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#1
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The Rest of the Story
After discovering the error on Roy's web page at:
http://eznec.com/misc/Food_for_thought.pdf I have begun a series of articles that convey "The Rest of the Story" (Apologies to Paul Harvey). Part 1 of these articles can be found at: http://www.w5dxp.com/nointfr.htm Stand by for the other three articles. -- 73, Cecil http://www.w5dxp.com |
#2
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The Rest of the Story
On Mar 4, 3:36*pm, Cecil Moore wrote:
After discovering the error on Roy's web page at: http://eznec.com/misc/Food_for_thought.pdf I have begun a series of articles that convey "The Rest of the Story" (Apologies to Paul Harvey). Part 1 of these articles can be found at: http://www.w5dxp.com/nointfr.htm Looks good. And well presented. There is only one small problem with the analysis. When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. Taking just the second example (12.5 ohm load) for illustrative purposes... The power dissipated in Rs before the reflection arrives is Prs.before = 50 + 50cos(2wt) watts The reflected power at the source is Pref.s = 18 + 18cos(2wt) watts But the power dissipated in Rs after the reflection arrives is Prs.after = 68 + 68cos(2wt-61.9degrees) watts Prs.after is not Prs.before + Pref, though the averages do sum. And since the energy flows must be accounted for on a moment by moment basis (or we violate conservation of energy), it is the instantaneous energy flows that provide the most detail and allow us to conclude with certainty that Prs.after is not Prs.before + Pref. The same inequality holds for all the examples except those with Pref equal to 0. Thus these examples do not demonstrate that the reflected power is dissipated in the source resistor. ...Keith |
#3
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The Rest of the Story
On Mar 4, 8:00*pm, Keith Dysart wrote:
On Mar 4, 3:36*pm, Cecil Moore wrote: After discovering the error on Roy's web page at: http://eznec.com/misc/Food_for_thought.pdf I have begun a series of articles that convey "The Rest of the Story" (Apologies to Paul Harvey). Part 1 of these articles can be found at: http://www.w5dxp.com/nointfr.htm Looks good. And well presented. There is only one small problem with the analysis. When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. Taking just the second example (12.5 ohm load) for illustrative purposes... The power dissipated in Rs before the reflection arrives is Prs.before = 50 + 50cos(2wt) watts The reflected power at the source is Pref.s = 18 + 18cos(2wt) watts But the power dissipated in Rs after the reflection arrives is Prs.after = 68 + 68cos(2wt-61.9degrees) watts Prs.after is not Prs.before + Pref, though the averages do sum. And since the energy flows must be accounted for on a moment by moment basis (or we violate conservation of energy), it is the instantaneous energy flows that provide the most detail and allow us to conclude with certainty that Prs.after is not Prs.before + Pref. The same inequality holds for all the examples except those with Pref equal to 0. Thus these examples do not demonstrate that the reflected power is dissipated in the source resistor. ...Keith I should have mentioned that there are some energy flows that do add, as expected. The energy delivered by the generator to the line (or equivalently, the energy flowing in the line at the generator end) is the sum of the forward and reverse energy flows... Pf.g = 50 + 50cos(2wt) Pr.g = -18 + 18cos(2wt) Pline.g = 32 + 68cos(2wt) And the energy delivered by the source is always equal to the energy being dissipated in the resistor plus the energy being delived to the line... Prs = 68 + 68cos(2wt-61.9degrees) Rline.g = 32 + 68cos(2wt) Psource = 100 + 116.6cos(2wt-30.96degrees) Psource is equal to Prs + Pline.g So the energy flows that should add up, do add up. ...Keith |
#4
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The Rest of the Story
Keith Dysart wrote:
So the energy flows that should add up, do add up. How did you take care of the fact that the forward wave and reflected wave are flowing in opposite directions through the resistor? How did you take care of the 90 degree phase difference between the forward wave and the reflected wave through the resistor? -- 73, Cecil http://www.w5dxp.com |
#5
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The Rest of the Story
Keith Dysart wrote:
When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. That is irrelevant. The power (irradiance) model doesn't apply to instantaneous energy and power. Hecht says as much in "Optics". Nobody has ever claimed that the energy/power analysis applies to instantaneous values. The energy/power values are all based on RMS voltages and currents. There is no such thing as an instantaneous RMS value. -- 73, Cecil http://www.w5dxp.com |
#6
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The Rest of the Story
Cecil Moore wrote:
Keith Dysart wrote: When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. That is irrelevant. The power (irradiance) model doesn't apply to instantaneous energy and power. Hecht says as much in "Optics". Nobody has ever claimed that the energy/power analysis applies to instantaneous values. The energy/power values are all based on RMS voltages and currents. There is no such thing as an instantaneous RMS value. Interesting. Do you also use only the RMS phase and RMS interference to come up with your RMS answers? 8-) 73, Gene W4SZ |
#7
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The Rest of the Story
Gene Fuller wrote:
Cecil Moore wrote: Keith Dysart wrote: When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. That is irrelevant. The power (irradiance) model doesn't apply to instantaneous energy and power. Hecht says as much in "Optics". Nobody has ever claimed that the energy/power analysis applies to instantaneous values. The energy/power values are all based on RMS voltages and currents. There is no such thing as an instantaneous RMS value. Interesting. What is interesting is that in the formula for power dissipated in the source resistor, the 50 watts is an average power. It is an invalid procedure to try to add instantaneous power to an average power. Do you also use only the RMS phase and RMS interference to come up with your RMS answers? I didn't say anything about "RMS phase and RMS interference". The phase angle used in Hecht's irradiance equation is the phase between the electric fields of the two waves. The magnitude of the interference is an average magnitude based on the RMS values of voltage and current. I do exactly what Eugene Hecht did in "Optics". He said: "Furthermore, since the power arriving cannot be measured instantaneously, the detector must integrate the energy flux over some finite time, 'T'. If the quantity to be measured is the net energy per unit area received, it depends on 'T' and is therefore of limited utility. If however, the 'T' is now divided out, a highly practical quantity results, one that corresponds to the average energy per unit area per unit time, namely 'I'." 'I' is the irradiance (*AVERAGE* power density). i.e. The irradiance/interference equation does not work for instantaneous powers which are "of limited utility". -- 73, Cecil http://www.w5dxp.com |
#8
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The Rest of the Story
On Mar 4, 10:25*pm, Cecil Moore wrote:
Keith Dysart wrote: When the instantaneous energy flows are examined it can be seen that Prs is not equal to 50 W plus Pref. That is irrelevant. The power (irradiance) model doesn't apply to instantaneous energy and power. Hecht says as much in "Optics". Nobody has ever claimed that the energy/power analysis applies to instantaneous values. Are you saying that conservation of energy does NOT apply to instantaneous values? The energy/power values are all based on RMS voltages and currents. There is no such thing as an instantaneous RMS value. I understand the analysis technique you are proposing. That it leads to the wrong conclusion can be easily seen when the instantaneous energy flows are studied. This merely demonstrates that the analysis technique has its limitations. The bottom line remains that the reflected energy is not dissipated in the source resistor, even for the special cases under discussion. ...Keith |
#9
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The Rest of the Story
Keith Dysart wrote: .... The bottom line remains that the reflected energy is not dissipated in the source resistor, even for the special cases under discussion. ...Keith What if the source resistor is of finite length Alan |
#10
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The Rest of the Story
Keith Dysart wrote:
On Mar 4, 10:25 pm, Cecil Moore wrote: Nobody has ever claimed that the energy/power analysis applies to instantaneous values. Are you saying that conservation of energy does NOT apply to instantaneous values? Of course not. I am saying that the 50 watts in the source resistor power equation is an average power. It is invalid to try to add instantaneous power to an average power, as you tried to do. The energy/power values are all based on RMS voltages and currents. There is no such thing as an instantaneous RMS value. I understand the analysis technique you are proposing. That it leads to the wrong conclusion can be easily seen when the instantaneous energy flows are studied. This merely demonstrates that the analysis technique has its limitations. The proposed analysis technique is a tool. Trying to apply that tool to instantaneous powers is like trying to use a DC ohm-meter to measure the feedpoint impedance of an antenna. Only a fool would attempt such a thing. The bottom line remains that the reflected energy is not dissipated in the source resistor, even for the special cases under discussion. Saying it doesn't make it so, Keith. There is nothing to keep the reflected energy from being dissipated in the source resistor. If the reflected energy is not dissipated in the source resistor, where does it go? Please be specific because it is obvious to me that there is nowhere else for it to go in the special zero interference case presented. Here are some of your choices: 1. Reflected energy flows through the resistor and into the ground without being dissipated. 2. The 50 ohm resistor re-reflects the reflected energy back toward the load. (Please explain how a 50 ohm load on 50 ohm coax can cause a reflection.) 3. There's no such thing as reflected energy. 4. Reflected waves exist without energy. 5. ______________________________________________. -- 73, Cecil http://www.w5dxp.com |
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