveling wave logic. Using identical logic but using current instead of voltage, the same relationship can be found from Zo*If^2 = Zl*Il^2 + Zr*Ir^2 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. Here is a link to additional information about transmission lines: http://www.astrosurf.com/luxorion/qs...sion-line2.htm 73, Roger, W7WKB |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote in
: ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen |
Derivation of Reflection Coefficient vs SWR
Owen Duffy wrote:
Roger Sparks wrote in : ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen It's reasonable, though. Looking at demo 4 with the TLVis1 program, you can see that there's power all along the line except at specific nodal points (where I or V is always zero), yet there's no power at all being delivered to the load. Roy Lewallen, W7EL |
Derivation of Reflection Coefficient vs SWR
Roy Lewallen wrote in news:13pirk5h1cpt4f5
@corp.supernews.com: Owen Duffy wrote: Roger Sparks wrote in : ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen It's reasonable, though. Looking at demo 4 with the TLVis1 program, you can see that there's power all along the line except at specific nodal points (where I or V is always zero), yet there's no power at all being delivered to the load. Roy, my though was that on anything but a lossless line with VSWR=1, instantaneous power (being the rate of flow of energy) varies with time and location, so to make the statement that "power is present" and to quantitatively compare it with the power at a point (being the end of the line where the load is attached) seems to not be so reasonable. If the statement is about average power in both cases, then it is reasonable, obvious even, that power decreases with distance from the source. Perhaps "power is present" is an avoidance of the somewhat tautological form "power flows to the load". Owen |
Derivation of Reflection Coefficient vs SWR
Owen Duffy wrote:
Perhaps "power is present" is an avoidance of the somewhat tautological form "power flows to the load". Want to muddy the waters even more? Ramo & Whinnery say: "Another very important case is that of a perfect conductor, which by definition must have a zero tangential component of electric field at its surface. Then ^P^ [Poynting vector] can have no component normal to the conductor and there can be no power flow through the perfect conductor." -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
On Fri, 25 Jan 2008 05:32:33 GMT
Owen Duffy wrote: Roy Lewallen wrote in news:13pirk5h1cpt4f5 @corp.supernews.com: Owen Duffy wrote: Roger Sparks wrote in : ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen It's reasonable, though. Looking at demo 4 with the TLVis1 program, you can see that there's power all along the line except at specific nodal points (where I or V is always zero), yet there's no power at all being delivered to the load. Roy, my though was that on anything but a lossless line with VSWR=1, instantaneous power (being the rate of flow of energy) varies with time and location, so to make the statement that "power is present" and to quantitatively compare it with the power at a point (being the end of the line where the load is attached) seems to not be so reasonable. If the statement is about average power in both cases, then it is reasonable, obvious even, that power decreases with distance from the source. Perhaps "power is present" is an avoidance of the somewhat tautological form "power flows to the load". Owen Nothing mysterious was hinted with the words "power is present". As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. 73, Roger, W7WKB |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote:
As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. The amount of energy existing in a transmission line is exactly the amount required to support the measured forward power and reflected power. If the steady-state forward power is 200 watts, the reflected power is 100 watts, and the lossless transmission line is one microsecond long, it contains 300 microjoules of energy. I don't think that is a sheer coincidence. :-) -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote:
Nothing mysterious was hinted with the words "power is present". As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. A better reason to avoid "stored" is that power isn't stored at all, anywhere. Anyone who believes so should be able to tell us how many watts of power are stored in a 50 Ah, 12 volt battery. Roy Lewallen, W7EL |
Derivation of Reflection Coefficient vs SWR
On Fri, 25 Jan 2008 16:15:33 GMT
Cecil Moore wrote: Roger Sparks wrote: As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. The amount of energy existing in a transmission line is exactly the amount required to support the measured forward power and reflected power. If the steady-state forward power is 200 watts, the reflected power is 100 watts, and the lossless transmission line is one microsecond long, it contains 300 microjoules of energy. I don't think that is a sheer coincidence. :-) -- 73, Cecil http://www.w5dxp.com Yep, and if we quickly replaced the source with a termination having the impedance of the transmission line, 100 watts of power would continue to be delivered to the load for one microsecond, delivering 100 microjoules of energy. 100 watts of power would be delivered to the reflected wave termination for two microseconds, delivering 200 microjoules of energy. The transmission line was a dynamic power storage device for two microseconds after the power source was disconnected. 73, Roger, W7WKB |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote in
: On Fri, 25 Jan 2008 05:32:33 GMT Owen Duffy wrote: Roy Lewallen wrote in news:13pirk5h1cpt4f5 @corp.supernews.com: Owen Duffy wrote: Roger Sparks wrote in : ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen .... Nothing mysterious was hinted with the words "power is present". As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. Roger, If you were wanting to mean "stored", perhaps it is energy that is stored (over a non-zero length of line) rather than power. In that sense, energy is "present" on the line, and the load may store energy (only if it has reactive elements, and irrespective of whether it looks resistive at its terminals). Owen |
Derivation of Reflection Coefficient vs SWR
On Fri, 25 Jan 2008 19:33:41 GMT
Owen Duffy wrote: Roger Sparks wrote in : On Fri, 25 Jan 2008 05:32:33 GMT Owen Duffy wrote: Roy Lewallen wrote in news:13pirk5h1cpt4f5 @corp.supernews.com: Owen Duffy wrote: Roger Sparks wrote in : ... The reader can also see that more power is present on the transmission line than is delivered to the load. The notion that "power is present" is a different one. Owen ... Nothing mysterious was hinted with the words "power is present". As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. So I substituted "present" for "stored. Roger, If you were wanting to mean "stored", perhaps it is energy that is stored (over a non-zero length of line) rather than power. In that sense, energy is "present" on the line, and the load may store energy (only if it has reactive elements, and irrespective of whether it looks resistive at its terminals). Owen I think everyone agrees that energy is stored on a transmission line in the sense that energy enters at time one and does not exit until some time later at time two. It is important to be aware that the time shape of the energy package is preserved on a transmission line. The time shape information is contained in the power term for every instant of passing time. I can understand why many hesitate to think of power as being "stored" on a transmission line, because at best, such storage is dynamic and fleeting. Thinking of power being "present" on a transmission line is better than "stored" because the concept of a time component is not lost. -- 73, Roger, W7WKB |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote:
If the steady-state forward power is 200 watts, the reflected power is 100 watts, and the lossless transmission line is one microsecond long, it contains 300 microjoules of energy. I don't think that is a sheer coincidence. :-) Yep, and if we quickly replaced the source with a termination having the impedance of the transmission line, 100 watts of power would continue to be delivered to the load for one microsecond, delivering 100 microjoules of energy. 100 watts of power would be delivered to the reflected wave termination for two microseconds, delivering 200 microjoules of energy. Can we consider the old wives' tale of no energy in reflected waves to be laid to rest? -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
On Jan 25, 11:15*am, Cecil Moore wrote:
Roger Sparks wrote: As I finished writing the post, I wanted to call attention to the assumption that the reflected power is true power and adds to the amount of energy "stored" on the transmission line. * But "stored" is a word that implies static conditions, and static conditions are not found on a transmission line. *So I substituted "present" for "stored. The amount of energy existing in a transmission line is exactly the amount required to support the measured forward power and reflected power. If the steady-state forward power is 200 watts, the reflected power is 100 watts, and the lossless transmission line is one microsecond long, it contains 300 microjoules of energy. Are you sure? Check your answer by trying 100 kHz sinusoidal steady-state excitation. Even easier, ignore the reflected power and test your assertion just for the forward power. For fun, work out the line lengths for which your claim is true. ...Keith |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
Check your answer by trying 100 kHz sinusoidal steady-state excitation. Good grief, Keith, get real. I guess I forgot to say the assertion was for an integer multiple of MHz. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
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 |
Derivation of Reflection Coefficient vs SWR
On Jan 25, 5:31*pm, Cecil Moore wrote:
Keith Dysart wrote: Check your answer by trying 100 kHz sinusoidal steady-state excitation. Good grief, Keith, get real. I guess I forgot to say the assertion was for an integer multiple of MHz. Yes, so it would seem. And that would seem to narrow the applicability of the original assertion rather severely. ...Keith |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
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. Why would you compute Pf and Pr when no DC current is flowing? It is an invalid thing to do and unrelated to reality. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. I know of no one who will claim that for static DC. There are obviously no photons being emitted and therefore, no waves. Your example is unrelated to standing waves on an RF transmission line where energy is in motion, photons are continuously being emitted and absorbed, and current and voltage loops are active. One must realize the limitations of one's model. The wave model obviously fails where there are no waves. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
And that would seem to narrow the applicability of the original assertion rather severely. What do you know? It narrows it to amateur radio, the subject of this newsgroup. To be entirely technically correct, since my assertion was about average powers, the example transmission line must be an integer multiple of 1/4 wavelength. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
On Jan 26, 9:12*am, Cecil Moore wrote:
Keith Dysart wrote: And that would seem to narrow the applicability of the original assertion rather severely. What do you know? It narrows it to amateur radio, the subject of this newsgroup. I was unaware that all Amateur transmission lines were a multiple of 1 wavelength long. Are you sure? To be entirely technically correct, since my assertion was about average powers, the example transmission line must be an integer multiple of 1/4 wavelength. I would suggest 1/2 wavelength. For an intuitive proof, consider a line with only forward power. Then think of a quarter wave section with a voltage peak in the middle. Then consider when the voltage 0 is in the middle. Lots more energy in the former than the latter. At 1/2 wavelength, the total energy in the line section is constant. ...Keith ...Keith |
Derivation of Reflection Coefficient vs SWR
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. -- 73, Roger, W7WKB |
Derivation of Reflection Coefficient vs SWR
On Jan 26, 9:07*am, Cecil Moore wrote:
Keith Dysart wrote: 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. Why would you compute Pf and Pr when no DC current is flowing? To facilitate learning about how the equations work and what they may mean. It is an invalid thing to do Not at all. The equations don't just stop working at 0 frequency. In their general form F(t), there is no hint at all that F can not be a constant. Or, if you prefer, a square wave with a width several times longer than the length of the line. and unrelated to reality. Anything unreal will also be unreal for the specific case of sinusoids. And yet some will claim that 50 W is flowing forward and 50 W is flowing backwards. I know of no one who will claim that for static DC. There are obviously no photons being emitted and therefore, no waves. You really should try to stop thinking about photons for just a short while. All the behaviours of a transmission line can be understood and characterized without reference to photons. Analysis using classic circuit principles works quite fine and has no difficulty at low frequencies. Your example is unrelated to standing waves on an RF transmission line where energy is in motion, photons are continuously being emitted and absorbed, and current and voltage loops are active. There is no standing wave, but the example is quite valid none-the-less. If you like, consider it as a long pulse. And if you only want sinusoids, Fourier will convert the pulse to sinusoids which you can, using superposition, use to solve the problem. The simplicity of the constant voltage makes it easy to check your results. One must realize the limitations of one's model. The wave model obviously fails where there are no waves. Think of it as a long pulse. That should satisfy your need to have 'waves'. ...Keith |
Derivation of Reflection Coefficient vs SWR
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?" 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 |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
Not at all. The equations don't just stop working at 0 frequency. As a matter of fact, EM waves cannot exist without photons. There is zero wave activity at DC. Therefore, the forward power and reflected power is zero at DC steady-state. You really should try to stop thinking about photons for just a short while. Yep, you guys would like to sweep the technical knowledge from the field of optical physics and quantum electro- dynamics under the rug. One wonders why. Think of it as a long pulse. That should satisfy your need to have 'waves'. No, only photons will satisfy the definition of EM waves. There are no photons. There are no waves. There are no forward and reflected powers. There are no changing E-fields or H-fields. There is not even any movement of electrons associated with the source voltage. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
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), ... On the contrary, it is redistributed back toward the load in the process of destructive interference and becomes constructive interference associated with the forward wave. Whether you call that a reflection or not, the fact that the forward power equals the source power plus the reflected power tells us that reflected power being dissipated in the source would violate the conservation of energy principle. where does the reflected power go? Power doesn't flow so reflected power doesn't "go" anywhere. It is the reflected energy that is flowing, i.e. going somewhere. If the power were flowing, its dimensions would be joules/sec/sec. Maybe you would like to try to explain the physical meaning of those dimensions? Does it enter the generator? forward power = source power + reflected power A component of the forward energy is equal in magnitude to the reflected energy so no, it doesn't enter the source. Is it dissipated somewhere? Not during steady-state. During steady-state it is being used for impedance transformation. After steady-state, it is dissipated either in the source or in the load as a traveling wave. Answers to these questions will quickly lead to doubts about the *reality* of "reflected power". Reflected power is the Poynting vector associated with the reflected wave. It exists at a point. It's average magnitude (indirectly measured by a Bird) is Re(ExH*)/2. It's direction is the direction of the flow of reflected energy. If you don't believe in reflected energy, let your fingers become the circulator load resistor for an open-circuit stub being driven by a KW source. -- 73, Cecil http://www.w5dxp.com |
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 |
Derivation of Reflection Coefficient vs SWR
Cecil Moore wrote in news:mO0nj.4140$J41.257
@newssvr14.news.prodigy.net: Keith Dysart wrote: Not at all. The equations don't just stop working at 0 frequency. As a matter of fact, EM waves cannot exist without photons. There is zero wave activity at DC. Therefore, the forward power and reflected power is zero at DC steady-state. You really should try to stop thinking about photons for just a short while. Yep, you guys would like to sweep the technical knowledge from the field of optical physics and quantum electro- dynamics under the rug. One wonders why. Think of it as a long pulse. That should satisfy your need to have 'waves'. No, only photons will satisfy the definition of EM waves. There are no photons. There are no waves. There are no forward and reflected powers. There are no changing E-fields or H-fields. There is not even any movement of electrons associated with the source voltage. Food for thought! There is no such thing as DC! How’s that you say? You have to turn it on sometime and someday you may turn it off. There for, DC is just very low frequency AC. As another example of physics over thinking, I once had a physics professor describe in detail how an electric motor works using Quark physics. Very interesting but it has no practical value in using electric motors. Much like this long thread has nothing much to do with antennas. John Passaneau W3JXP |
Derivation of Reflection Coefficient vs SWR
Roy Lewallen wrote:
"A better reason to avoid "stored" is that power isn`t stored at all, anywhere. Anyone who believes so should be able to tell us how many watts are stored in a 50 Ah, 12 volt battery." The 50 Ah of energy stored in a battery may be withdrawn at a rate determined by the load, so it is a variable. Velocity in a transmission line is a constant determined by constructtion of the line. Thus, energy stored in the line is determined by its length, voltage, current, and phase angle. These predict the rate of energy transfer (power). Best regards, Richard Harrison, KB5WZI |
Derivation of Reflection Coefficient vs SWR
"JOHN PASSANEAU" wrote in message ... There is no such thing as DC! How's that you say? You have to turn it on sometime and someday you may turn it off. There for, DC is just very low frequency AC. John Passaneau W3JXP That's false reasoning OM! Alternating current is not the same as discontinuous current. In the example you provide, a DC supply is either off or on; it does not reverse polarity! You do not make AC by switching on and off DC, even at 50 Hz (or your 60 Hz) |
Derivation of Reflection Coefficient vs SWR
Suzy wrote:
"You do not make AC by switching on and off DC, even at 50 Hz (or your 60 Hz)" Not without inductance to provide the missing half cycle. Remember vibrator supplies and their solid-state equivalents? Best regards, Richard Harrison, KB5WZI |
Derivation of Reflection Coefficient vs SWR
Richard Harrison wrote:
Roy Lewallen wrote: "A better reason to avoid "stored" is that power isn`t stored at all, anywhere. Anyone who believes so should be able to tell us how many watts are stored in a 50 Ah, 12 volt battery." The 50 Ah of energy stored in a battery may be withdrawn at a rate determined by the load, so it is a variable. Ah is a unit of charge, not energy. The battery, making the simplifying (and invalid) assumption of constant voltage during discharge, contains 2.16 Mj of energy. Velocity in a transmission line is a constant determined by constructtion of the line. Thus, energy stored in the line is determined by its length, voltage, current, and phase angle. These predict the rate of energy transfer (power). So the rate at which a transmission line transfers energy depends on its length? If I put 100 watts into a one wavelength cable and get 100 watts out, will I get 200 watts out if I extend the cable to two wavelengths? Roy Lewallen, W7EL |
Derivation of Reflection Coefficient vs SWR
Suzy wrote:
"JOHN PASSANEAU" wrote in message ... There is no such thing as DC! How's that you say? You have to turn it on sometime and someday you may turn it off. There for, DC is just very low frequency AC. John Passaneau W3JXP That's false reasoning OM! Alternating current is not the same as discontinuous current. In the example you provide, a DC supply is either off or on; it does not reverse polarity! You do not make AC by switching on and off DC, even at 50 Hz (or your 60 Hz) But through the techniques of linear circuit analysis, we can split the pulsed DC into two components, a pure steady DC component and a symmetrical AC component. We can do two separate analyses with the two (AC and DC) excitations, and sum the results. The answer will be exactly the same as if we had done the calculations directly. One can then reasonably claim that the switched DC is the sum of an AC waveform and a pure DC component. Roy Lewallen, W7EL |
Derivation of Reflection Coefficient vs SWR
Arrgh! I did it again!
Roy Lewallen wrote: Ah is a unit of charge, not energy. The battery, making the simplifying (and invalid) assumption of constant voltage during discharge, contains 2.16 Mj of energy. That's 2.16 MJ, not Mj. It'll sink in eventually . . .I hope. Roy Lewallen, W7EL |
Derivation of Reflection Coefficient vs SWR
Roy Lewallen wrote:
"Ah is a unit of charge, not energy." The most common 12-volt battery is the lead-acid storage battery used in automobiles. It should not be allowed to become completely discharged nor to remain less than fully charged for a long time. The battery`s capacity is rated in amperes x hours. The discharge rate is assumed to be 8 hours. Slower discharges can be supported for more ampere-hours and faster discharges likely won`t meet the rated ampere-hour product. A 50 Ah battery would be expected to deliver about 6.25 A for a period of 8 hours provided its electrolyte does not rise to more than 110 degrees F. 2-volt cells can be discharged down to 1.75 volts per cell or a voltage of 10.5 volts for the 6 cells of a 12-volt battery. Best regards, Richard Harrison, KB5WZI |
Derivation of Reflection Coefficient vs SWR
Roy Lewallen wrote:
"So the rate at which a transmission line transfers energy depends on its length?" No, it depends on the power fed into the line. Storage in the line depends on its length, plus the incident and reflected energies per unit length of the line. Velocity is fixed by construction of the line so a slow velocity factor allows more energy storage as the source energy output is constant and independent of the line`s velocity factor. Best regards, Richard Harrison, KB5WZI |
Derivation of Reflection Coefficient vs SWR
On Jan 27, 9:45*am, Cecil Moore wrote:
Keith Dysart wrote: Not at all. The equations don't just stop working at 0 frequency. As a matter of fact, EM waves cannot exist without photons. There is zero wave activity at DC. Therefore, the forward power and reflected power is zero at DC steady-state. And yet all the circuit theory derivations of reflection coefficient, power, voltage and current distributions work just fine for DC (or, if you prefer, low rate pulses). Digital designers use exactly that for solving real world problems. They do not refuse to solve problems when the conditions approach DC. The equations all work. You really should try to stop thinking about photons for just a short while. Yep, you guys would like to sweep the technical knowledge from the field of optical physics and quantum electro- dynamics under the rug. One wonders why. An intriguing accusation. Transmission lines can be understood well, and real world problems solved without reference to photons and EM waves. Just use the well known circuit theory based equations. And they extend all the way to DC. For those who like EM waves and photons... Why do you want to limit yourselves? Why won't you use the circuit theory bases equations to solve problems for which they work? Just because EM waves and photons do not? Think of it as a long pulse. That should satisfy your need to have 'waves'. No, only photons will satisfy the definition of EM waves. There are no photons. There are no waves. There are no forward and reflected powers. There are no changing E-fields or H-fields. There is not even any movement of electrons associated with the source voltage. May be true. But why do you want to use that as an excuse not to solve solveable problems? ...Keith |
Derivation of Reflection Coefficient vs SWR
On Jan 27, 10:26*am, Cecil Moore wrote:
Keith Dysart wrote: 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), ... On the contrary, it is redistributed back toward the load in the process of destructive interference and becomes constructive interference associated with the forward wave. Whether you call that a reflection or not, the fact that the forward power equals the source power plus the reflected power tells us that reflected power being dissipated in the source would violate the conservation of energy principle. Unfortunately, this is quite wrong. And I continue to be surprised that you argue that there is a reflection where there is not an impedance discontinuity. Some parts of the rest of your post are correct by coincidence, but since the underlying premise of reflections where there is no discontinuity is incorrect, I have snipped it. But this debate has been had before. You do not want to understand how the output impedance of a generator affects a returning signal. I have offerred references and you have refused to look. I have offerred spice simulations, and you have refused to look. When the discussion moves to simpler generators so that the behaviour can be studied, you will declare them uninteresting because they do not represent "real ham transmitters". You will make jokes about 10 cent resistors, not realizing that is how real test equipment prevents re-reflection. (How well would a TDR work, if any substantial amount of the return was reflected?) When you decide that you do not want to argue that reflections occur where there is no impedance discontinuity, and are willing to study output immpedance, the learning can begin. ...Keith |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
Transmission lines can be understood well, and real world problems solved without reference to photons and EM waves. If that were true, we would not be having this argument. The real world problem is - where does the reflected EM energy go? Since you have not "solved that real world problem", your methods are suspect. OTOH, optical physicists solved that same problem long before any of us were born. Why won't you use the circuit theory bases equations to solve problems for which they work? The main reason not to use your methods is that you use them to arrive at wrong concepts. EM waves cannot exist without energy. If there exists no EM wave energy, there are no EM waves. If EM waves exist, they are necessarily associated with energy and momentum, both of which must be conserved. The amount of that energy flowing past a measurement point/plane in a unit-time is the power (density) associated with the reflected wave. Even the energy and momentum of a single photon can be calculated. Any length of transmission line with reflections contains exactly the amount of energy necessary to support the forward and reflected waves. That amount of energy exists in the transmission line and is not delivered to the load during steady-state. Because your model doesn't tell you where the reflected energy goes, you assume there is zero energy in reflected waves. Again, I challenge you to use your fingers to replace the reflected power circulator load in a system with a KW source driving an open-circuit. That shock therapy will, no doubt, change your mind about the non-existence of reflected power. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
Keith Dysart wrote:
Unfortunately, this is quite wrong. And I continue to be surprised that you argue that there is a reflection where there is not an impedance discontinuity. Since an absence of reflections violates the conservation of energy principle, there is something wrong with your assertion and your earlier example was proved to contain a contradiction. Psource = Pfor - Pref = Pload Pfor = Psource + Pref = Pload + Pref Those equations are true only if reflected energy does not flow back into the source. I suspect that, contrary to your assertions, the actual real-world source presents an infinite impedance to reflected waves. When you decide that you do not want to argue that reflections occur where there is no impedance discontinuity, ... You simply fail to recognize the impedance discontinuity. Please perform the following experiment to prove there is no impedance discontinuity and no distortion and get back to us. zero ohm TV RCVR--+--TV source--+--Z0 stub----------open | Z0 source impedance resistor | GND The source output goes into the stub. Reflections occur at the open end of the stub and flow back through the zero impedance source to be dissipated in the Z0 source resistor and displayed without distortion on the TV RCVR. If what you say is true, it should be duck soup for you to prove. -- 73, Cecil http://www.w5dxp.com |
Derivation of Reflection Coefficient vs SWR
Keith Dysert wrote:
"(How well would a TDR worh, if any substantial amount of return was reflected?)" A properly terminated line does not make reflections. I would imagine multiple reflections on an oscilloscope produce the same smear as as they do on TV. TDR is suggested for monitoring bridge integrity and performance. Where was it when we needed it? TDRs are likely cheaper than replacing all the questionable bridges. TDR is used to determine the characteristics of electrical lines by observing reflected waveforms.Tektronnix is a leader with its "I Connect" software. Roy can likely describe it. Agilent suggests TDR is the most general approach to evaluating the time domain response of any electromagnetic system is to solve Maxwell`s equations in the time domain. The foregoing is courtesy of Wikipedia. The incoherent structure of the last sentence was theirs too. Best regards, Richard Harrison, KB5WZI |
Derivation of Reflection Coefficient vs SWR
Roger Sparks wrote:
"It is not too hard to use the concept of traveling waves to derive the familiar reflection coefficient to SWR relationship." Yes. Terman has done it for us in his 1955 opus. He just uses the letter S to represent SWR. On page 86: "The voltage and current of the incident wave at the load must satisfy Eq. (4-8) = Eprime / Iprime = Zo." And at the top of page 86: "The reflected wave.----is identical with the incident wave except that it is traveling toward the generator. Eq. (4-11) = Edouble prime / Idouble prime = -Zo." "The load voltage is the sum of the voltages of the incident and reflected waves at the load,.... The load current is the sum of the currents of the incident and reflected waves at the load,.... The vector ratio EL / IL must equal the load impedance ZL." "The vector ratio E2 / E1 of the voltage of the reflected wave to the voltage of the incident wave at the load is termed the reflection coefficient of the load. Reflection coefficient = rho = E2/E1 = (ZL/Zo)-1 / (ZL/Zo)+1." And on page 97: "Standing-wave ratio = S = Emax/Emin, Eq.(4-20) And: S= [E1] + [E2] / [E1] - [E2], Eq. (4-21)" The standing-wave ratio S is one means of expressing the magnitude of the reflection coefficient; the exact relation between the two is S = 1+[rho] / 1- [rho] or [rho] = S-1 / S +1 This relationship is illustrated graphically in Fig. 4-9. Best regards, Richard Harrrison, KB5WZI |
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