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Author Topic: current and voltage along a non resonant dipole  (Read 18106 times)
WS3N
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« Reply #30 on: November 14, 2013, 10:08:01 AM »

The standing-wave current is non-zero, so there will clearly be losses if you choose to include them.

But pure standing wave current has no direction and is standing still so how can something that is not moving possibly cause losses? Could it be that the losses are actually caused by the existence and superposition of the forward and reflected waves?


Why do you say it is standing still? Look at the equation. From the example,

i = 2 sin(kx) cos(wt).

At point x the current has an amplitude 2 sin(kx) and it oscillates at frequency w.




This is getting tiresome, but let's look at one more example. You claim that there is no energy flow in a standing-wave field. Consider a simple example of the EM field in a one-dimensional vacuum cavity.


E = y E0 sin(kx) sin(wt)

dB/dt = - curl(E) = - z k E0 cos(kx) sin(wt)

B = z (k E0/w) cos(kx) cos(wt)


The energy density is

U = 0.5 eps0 E2 + 0.5 mu0 H2

   = 0.5 eps0 E02 sin2(kx) sin2(wt) + 0.5 mu0 (k E0/ w mu0)2 cos2(kx) cos2(wt)

  = 0.5 eps0 E02 [ sin2(kx) sin2(wt) + cos2(kx) cos2(wt) ].


The Poynting flux is

S = E x H = x (k E02/ w mu0) sin(kx) cos(kx) sin(wt) cos(wt)

 = x (E02 / 4 Z0) sin(2kx) sin(2wt)


The time-averaged energy density is

<U> = 0.25 eps0 E02


and the time-averaged energy/momentum flux is zero.



While the averages are zero it is clearly wrong that there is no energy flow. The energy moves from the center of the cavity to the edges twice per cycle.
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W5DXP
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« Reply #31 on: November 14, 2013, 11:41:16 AM »

Why do you say it is standing still? Look at the equation. From the example,

i = 2 sin(kx) cos(wt).

At point x the current has an amplitude 2 sin(kx) and it oscillates at frequency w.

The fact that the phase angle is the same (wt) at a particular time and at all possible 'x' points on the wire (for 0<kx<pi) indicates that the current 'i' is standing still with an oscillating-in-place amplitude. In fact, since the standing wave current is not moving in either direction, one can just as easily write the standing wave current equation as:

i = 2*sin(kx)*cos(-wt)

and get exactly the same results. Putting a negative sign on the (wt) of a traveling wave reverses the direction of flow. But since a pure standing wave has no direction of flow, putting a negative sign on the (wt) term has no effect at all because  cos(wt)=cos(-wt).

When i=2*sin(kx)*cos(wt)=2*sin(kx)*cos(-wt)

The standing wave current flow does not have a direction. This has been used by some to try to prove that reflected power doesn't actually exist.
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #32 on: November 14, 2013, 12:17:01 PM »

So what? Wait a half cycle and it certainly reverses direction. Your argument is akin to saying that the current in a dipole has no direction because, if I measure distance from the center, the amplitude is cos(kx), and cos(-kx) = cos(kx). It's simply a matter of where we choose our zero.


This is conceptually the same as a vibrating string. If I tell you the equation for the string's lateral displacement is

y(x,t) = sin(kx) cos(wt)

would you say the string doesn't move?


More trivially, I could have just as easily started with the example

sin(kx + wt) - sin(kx - wt) = [sin(kx) cos(wt) + cos(kx) sin(wt)] - [sin(kx) cos(wt) - cos(kx) sin(wt)] = 2 cos(kx) sin(wt).

The fact that it now changes sign is meaningless.
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W5DXP
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« Reply #33 on: November 14, 2013, 02:32:57 PM »

Wait a half cycle and it certainly reverses direction.

Sorry, that's not true. The wire is one-dimensional. The base of the pure standing wave current phasor is anchored at a point 'x' and doesn't move away from point 'x'. It is true that the mathematical model of a current phasor reverses direction in 'y''z' space but for pure standing wave current phasors, its base is always anchored to exactly the same point 'x' on that one-dimensional wire. The current phasor has a constant amplitude, A*sin(kx), is perpendicular to the wire, and anchored to one and only one point 'x'. If you hang a crescent wrench on a wire by the hole in its handle and spin it at a single point on the wire, you will get a feel for what the standing wave current phasor looks like, i.e. it doesn't have a direction up and down the wire - only perpendicular around one point on the wire. This is essentially the same conceptual problem that W8JI had when "measuring" the 3ns delay of the current through a very large air-core loading coil. I tried explaining it to him almost 10 years ago but to no avail.

Quote
y(x,t) = sin(kx) cos(wt)

would you say the string doesn't move?

No molecule changes its 'x' position on the string. All vibrations are 'y' and 'z' excursions perpendicular to the unplucked string and are centered at 'x' on the string when the string is at rest. (An EM-wave/string analogy is riddled with conceptual problems.)
 
Quote
The fact that it now changes sign is meaningless.

Exactly! Meaningless to its 'x' position which has absolutely nothing to do with that phase angle. For a pure standing wave, (wt) is the same over 180 degrees at any time 't' all up and down the line. Over that 180 degree span no point changes sign while another point keeps its sign. At any time 't' all points over that 180 degrees have exactly the same phase angle. All you have proved is my point that the standing wave current doesn't move in the 'x' dimension.
« Last Edit: November 14, 2013, 02:36:36 PM by W5DXP » Logged

73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #34 on: November 14, 2013, 02:49:18 PM »

Sorry, that's not true. The wire is one-dimensional. The base of the pure standing wave current phasor is anchored at a point 'x' and doesn't move away from point 'x'. It is true that the mathematical model of a current phasor reverses direction in 'y''z' space but for pure standing wave current phasors, its base is always anchored to exactly the same point 'x' on that one-dimensional wire. The current phasor has a constant amplitude, A*sin(kx), is perpendicular to the wire, and anchored to one and only one point 'x'. If you hang a crescent wrench on a wire by the hole in its handle and spin it at a single point on the wire, you will get a feel for what the standing wave current phasor looks like, i.e. it doesn't have a direction up and down the wire - only perpendicular around one point on the wire. This is essentially the same conceptual problem that W8JI had when "measuring" the 3ns delay of the current through a very large air-core loading coil. I tried explaining it to him almost 10 years ago but to no avail.

Exactly! Meaningless to its 'x' position which has absolutely nothing to do with that phase angle. For a pure standing wave, (wt) is the same over 180 degrees at any time 't' all up and down the line. Over that 180 degree span no point changes sign while another point keeps its sign. At any time 't' all points over that 180 degrees have exactly the same phase angle. All you have proved is my point that the standing wave current doesn't move in the 'x' dimension.

I've read this a couple of times but I must be missing something. Are you really trying to tell me that the current is not along the wire, and that your "crescent wrench" spinning around the wire is the current, and its vector components are perpendicular to the wire?
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W5DXP
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« Reply #35 on: November 14, 2013, 04:07:25 PM »

I've read this a couple of times but I must be missing something. Are you really trying to tell me that the current is not along the wire, and that your "crescent wrench" spinning around the wire is the current, and its vector components are perpendicular to the wire?

Essentially correct. The standing wave current is not flowing along the wire. It is standing still. If it was flowing along the wire, it would be a traveling wave. The crescent wrench represents the phasor of the current at point 'x'. Remember phasors are math models that don't exist in reality. Phasors have an imaginary component that we cannot measure. What we can measure is the real component. Look at the equation. What is 'x'? It's the location of a single physical point on the line. Does 'x' change with (wt)? No, it doesn't.

The current that W7EL and W8JI used for their coil group delay measurements was mostly standing wave current and cannot be used to measure propagation delay. The only way to obtain a valid propagation delay measurement is to completely eliminate the standing waves and use a traveling wave for the phase measurement. Here's an article I wrote about 75m Bugcatcher Coil measurements made at Louisiana Tech.

http://w5dxp.com/coilmeas.htm

One of the best references I have is Optics, by Hecht. It has a very good explanation of traveling waves, standing waves, interference, and superposition.
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #36 on: November 14, 2013, 04:48:06 PM »

I've read this a couple of times but I must be missing something. Are you really trying to tell me that the current is not along the wire, and that your "crescent wrench" spinning around the wire is the current, and its vector components are perpendicular to the wire?

Essentially correct. The standing wave current is not flowing along the wire. It is standing still. If it was flowing along the wire, it would be a traveling wave. The crescent wrench represents the phasor of the current at point 'x'. Remember phasors are math models that don't exist in reality. Phasors have an imaginary component that we cannot measure. What we can measure is the real component. Look at the equation. What is 'x'? It's the location of a single physical point on the line. Does 'x' change with (wt)? No, it doesn't.

OMG

I know this is pointless but, just for fun, let's try one more. An AC source is connected to a resistor with short wires. Now there is no x dependence. All the little wrenches are the same length and they're all spinning in unison. Is the current standing still?
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W5DXP
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« Reply #37 on: November 15, 2013, 09:56:04 AM »

I know this is pointless but, just for fun, let's try one more.

I'm not trying to drive you away and would like for you to continue this discussion until we agree on the technical concepts.

Quote
An AC source is connected to a resistor with short wires. Now there is no x dependence. All the little wrenches are the same length and they're all spinning in unison. Is the current standing still?

There is no x dependence because there is no x in a lumped circuit. Phase shifts and delays are not allowed in a lumped circuit. That is one of its shortcomings and is unfortunately what most people carry around in their heads as a model of reality.

In the real world, there will always be a phase shift on the short wires from the source to a load with a resistive component. If it is a matched load, i.e. SWR=1:1, then the phase shift will be proportional to the speed of light in the medium. As the SWR rises from 1:1, the phase shift decreases until it disappears completely when SWR=infinity, e.g. with a purely reactive load.

It is a mathematical fact that if three phasors at points x, x+1, and x+2 all have the same phase angle at the same time, then they are not moving along x and are simply oscillating in place at a fixed x location. Those three phasors have to have different phase angles at the same time for them to be moving and one can tell from those phase angles which way they are moving.

I'm going to try to illustrate the above with graphics from EZNEC. The system is a 60 ft. wire running horizontal above mininec ground. On one end we have a source installed in a 1 ft wire to ground. For the first case, we have no load, i.e. an open-circuit exists at the end of the wire so the SWR is close to infinity (pure standing wave). For the second case, we have a 415 ohm load installed in a 1 ft wire to ground to get the SWR on the wire close to 1:1 (pure traveling wave).

In the case of the open-circuit at the end of the wire, the current phase is constant up and down the wire as can be seen from the end view. The current is obeying the standing wave equation. In the case of the 415 ohm load, the current phase can be seen to have rotated about 90 degrees as seen from the end view. The current is obeying the traveling wave equation.

In the open-circuit case, the standing wave current phasors are not advancing along the wire. They are oscillating in fixed x positions. In the 415 ohm load case, the traveling wave current phasors are advancing toward the load at the speed of light in the medium.

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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #38 on: November 15, 2013, 11:19:53 AM »

I know this is pointless but, just for fun, let's try one more.

I'm not trying to drive you away and would like for you to continue this discussion until we agree on the technical concepts.

That doesn't seem possible because you continue to ascribe some kind of reality to what is only a visualization aid (your wrenches), and talk about current standing still.

A current that stands still is completely ridiculous. It's an oxymoron. Current cannot stand still. Charges can be stationary. When charge moves it's called current. A current at some point can be constant (i.e. the same amount of charge flowing, in the same direction, past the point in a given time), or it can have a constant amplitude that periodically reverses direction in the time-harmonic case, but it makes no sense to say it stands still.

Quote
It is a mathematical fact that if three phasors at points x, x+1, and x+2 all have the same phase angle at the same time, then they are not moving along x and are simply oscillating in place at a fixed x location. Those three phasors have to have different phase angles at the same time for them to be moving and one can tell from those phase angles which way they are moving.

This also makes no sense. Your little wrenches are, as I said, a visualization aid used in antenna modeling software. They do not flow up and down the wire, even for a traveling wave. They aren't real. Your wrench will still stay at point x and spin around in the traveling-wave case. It represents the magnitude and phase of the current at a point, whether the wave is traveling or stationary.

Quote
I'm going to try to illustrate the above with graphics from EZNEC. The system is a 60 ft. wire running horizontal above mininec ground. On one end we have a source installed in a 1 ft wire to ground. For the first case, we have no load, i.e. an open-circuit exists at the end of the wire so the SWR is close to infinity (pure standing wave). For the second case, we have a 415 ohm load installed in a 1 ft wire to ground to get the SWR on the wire close to 1:1 (pure traveling wave).

In the case of the open-circuit at the end of the wire, the current phase is constant up and down the wire as can be seen from the end view. The current is obeying the standing wave equation. In the case of the 415 ohm load, the current phase can be seen to have rotated about 90 degrees as seen from the end view. The current is obeying the traveling wave equation.

In the open-circuit case, the standing wave current phasors are not advancing along the wire. They are oscillating in fixed x positions. In the 415 ohm load case, the traveling wave current phasors are advancing toward the load at the speed of light in the medium.

You say there is a current in the standing-wave case. Please describe its behavior as a function of time. If you are going to tell me it's standing still then please describe this phenomenon more fully. What does it mean for a current to stand still?
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W5DXP
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« Reply #39 on: November 15, 2013, 01:14:51 PM »

A current that stands still is completely ridiculous. It's an oxymoron. Current cannot stand still.

I agree, that's my point exactly, and it means there is something very wrong with the standing wave model. When one is dealing with standing waves, one is dealing with an abstract mathematical construct that does not correspond to the real world. Just because one may come up with the correct answers doesn't mean that the math model matches reality. What is an oxymoron is a "standing wave" because EM waves cannot stand still. A standing wave is a human abstraction and is simply not a wave at all. Waves cannot stand still. Current cannot stand still. Seems we agree.

In a pure standing wave, the total current is the superposition of two currents traveling in opposite directions at the speed of light in the medium. When we perform the following trig function, we are divorcing ourselves from reality by merging those two waves and this thread is exposing the consequences of such actions.

sin(kx + wt) - sin(kx - wt) =  2 cos(kx) sin(wt)

The left side of the equation correctly represents the forward wave and reflected wave traveling in opposite directions at the speed of light in the medium while obeying the laws of physics for EM waves. The right side of the equation does not represent the real world and cannot exist in the real world of EM waves because, as you have pointed out, that equation leads to contradictions that violate the laws of physics governing EM waves. The right side of the equation is standing still, something that is impossible for EM waves to do.

Quote
You say there is a current in the standing-wave case. Please describe its behavior as a function of time. If you are going to tell me it's standing still then please describe this phenomenon more fully. What does it mean for a current to stand still?

You missed my point. I did not say the current is standing still. I said that the standing wave model/equation tells us that the current is standing still. Therefore it is invalid because it doesn't agree with reality. I believe that any math expert will verify that's what the standing wave equation is telling us.

I believe that there are two currents moving at the speed of light in opposite directions just as they are supposed to. I believe that the equation:

i=2 cos(kx) sin(wt)

does not represent the real world because it turns the two underlying EM waves into standing wave mashed potatoes and violates the laws/definitions of physics. It indicates that the current is not moving and that is impossible. As Bueche and Hecht say in College Physics:

"These ... patterns are called standing waves, as compared to the propagating waves considered above. They might better not be called waves at all, since they do not transport energy and momentum."
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #40 on: November 15, 2013, 01:51:17 PM »

A current that stands still is completely ridiculous. It's an oxymoron. Current cannot stand still.

I agree, that's my point exactly, and it means there is something very wrong with the standing wave model. When one is dealing with standing waves, one is dealing with an abstract mathematical construct that does not correspond to the real world. Just because one may come up with the correct answers doesn't mean that the math model matches reality. What is an oxymoron is a "standing wave" because EM waves cannot stand still. A standing wave is a human abstraction and is simply not a wave at all. Waves cannot stand still. Current cannot stand still. Seems we agree.

In a pure standing wave, the total current is the superposition of two currents traveling in opposite directions at the speed of light in the medium. When we perform the following trig function, we are divorcing ourselves from reality by merging those two waves and this thread is exposing the consequences of such actions.

sin(kx + wt) - sin(kx - wt) =  2 cos(kx) sin(wt)

The left side of the equation correctly represents the forward wave and reflected wave traveling in opposite directions at the speed of light in the medium while obeying the laws of physics for EM waves. The right side of the equation does not represent the real world and cannot exist in the real world of EM waves because, as you have pointed out, that equation leads to contradictions that violate the laws of physics governing EM waves. The right side of the equation is standing still, something that is impossible for EM waves to do.

The left and right sides are completely equivalent. There is only one field. It is what it is. It can be described in two ways but that doesn't change the field or the math.

Quote
Quote
You say there is a current in the standing-wave case. Please describe its behavior as a function of time. If you are going to tell me it's standing still then please describe this phenomenon more fully. What does it mean for a current to stand still?

You missed my point. I did not say the current is standing still. I said that the standing wave model/equation tells us that the current is standing still. Therefore it is invalid because it doesn't agree with reality. I believe that any math expert will verify that's what the standing wave equation is telling us.

It doesn't take a math expert to tell you that you are wrong. The right side says no such thing.

i(x,t) = [2 cos(kx)] sin(wt) = I(x) sin(wt)

The amplitude I(x) varies with position but the current is most certainly not standing still.

Look at this link. Someone has done us the favor of creating animated gifs of the current on a transmission line in both cases (traveling wave at the top, standing waves at about the middle of the page).

http://en.wikipedia.org/wiki/Transmission_line

Quote
"These ... patterns are called standing waves, as compared to the propagating waves considered above. They might better not be called waves at all, since they do not transport energy and momentum."

Whether one chooses to call them standing waves (a term which is, of course, widely used and understood) or something else is irrelevant. As I showed in my worked example of the cavity oscillator, to which you failed to respond, these fields do transport energy locally, but there is no net transport.
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W5DXP
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« Reply #41 on: November 15, 2013, 04:53:27 PM »

The left and right sides are completely equivalent. There is only one field.

The left and right sides are mathematically equivalent. That doesn't mean that there is only one current. There is, in fact, two currents and without either one that field could not exist as a standing wave. So in reality, there exist two superposed fields, not just one. Each field retains its own independent existence without interacting with the other until they encounter an impedance discontinuity at the same place at the same time. People who ignore that fact have come up with some really far out ideas, e.g. reflected power doesn't exist.

Have you ever tried to create a standing wave using only one field generator? No fair causing reflections.Smiley

On the subject of trusting our math models to represent reality, quite often our math models result in a negative resistance solution. Does that mean that one can go out and buy a negative resistor?

Quote
It doesn't take a math expert to tell you that you are wrong. The right side says no such thing.

I suggest you consult with a math expert as I have. Any time this identity exists,

i=2 cos(kx) cos(wt)=2 cos(kx) cos(-wt)

there is no movement of the current because at any particular time, there is no difference in the phase on each side of any particular point 'x'. When that condition is true, nothing is moving in the 'x' direction. Check it out if you don't believe me.

Quote

Unfortunately, those plots don't represent RF reality. At RF frequencies, the electrons move hardly at all. They are better visualized by assuming they oscillate in place. The wikipedia "drift velocity" web page indicates that the movement of an electron at 60 MHz would be about 2x10-12 meter. Here's a better example. Assuming the blue trace is standing wave current, in which direction is it flowing?

http://www.csupomona.edu/~ajm/materials/animations/stwaves/swr11.mov
« Last Edit: November 15, 2013, 05:18:50 PM by W5DXP » Logged

73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #42 on: November 15, 2013, 06:20:48 PM »

The left and right sides are completely equivalent. There is only one field.

The left and right sides are mathematically equivalent.

They are completely equivalent. The charges in the medium cannot do two things at the same time. There is only one total current. As long as we are in a linear medium the two cases are indistinguishable. The total current is the linear superposition of the two traveling waves, physically and mathematically.

Quote
Quote
It doesn't take a math expert to tell you that you are wrong. The right side says no such thing.

I suggest you consult with a math expert as I have. Any time this identity exists,

i=2 cos(kx) cos(wt)=2 cos(kx) cos(-wt)

there is no movement of the current because at any particular time, there is no difference in the phase on each side of any particular point 'x'. When that condition is true, nothing is moving in the 'x' direction. Check it out if you don't believe me.

How can you keep insisting that there is no current? At, say, x = 0,

i(0,t) = 2 cos(wt)

The current is obviously oscillating. It is positive and flows in the +x direction until it reaches a maximum value of +2, then reverses, passes through zero, and goes negative, flowing in the -x direction until it equals -2, then back again.

Please tell me how this means there is no current.

Quote
Quote

Unfortunately, those plots don't represent RF reality. At RF frequencies, the electrons move hardly at all. They are better visualized by assuming they oscillate in place. The wikipedia "drift velocity" web page indicates that the movement of an electron at 60 MHz would be about 2x10-12 meter.

Now you are purposely being obstinate. Would it be satisfactory if the dots were the size of electrons and they only moved 10-12 m? Maybe it would be better if you viewed it on a very tiny screen. If you really object to this then all of your plots are similarly incorrect because they only demonstrate concepts and are not at the true scale. That is just silly.

Quote
Here's a better example. Assuming the blue trace is standing wave current, in which direction is it flowing?

http://www.csupomona.edu/~ajm/materials/animations/stwaves/swr11.mov

Again, OMG. Now I finally see the problem. I can't believe I have been wasting my time because of this. It's no wonder you didn't respond to my worked example of the field in the cavity.

You said, "Assuming the blue trace is standing wave current, in which direction is it flowing?"

Unbelievable. You have no idea what the blue trace means. The direction of current flow has nothing to do with whether or not the trace appears to move left or right. Current is a vector quantity. In one dimension, the direction of the current is indicated by its sign. Positive means it flows in the +x direction, negative means it flows in the -x direction, as I wrote a few lines above this. When the blue trace is above the axis the current is flowing to the right, and when it's below the axis the current is flowing to the left.

I don't know what your background is but you seem to be lacking a fundamental appreciation of the relationship between the mathematics and the physical concepts it represents.
« Last Edit: November 15, 2013, 06:33:01 PM by WS3N » Logged
W5DXP
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« Reply #43 on: November 16, 2013, 07:57:10 AM »

The current is obviously oscillating.

Sorry, I thought it was obvious that I was asking you to take a look at the current NODES. I'll rephrase the question: "Assuming the blue trace is standing wave current, in which direction is it flowing at the current nodes?"

How is it possible for the current to just slosh back and forth between current nodes? Exactly what happens when that alleged flowing standing wave current encounters a current node? The mathematics says the conditions are identical to an open circuit. But we know it is not an open circuit because if we cut the wire, things change.

What is actually happening in reality is easy to understand when a laser is used to create the standing waves in free space without the encumbrance of wires and currents.

Quote
I don't know what your background is but you seem to be lacking a fundamental appreciation of the relationship between the mathematics and the physical concepts it represents.

My credentials are listed on my QRZ bio page. I don't respond well to ad hominem attacks so I will bow out.
« Last Edit: November 16, 2013, 08:13:33 AM by W5DXP » Logged

73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
WS3N
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Posts: 732




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« Reply #44 on: November 16, 2013, 08:24:29 AM »

The current is obviously oscillating.

Sorry, I thought it was obvious that I was asking you to take a look at the current NODES. I'll rephrase the question: "Assuming the blue trace is standing wave current, in which direction is it flowing at the current nodes?"

Why does the current just slosh back and forth between current nodes? Exactly what happens when that alleged flowing standing wave current encounters a current node? The mathematics says the conditions are identical to an open circuit. Why can't we just cut the wire?

Quote
I don't know what your background is but you seem to be lacking a fundamental appreciation of the relationship between the mathematics and the physical concepts it represents.

My credentials are listed on my QRZ bio page. I don't respond well to ad hominem attacks so I will bow out.

You never said anything about nodes, not that it matters. That is just more smoke.

You have listed you credentials, so I'll give you mine. I have BS degrees in math and physics from MIT and a PhD in theoretical physics from Penn State. I have worked at one of the Navy's research facilities for 25 years, where I was originally hired to fill a slot in EM theory. I have worked on many problems in EM propagation and scattering, and written my own FEM, BEM and MoM (what's used in NEC) codes.

My comment was hardly an attack but this is also my last post in this thread. This is a waste of time because you have demonstrated that you know just enough to be dangerous.
« Last Edit: November 16, 2013, 08:43:14 AM by WS3N » Logged
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