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#251
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Standing-Wave Current vs Traveling-Wave Current
On Dec 27, 10:53*am, Cecil Moore wrote:
Keith Dysart wrote: It is worth doing to convince yourself. Then examine P(t) to understand how the instaneous energy transfer varies with time. Oh, I know how to integrate P(t). But did you know that your favourite V * I * cos(theta) was derived from the function describing instantaneous power? But I don't comprehend the utility of the following: The instantaneous value of voltage is 10 volts. The instantaneous value of current is 1 amp. The voltage and current are in phase. The instantaneous power is 10 joules per 0 sec? There is definitely a problem with that. But an instantaneous value of 10 joules/sec; that is useful. With the function describing the intantaneous values with respect to time, you can integrate. You can find the total energy transfered. You can find when it is transferred. Is it steady? Or does it vary? There is lots to learn. You can even learn that when the instantaneous power at some point is 0 for all instances, then no energy is transferred. That would be a useful learning. ...Keith |
#252
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Standing-Wave Current vs Traveling-Wave Current
Roy Lewallen wrote:
Roger wrote: I think we are in sync here, but something is missing. When I think of a traveling sine wave, it must have a beginning as a point of beginning discussion. I pick a point which is the zero voltage point between wave halves. It follows that the maximum voltage point will be 90 degrees later. I think you are doing the same thing, but maybe not. Next I imagine the whole wave moving down the transmission line as an intact physical object, with the peak always 90 degrees behind the leading edge. In our example 1/2 wave line, the leading edge would reach the open end 180 degrees in time after entering the example. We can see then, that the current peak will be at the center of the transmission line when the leading edge reaches the end. Yes, you're describing some of the properties of a sinusoidal traveling wave. I generally describe them mathematically. Again, we seem to be in complete agreement except for the statement "In those situations, infinite currents or voltages occur during runup". For many years I thought that "initial current into a transmission line at startup" would be very high, limited only by the inductive characteristics of the line. With this understanding, I thought that voltage would lead current at runup. It was not until I saw the formula Zo = 1/cC that I realized that a transmission line presents a true resistive load at startup. Current and voltage are always in phase at startup. They are provided that Z0 is purely resistive. That follows from the simplifying assumption that loss is zero or in the special case of a distortionless line, and it's often a reasonable approximation. But it's generally not strictly true. But that doesn't have anything to do with my statement, which deals with theoretical cases where neither end of the line has loss. For example, look at a half wavelength short circuited line driven by a voltage source. Everything is fine until the initial traveling wave reaches the end and returns to the source end. If we agree that voltage and current are always in phase in the traveling wave, then we should find that in our example, the system comes to complete stability after one whole wave (two half cycles) is applied to the system. Assuming you're talking about the half wavelength open circuited line driven by a voltage source -- please do the math and show the magnitude and phase of the initial forward wave, the reflected wave, the wave re-reflected from the source, and so forth for a few cycles, to show that what you say is true. My calculations show it is not. I'd do it, but I find that the effort of showing anything mathematically is pretty much a waste of effort here, since it's generally ignored. It appears that the general reader isn't comfortable with high school level trigonometry and basic complex arithmetic, which is a good explanation of why this is such fertile ground for pseudo-science. But I promise I'll read your mathematical analysis of the transmission line run-up. Roy Lewallen, W7EL OK. I think I should tweak the example just a little to clarify that our source voltage will change when the reflected wave arrives back at the source end. To do this, I suggest that we increase our transmission line to one wavelength long. This so we can see what happens to the source if we pretended that we had not moved it all. We pick our lead edge at wt-0 and define it to be positive voltage. The next positive leading edge will occur at wt-360. Of course, a half cycle of positive voltage will follow for 180 degrees following points wt-0 and wt-360. Initiate the wave and let it travel 540 degrees down the transmission line. At this point, the leading edge wt-0 has reflected and has reached a point 180 degrees from the full wave source. This is the point that was originally our source point on the 1/2 wave line. Mathematically, wt-0 is parallel/matched with wt-360, but because the wt-0 has been reflected, the current has been reversed but the voltage has not been changed. Lets move to wave point wt-1 and wt-361 so that we will have non-zero voltage and current. vt = vr(wt-1) + vf(wt-361) = 2*.5*sin(1) where 1v p-p has been originally applied and vf(t) = vr(t) and vt(t) is total voltage at any time point. Notice that the total voltage is now 2vr(t) = 2vf(t). This doubling continues as the wave moves forward, with vt(t) = vr(wt-2) + vf(wt-362) ......... = 2vf(t) = 2vr(t) The current is similar except, very important, the current was reversed when reflected from the open end. it(t) = vf(wt-362) - vr(wt-2) ...... = vf(t) - vr(t) = 0 The effect on the old source point is to make the impedance infinitely high for all ongoing wave forward motion, which is not stopping the wave, only indicating that power no longer moves past this point. At time 720 degrees, the reflected wave (wt-0) reaches our revised source point where it matches with wt-720 and begins raising the source impedance, stopping power movement into the system. From this time on, no further power enters the revised system because of the high impedance. We should notice here that no power leaves the system after this time as well. The high impedance works both ways, for forward and reflected wave. There is no need for additional reflection analysis because both source and full wave systems are stable and self contained after this 720 degree point. The source is effectively "turned off", and the full wave system isolated. If the source was parallel with a 50 ohm resistor (assuming a 50 ohm transmission line), then the reflected wave would be matched with the resistor and absorbed. Power would be continually moved through the transmission line, giving hot spots on the line at 90 and 270 degree points. We would still see the doubled voltage points at the end (360 degrees) and 180 degree points. If we move to the shorted transmission line case, the math is identical except that the voltages are reversed but currents add. The result at the source is a low impedance where power can no longer be applied because the voltage is always zero. Could we make current flow through a resistor in parallel to the transmission line at the source in this case? I think not. So I think. Thanks for taking time to consider these words. It takes real time to carefully consider the arguments (and to present them). 73, Roger, W7WKB |
#253
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Standing-Wave Current vs Traveling-Wave Current
Roger wrote:
There is a third possibility. The interaction of the two waves can establish a very high resistance, so high that no current flows-zero. This is a common confusion of cause and effect. Take a short-circuit 1/4WL stub for instance. A very high resistance is established at the mouth of the stub but that high resistance has zero effect on the forward current which keeps on flowing into the stub. Without the forward current flowing uninhibited into the stub, the very high resistance could not be maintained. In fact, the current is a maximum at the shorted end of a 1/4WL stub. If you don't believe it, measure it. Where did that current come from if current cannot flow into the stub? The stub impedance is the result of the ratio of voltage to current. It is a virtual impedance and since it is an effect, it cannot be the cause of anything. The people who say that a virtual impedance is the same thing as an impedor have not read the definitions of those things in the IEEE Dictionary. -- 73, Cecil http://www.w5dxp.com |
#254
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Standing-Wave Current vs Traveling-Wave Current
Dave Heil wrote:
Please note that I now say and have previously written that I do not believe that the Sun rises, ... Good, that is all I was trying to get you to admit - that the "rising of the sun" is an illusion caused by the rotation of the earth. -- 73, Cecil http://www.w5dxp.com |
#255
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Standing-Wave Current vs Traveling-Wave Current
Keith Dysart wrote:
Cecil Moore wrote: The instantaneous power is 10 joules per 0 sec? There is definitely a problem with that. But an instantaneous value of 10 joules/sec; that is useful. But that instantaneous instant is NOT one second long. Exactly how long is that instantaneous instant? 1 ms? 1 us? 1 ns? more? less? -- 73, Cecil http://www.w5dxp.com |
#256
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Standing-Wave Current vs Traveling-Wave Current
Dave Heil wrote:
Please note that I now say and have previously written that I do not believe that the Sun rises, sets or travels across the sky. Very good, that is all I was trying to get you to admit - that the "rising of the sun" is an illusion which was my original point. Incidentally, Webster's says the sun does actually rise. :-) -- 73, Cecil http://www.w5dxp.com |
#257
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Standing-Wave Current vs Traveling-Wave Current
Cecil Moore wrote:
[...] OK Cecil, good job well done ... again, you logic is flawless--I BELIEVE! Time to come home now. (to reality) Heils' got a "hardon", let him be--time'll fix it ... maybe ... ;-) He still ain't done nothin' I ain't ever done. Regards, JS |
#258
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Standing-Wave Current vs Traveling-Wave Current
Cecil Moore wrote:
... But that instantaneous instant is NOT one second long. Exactly how long is that instantaneous instant? 1 ms? 1 us? 1 ns? more? less? TIME? I thought we already dealt with that; ain't no such thing--there IS movement ... you will argue these points forever--until you STOP believing in time (like Santa.) Regards, JS |
#259
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Standing-Wave Current vs Traveling-Wave Current
Cecil Moore wrote:
Roger wrote: There is a third possibility. The interaction of the two waves can establish a very high resistance, so high that no current flows-zero. This is a common confusion of cause and effect. Take a short-circuit 1/4WL stub for instance. A very high resistance is established at the mouth of the stub but that high resistance has zero effect on the forward current which keeps on flowing into the stub. Without the forward current flowing uninhibited into the stub, the very high resistance could not be maintained. In fact, the current is a maximum at the shorted end of a 1/4WL stub. If you don't believe it, measure it. Where did that current come from if current cannot flow into the stub? Stored in the 1/4 WL between the short and mouth. No more current needed once stability is reached. The stub impedance is the result of the ratio of voltage to current. It is a virtual impedance and since it is an effect, it cannot be the cause of anything. The people who say that a virtual impedance is the same thing as an impedor have not read the definitions of those things in the IEEE Dictionary. Measured in ohms, virtual, and impedance is not the same as impedor. OK An effect caused by earlier events. Agreed. 73, Roger, W7WKB |
#260
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Standing-Wave Current vs Traveling-Wave Current
On Dec 27, 6:28*pm, Cecil Moore wrote:
Keith Dysart wrote: Cecil Moore wrote: The instantaneous power is 10 joules per 0 sec? There is definitely a problem with that. But an instantaneous value of 10 joules/sec; that is useful. But that instantaneous instant is NOT one second long. Exactly how long is that instantaneous instant? 1 ms? 1 us? 1 ns? more? less? Time for some calculus review. Look up differentiation. Perhaps try googling "in the limit as t approaches 0..." But at least you now see the utility. ...Keith |
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