What happens in a low loss feed-line with a high SWR

Question

I was recently reading an interesting article from the ARRL to get a better understanding of the SWR.

The following case is still unclear: A low loss feed-line with an impedance that doesn't match the antenna's impedance and the receiver's impedance.

In this case a large part of the signal should "bounces" back and forth into the feed-line due to the impedance mismatch. At this point the article states that:

The energy bounces back and forth inside the cable until it’s all radiated by the antenna for a lossless transmission line. An important point to realize is that with extremely low loss transmission line, no matter what the SWR, most of the power can get delivered to the antenna.

I understand that during each "bounce", due to the impedance mismatch, some amount of energy will be transmitted and the rest reflected.

I don't understand how this transmitted power could be useful. After "bouncing" back and forth the part of the signal that will be transmitted will probably be out of phase with the signal sent by the transmitter. Even if by any luck the reflected signal and the signal currently sent by the transmitter happened to be in phase, the information conveyed wouldn't be the same.

So to me, even if almost of the power is transmitted, due to the high SWR most of this power should be just noise and don't improve the quality of the transmission in any case. But it's not what the article seems to explain. What did I miss ?

Answer 1

For many modulations, the modulation is very slow compared to the propagation delay of the feedline. For example, SSB is typically limited to no more than 4 kHz. That corresponds to a wavelength of of 75 km. As long as the feedline is significantly shorter than this, then the delay due to the feedline is negligible.

It may be easier to understand intuitively in a digital case. For example, PSK31 sends 31.25 symbols per second. 31.25 Hz corresponds to 9600 km, meaning by the time you are sending a bit, the previous bit is 9600 km away.

This breaks down for very high-speed modulations. For example, 8VSB modulation used by HDTV broadcasts transmits 10.76 million symbols per second, equivalent to a 29 meter wavelength. At these speeds, a feedline is long enough to introduce significant delay, which could come out looking like multipath distortion. Then again, TV channels are 6 MHz wide. Most amateur transmissions are several orders of magnitude narrower. Protip: don't operate your commercial TV broadcast station with a poorly matched feedline.

But for most amateur transmissions, we can consider the transmission as a pure sine wave, which is a reasonable approximation given the timescales dictated by the length of the feedline and the modulation. Then, it helps to visualize what a standing wave in the feedline looks like. From Wikipedia:

If we regard the transmitter to be on the left and the antenna to be on the right, then the blue wave represents the transmitted wave, and the red wave the reflected wave.

Now here's the thing to realize: this particular image depicts a complete standing wave on a lossless transmission line. In this case, we are delivering 0 power to the antenna, the VSWR is infinite, and the transmitter's finals are probably about to explode. This doesn't happen in practice because our antennas always accept at least some of the power.

In practice, only some of the power is reflected back, and the result is a partial standing wave. Dan A Russel has a page of great animations, like this one:

In the case of a partial standing wave, we can see that the envelope (outlined by the dotted lines) does not reach 0 amplitude at the nodes. In this case, some power is transferred. This is also a good visualization of VSWR: it is the ratio of the voltage amplitude at the antinodes (envelope maximums) to the voltage amplitude at the nodes (envelope minimums).

Notice also that the reflected wave might arrive back at the transmitter in any phase, depending on the length of the feedline and the antenna's reflection coefficient. It may or may not be in phase, but it will be a constant phase, not just noise. By adding an antenna tuner we can reflect the reflected wave back at the antenna, and adjust the phase of this re-reflected wave to be whatever we want, within the limits of the tuner's capabilities of course.

Answer 2

...will probably be out of phase with the signal sent by the transmitter.

I think this might help you visualize what is happening when you have an untuned antenna and a high SWR on the line, tuned with an Antenna Tuner.

SWR stands for Standing Wave Ratio. An SWR of 1:1 means that the peaks and valleys of the wave are equal, which is desired. However, a high SWR means that the peaks and valleys (nodes) have a high ratio. If you could go along the feed line and measure the voltage (or current) at different places on the line, you would find that the voltage varied to the ratio of the SWR. In fact, in early radio (1920, for example) this was how they actually measured SWR. They would have a feed line and go with their measuring equipment to sample the voltages along the line.

But the fact is that the Standing Waves were just that - Standing still so they could be measured. The peaks and valleys stayed in place and didn't move around on the line.

This means that the power magically is in phase with itself. The power does not jitter around like you are thinking, instead, the power organizes itself into standing waves. Really. I know that this goes against your common sense. But this is the fact.

So when we say that the radio energy is bounced back and forth between the tuner and the antenna, it is in standing waves that are organized, and reach the antenna (the original signal and the bounced signals) together. And thus are radiated together. The bounced signals radiate a certain percentage on each bounce, so eventually are all radiated (except for heat loss in the line).

Which is a good reason for using ladder line instead of coax when using a Tuner and untuned antenna. Because coax will exhibit greater resistance and greater heat to the bouncy signals with high SWR. Ladder line is much better in this respect.

One more thing. The time lag between the original signal and the bounced signals is very small. Say you are on 7.268 MHz, and say "CQ". The audio will vary maybe 2 or 3 thousand times. But the radio will vary over 7 million times. Each cycle of audio is changed to 2 or 3 thousand radio "cycles". So if the bouncey radio Standing Waves bounce 5 or even 10 times until completely radiated, all of the bounces will be in approximately the same phase of the audio cycle. So it doesn't really matter the time delay of the bounces.

vry 73, Joe W3TTT

Answer 3

The OP quote was originally written by Walter Maxwell W2DU and repeated by others in many places over the years. That is an incorrect theory. Combining powers from two waves of the same frequency depends critically on the phase relationship. Your critical analysis is valid.

One common misconception is that, when a power is reflected back along the feedline to the transmitter, that reflected wave is again reflected back at the transmitter's connector (output port). That is a blind spot of overly abstract thinking. The reflected wave reaches the final amp transistor and increases the collector's voltage swing, or increases the collector current, or some combination, depending on the phase of the reflected wave. Such a consequence will decrease the safety margin of the transistor's operation and may reduce the reliability or blow the transistor. The transistor or the transmitter is an active device that alters its operating point (loadline) depending on perturbation like this, instead of passively causing a mismatch. Therefore, the reflected wave is not re-reflected in any significant way as depicted in the OP quote.

Summary outlines of key criticisms of Walter Maxwell's arguments are cataloged by Steve Stearns K6OIK in the following slide deck on page 22 forward.

https://www.fars.k6ya.org/docs/Stearns_K6OIK-Conjugate_Match_Myths.pdf

Walter Maxwell wrote a book titled "Reflections." "Reflections III" came out in 2010. Its PDF version is found on the web if you search for it. It has 425 pages. This is a very long book. The book is an enormous fiction that uses "technical terms," some borrowed from circuit theory, some from other branches of electrical engineering, but many others make loose uses of analogies from mechanical engineering and other everyday concepts without giving rigorous definitions or proofs. His main concepts are the "conjugate match theorem" and the "maximum power transfer theorem." Those are not theorems because what's stated there is not true. The author took the concept and terminology of maximum power transfer from circuit theory, where the maximum power is transferred from a Thevenin source if the load impedance is the source impedance's complex conjugate (Jacobi's theorem later expanded to the AC cases). However, the author dropped or modified the premises of that last statement quite freely to build his theory. That is the common problem scattered all across his book. Some of the critical mistakes are described in the Stearns K6OIK slide above.

A repeatedly seen mistake in his arguments is the omission of phase components when working with phasor representations of the waves, as explained in the OP's question. Another is using theorems that hold only under lossless conditions to lossy conditions. Another is calculating the reflection coefficient calculated from one condition (e.g., before inserting or adjusting a matching network like an antenna tuner) and continuing to use that number after inserting a matching network as if the reflection coefficient is invariant of such changes.

Building arguments using faulty logic leads to untrue conclusions. Some of them are bizarre, like the quote that appeared in the OP question. Look at Appendix 6 of Reflections III. He argues that the power reflected by a mismatched load is then reflected again at the transmitter and added to the original transmitted power. He shows examples where a 100W transmitter can deliver greater than 100W power to the load by creative uses of mismatches. The author invokes those two "theorems" and mistakes of the kinds mentioned above throughout Appendix 6 and elsewhere in the book.

Additionally, I should add that real transmitters are not approximated by Thevenin sources. The 50 ohm impedance is a nominal impedance with which the transmitter is designed to operate and not the source impedance in the Thevenin sense. When you design an RF power amplifier, it is not that the final transistor has a specific output impedance, but the loadline is designed so that near maximum power along with other necessary requirements (efficiency, distortion, etc.) are attained. When the load changes, simply the load line moves, and the amplifier's output characteristics change. This is a significant discrepancy from the Thevenin source assumption.

Owen Duffy also wrote several articles criticizing Walter Maxwell's statements, with several examples. His main criticisms center around Walter Maxwell ignoring "lossless assumptions" necessary to make specific arguments but still applying to lossy cases, demonstrating that even a reasonably small loss can make sizable departures from what is predicted from lossless cases and ignoring Thevenin source assumption.

https://owenduffy.net/blog/?p=5399 https://owenduffy.net/blog/?p=6427 https://owenduffy.net/blog/?p=9092 https://owenduffy.net/blog/?p=11618 https://owenduffy.net/blog/?p=11631 https://owenduffy.net/blog/?p=11643 https://owenduffy.net/blog/?p=15863 https://owenduffy.net/blog/?p=16207 https://owenduffy.net/blog/?p=16629 https://owenduffy.net/blog/?p=19901 https://owenduffy.net/transmissionline/folla/index.htm

Duffy also discusses anthropomorphism and utopian depiction (e.g., attractively and incorrectly simplified theories and how impedance-matching amateurs wished to work) liberally blended in the "technical" arguments presented in Reflections. The errors are apparent when anyone with an electrical engineering background takes a close look, but the errors are so widespread and wrapped around with loose uses of undefined terminologies, telling stories that some technically naive amateurs love to hear; so many of those statements repeatedly and tenaciously repeated by other authors in amateur radio publications and internet forums.

Answer 4

"After "bouncing" back and forth the part of the signal that will be transmitted will probably be out of phase with the signal sent by the transmitter."

This seems to be the crux of the question. The phase shift in the RF carrier caused by the reflected wave delay(s) is irrelevant because the length of the transmission line can vary the phase shift by any amount including 360 degrees if the feedline is one wavelength long. There is no HF amateur mode that I know of that depends on the phase of the RF signal for data transmission. It would be nice to be able to send a data bit with every HF RF cycle but Mother Nature seems to have other ideas.

So the real question is: What effect does the round trips made by the reflected waves on the transmission line have on the (audio) frequency phase of the modulation of the radiated waves?

With each round trip to the tuner and back to the antenna feedpoint, the magnitude of the reflected wave decreases until it has negligible effect. So let's assume after being re-reflected 20 times, the re-reflected wave has no effect. Let's assume that 20 re-reflections take four microseconds at the speed of light in the medium. Does it make sense that if an individual reflected wave is damped and disappears (losses and radiation) after four microseconds that it cannot possibly have much effect on a modulating signal with a cycle time of 1000 microseconds (e.g. 1000 Hz)?

Since we don't depend upon HF/RF phase shifts to convey any information, worrying about HF/RF phase shifts is a waste of time. Since the delay in the re-reflected waves traveling at the speed of light in the medium is negligible compared to the cycle time of our modulating waves, worrying about audio modulation frequency phase shifts is a waste of time at HF/RF (except maybe for software designers).

However, at UHF and higher frequencies, re-reflections can be a problem.