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I am very confused about Standing Waves on transmission lines.

Wikipedia says "a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space".

I'm getting the time domain and wave amplitude confused, I think.

I think I understand that a standing wave is caused by the superposition of the amplitude of a wave traveling in one direction upon that of one traveling in the opposite direction. In other words, the resultant wave caused by the addition and subtraction of amplitudes or 'interference' between two waves traveling in opposite directions. And that even though no one says it, they always mean the special case of two waves of the same frequency because one is usually a reflected wave of the other.

Is the voltage amplitude of a standing wave a DC value which you could measure with a multi-meter (with a theoretically infinite input impedance) ?

The pictures you normally see of standing waves which look like a sine wave, is this an instantaneous snapshot or does the amplitude of the standing wave actually stay fixed in space and time along say a transmission line ?

Does the amplitude of the actual standing waves in space oscillate in time at the same rate as the two waves traveling in opposite directions ?

What else have I missed?

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Thanks for citing the Wikipedia item on SWR; as well as being a solid overview of the subject as presented in textbooks, the animations reveal much that is not obvious from a static description.

Is the voltage amplitude of a standing wave a DC value which you could measure with a multi-meter (with a theoretically infinite input impedance) ?

Wikipedia tells us that the voltages along the line are AC:

"For example, the VSWR value 1.2:1 denotes an AC voltage due to standing waves along the transmission line reaching a peak value 1.2 times that of the minimum AC voltage along that line."

The RF voltage along the line could be measured with an ideal rectifier and smoothing filter connected to a DC multimeter. Non-ideal rectifiers may produce misleading measurements at low voltages because their response is not linear below their knee voltage.

The pictures you normally see of standing waves which look like a sine wave, is this an instantaneous snapshot or does the amplitude of the standing wave actually stay fixed in space and time along say a transmission line ?

The "picture you normally see of standing waves which look like a sine wave" is borne out in the animation for the special case of $\Gamma$=-1:

enter image description here

SWR=$\infty$ results from dividing the peak value by the value of zero at the nodes.

There are several noteworthy features in the subsequent graphs for SWR values of 4, 2 and 9, respectively: enter image description here

  • The superimposed forward and reflected waves form an envelope with "peaks" and "valleys"
  • The peaks and valleys are stationary ("standing") even though the underlying forward and reflected waves travel up and down the line
  • The higher the SWR, the greater the ratio between the peak and valley values of the standing wave

Does the amplitude of the actual standing waves in space oscillate in time at the same rate as the two waves traveling in opposite directions ?

Observing again the graphs, the forward and reflected waves have the same wavelength and, therefore, the same frequency, though they may be out of phase. While not explicitly stated in the Wikipedia item, the system is assumed to be linear, so there are no distortions which could introduce additional frequency components. Since linear combinations of signals of the same frequency can only produce resultant signals of the same frequency, the standing waves have the same frequency as the underlying RF signals that produce them.

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  • $\begingroup$ I think the keyword in the answer to my question is 'Envelope' which removes the confusion i had. Could you tell me if the following is correct ? The pictures i often see of standing waves are actually the standing wave envelope which is a graph with the maximum amplitude values of the addition of the forward and reflected waves on the y axis versus the position in space along the transmission line on the x axis. $\endgroup$
    – Andrew
    Apr 12, 2019 at 1:03
  • $\begingroup$ You could almost argue that the standing waves don't actually exist and are really just a visual representation of waveforms moving at the speed of light which is impossible to draw. $\endgroup$
    – Andrew
    Apr 12, 2019 at 1:03
  • $\begingroup$ So you could describe standing waves as an envelope showing the maximum resultant values of amplitude of two AC wave forms of the same frequency traveling in opposite directions. $\endgroup$
    – Andrew
    Apr 12, 2019 at 3:40
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    $\begingroup$ @Andrew The standing wave is the sum of the forward and rearward traveling waves. This is easiest to see in the first drawing ($\Gamma$=-1) $\endgroup$
    – Brian K1LI
    Apr 12, 2019 at 12:19
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    $\begingroup$ @Andrew I should have added: the sum is taken at each point along the length of the line. For example, note that the points where the standing wave crosses zero correspond to forward and rearward waves with equal and opposite values, whose sum is zero. $\endgroup$
    – Brian K1LI
    Apr 12, 2019 at 12:52
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If it was DC, there would be no wave.

With the wave, you have AC power; RF merely means that the frequency of the AC is high enough to be considered radio.

You can measure the voltage of the wave with a multimeter if it has an AC setting. This will measure either RMS voltage or simulated RMS voltage; these two are the same if the wave is a sine wave.

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In this case, a picture is worth a thousand words.

enter image description here

What is usually shown as a standing wave is the envelope, not the wave itself. The wave oscillates at the frequency of operation between 100% magnetic energy (current) and 100% electric energy (voltage). Standing wave current is easy to measure. The lack of a reference point makes standing wave voltage harder to measure so the electric field may be measured instead and converted to voltage.

Standing waves don't stand still. The energy in the two underlying waves on a standing wave antenna (forward and reflected) is traveling back and forth at the speed of light. Electromagnetic waves on an antenna cannot stand still. They must necessarily travel at the speed of light in the medium.

Note that all electromagnetic energy (including RF energy) is photonic, not electronic. The free electrons in the antenna conductor are simply oscillating in place while assisting the RF photons to travel at the speed of light back and forth on the standing wave antenna. Some of the photons are lost to radiation from the antenna. Antennas do not transmit or receive electrons! The exceptions to that statement are lightning and corona.

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  • $\begingroup$ -1 for the quasi-quantum physics explanation. By that logic, all "electronics" are "photonic". And thinking of electronics as photons shooting around is a dangerous path leading to a broken intuitive model, just as broken as the one involving electrons shooting around. $\endgroup$
    – Phil Frost - W8II
    Apr 10, 2019 at 13:47
  • $\begingroup$ @PhilF No, not all electronics are photonic. DC steady state is not photonic. But to the best of my knowledge (and according to The ARRL Handbook) all electromagnetic energy moves at the speed of light and of all things associated with the propagation of electromagnetic energy in a ham radio system, massless photons are the only things that are capable of moving at the speed of light. So all RF fields and waves are quantized photons which can transfer EM energy without a charge carrier, i.e. Maxwell's displacement current. $\endgroup$
    – Cecil - W5DXP
    Apr 10, 2019 at 19:17
  • $\begingroup$ Your understanding of quantum mechanics is wrong on so many levels I can't even decide how to begin to explain. I suggest you stick to the basics -- there's absolutely no reason to invoke photons to explain any of this. $\endgroup$
    – Phil Frost - W8II
    Apr 10, 2019 at 20:08
  • $\begingroup$ Was Einstein wrong to invoke photons to explain the nature of all quantized electromagnetic waves including RF waves? $\endgroup$
    – Cecil - W5DXP
    Apr 10, 2019 at 21:16
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    $\begingroup$ Photons on Wikipedia might be a start. I didn't mean to imply that Einstein said anything about RF waves. It's just a fact that light waves and RF waves are both electromagnetic waves just of different frequencies. To keep things manageable, maybe I should just start a new thread and ask questions that will alleviate my ignorance "on so many levels". $\endgroup$
    – Cecil - W5DXP
    Apr 11, 2019 at 0:31

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