Looking Inside the Mismatched RF Transmission Line

[W2DU]

     This post is not specific to AM, but is general to all modes that deliver power to antennas. I have observed that those of you who populate this great AM-Forum Community have a much greater depth of knowledge of what happens inside receivers and transmitters than the average radio amateur. The goal of this post is to advance the knowledge of what happens inside the feed line that allows delivery of all the available power to the antenna when there is even the slightest mismatch at the junction of the feed line and the antenna. I’m sure many of you will be surprised to learn what happens there.

     The original goal of my early writings concerning reflections in 1973 was to dispel myths and misconceptions concerning transmission line operation, such as SWR, reflected power damaging the output tubes in power amps, etc. These myths arose when cable transmission lines appeared after WW2, largely replacing open-wire lines. My writings on reflections culminated in the publishing of my book ‘Reflections—Transmission Lines and Antennas’.

     However, one myth remains among some RF engineers and many amateur radio operators. This myth is that open and short circuits on transmission lines cannot be obtained through wave interference—that open and short circuits can only be obtained by PHYSICAL open or short circuits. I’d like to explain why this concept is only a myth. To do this it will be helpful to first know a little background for perspective.

     In the late 1920s RCA research engineer Philip S. Carter discovered that impedance matching on transmission lines could be achieved by inserting a stub on the line at the appropriate place on the line. Later on, Slater and Alford independently observed that the stub on the line generates a reflection that cancels the reflection caused by a mismatched load terminating the line. But they did not explain the reflection mechanics of the waves that achieves the cancelation of the reflection caused by the mismatch terminating the line.

     While I was designing the rat races that couple four xmtrs operating simultaneously on different frequencies to the antenna array for the World’s first weather satellite, TIROS 1, at RCA’s antenna lab, I advanced on the works of Slater and Alford. In analyzing the rat race I discovered the wave-reflection mechanics that not only establishes the canceling reflection, but also that open and short circuits are involved in the canceling action without PHYSICAL open or short circuits. Because these open and short circuits occur only in the virtual sense I have called them ‘virtual’ open and short circuits. I first published my discovery in QST in October 1973 and have continued it into the three editions of Reflections. (To the best of my knowledge, the concept of virtual open and short circuits has not been published in any publication other than Reflections and QEX.)

An article I published in QEX in the Jul/Aug 2004 issue also contains a detailed explanation describing the wave actions that establish the virtual open and short circuits. At the end of the article I also describe the wave actions occurring in the hybrid ring, ring diplexer or rat-race circuit whose operation requires the use of open and short circuits. But since the hybrid ring consists of only a closed loop of transmission line with no physical opens or shorts, my description proves that virtual shorts and opens are indeed responsible for the wave actions produced in the rat race. I am including a portion of that article in the attachment that also includes the description of the wave actions occurring in the rat race.

I hope you’ll have time to review my discovery that wave action can establish virtual open and short circuits on transmission lines, and how they perform the impedance-matching function.

Walt

[W1RKW]

Not sure if this qualifies as a mismatched feedline but I once had a situation with an antenna where I had high SWR, over 5:1, when connected to the station but nearly 1:1 when using a different length of coax at the feedpoint to measure the SWR.  The main feedline checked OK using an ohmmeter but when connected into the system it just didn't work right.  Someone suggested adding or subtracting several feet and see what happens.  I added about 10ft and SWR was close to 1:1.  I never really understood why that was but figured it was may be something to do with a standing wave situation or where the SWR meter was located in the feed line or a combination of both. . 

[W2DU]

Hi Bob,

A question--after finding a low SWR on adding an additional length of line, did the 5:1 mismatch return if you then removed the additional line? If it did, then there could have been a bad connection at one end of the original line responsible for the mismatch. Simply adding an additional length of line would not normally cause a reduction from 5:1 to nearly 1:1.

In a normal situation the SWR along a line will be constant, except for the small change due to line loss, with the SWR somewhat less at the line input than at the load end. In other words, adding a length of line will not change the SWR significantly when using traditionally low-loss line.

If simply adding another length of feed line resulted in the change you stated, I cannot explain it, unless moving of the cable while attaching the additional line corrected a bad connection somewhere along the line. It would be helpful if you were to remove the additional line and measure the SWR again to see whether the 5:1 returns. If it does I would check all connectors, burnishing them, and then remeasuring the SWR. Hopefully, this will pinpoint the location of the problem. LOL!

Walt

[W1RKW]

Hi Walt,
This was a long time ago at another QTH.  The behavior was odd and I agree. It didn't/doesn't make sense.  But I thought the same about poor connections.  No matter what I did the difference in SWR was there. Maybe there was a problem with the coax itself and the extra 10 ft was a band aid.  Don't know. 

[AB2EZ]

Walt

A source of considerable confusion is the concept of SWR v. the measurement of SWR.

I think most people who are reasonably knowledgable with respect to the concept of SWR would recognize the following

1. There is a travelling wave moving in each of the two directions (East-West and West-East) along a transmission line of a given type (e.g. a 50 Ohm coaxial cable or a 450 Ohm balanced line)

2. At any point along the transmission line, the voltages of the two travelling waves add, and the currents of the two travelling waves add.

3. Because the travelling waves are moving in opposite directions, there are some points along the trasnsmission line (if it is sufficiently long) where the voltages associated with these waves will add in phase. There are points along the transmission line where the voltages associated with these waves will add out-of-phase (partially or completely cancel). Likewise there a points (but not the same points) along the transmission line where the currents associated with these waves will add in phase or out of phase.

4. At any point along the transmission line it is possible to use a directional coupler to determine the amplitude of each of the two travelling waves. This measurement (no matter where along the transmission line the measurerment is made] can be used to calculate the standing wave ratio: defined as: [the voltage at a point along the transmission line where the voltages of the two travelling waves add in phase] / [the voltage at a (different) point along the transmission line where the voltages of the two travelling waves add out of phase].

Therefore the calculated SWR does not change with the posistion at which the measurment is made, if you measure the forward and backward wave amplitudes using a directional coupler. Saying this another way, the reading obtained using an SWR meter will not change if you move the meter to a different point along the transmission line (provided the transmission line's impedance remains the same along its length).

A separate issue is what the ratio of voltage to current is at a particular point along the transmission line. This (complex) number will vary along ther length of the transmission line.

Therefore, it is possible to change the impedance seen (the ratio of voltage to current) at the end of a transmission line by adding or subtracting length to that transmission line. The SWR doesn't change, but the impedance seen at that point does change.

If you have a transmitter whose output circuit can match into a certain range of impedances, then you could significantly improve the match (to a combination of a transmission line and an antenna) by adding an additional length of transmission line... and thus changing the inmpedance at the transmiter's end from an unacceptable value to a value that the transmitter's output circuit can match.

Stu

[W2DU]

What you are saying, Stu, is that the line impedance changes along the line when there are reflected voltages and currents there, which is why adding a length of line can bring the input impedance of the line to one which can be matched to the output impedance of the source. This concept is known universally.

However, this concept occurs when there are only two waves on the line, the forward and reflected waves, which we all know establishes the standing wave.

But that is not the point of my post. If you also review the attachment you will see that there are THREE waves of interest involved in impedance matching on the line: The forward wave delivered by the source (Wave 1), the primary reflected wave resulting from the terminating load mismatch (Wave 2) and the mismatch generated by the stub (Wave 3). When the stub generates a reflection whose reflection coefficient is the conjugate of that generating the load mismatch, the combination of those three waves establish either an open or short circuit at their junction point on the line. Either the open or short circuit totally impedes any further rearward travel of the reflected waves, reversing their direction and adding their power to the source wave.

This is what my post is all about.

Walt

[W2DU]

     Sorry All, I made a serious error of omission in my original post on this thread.  Although the title of the thread “Looking Inside the Mismatched RF Transmission Line.” is technically correct, I can see where it misled you into territory somewhat foreign to those unfamiliar with transmission-line techniques.

     A more appropriate title, still technically correct, I believe would have led more readers to venture into the attachment containing the significant material in the post is the more alluring and enticing, “Looking Inside the Antenna Tuner.”

     We all know the tuner matches the input of the xmsn line to the output of the transceiver, but the question is: “HOW do it do it”? The material appearing in the attachment describes the ‘how’ in meticulous detail.

     We learned from Carter that to establish the impedance match mentioned above, the reflection generated by the mismatch at the antenna-feed line junction is canceled by a compensating reflection generated by a stub on the line. However, what I failed to include is that in our usage, the TUNER generates the compensating reflection that establishes the match at its input terminals.

     What can be learned from viewing the material in the attachment is that when the tuner is adjusted to achieve zero reflected power in the line between the tuner and the transceiver, a virtual one-way open or short circuit to reflected waves is established at the input of the tuner. Thus, when the tuner is so adjusted, it generates a reflection that is the exact conjugate of the reflection generated at the antenna-feed line junction. When these two conjugately-related reflections arrive simultaneously at the tuner input, the result is the one-way open or short circuit to the reflected waves that reverses their direction of travel, thus adding their power in phase with the source power to form the total forward power.

     I hope this belated explanation will entice you all to give a second thought to the material appearing in the attachment. It will explain how the virtual one-way open and short circuits are established that effect the matching.

Walt

[w9ac]

A more appropriate title, still technically correct, I believe would have led more readers to venture into the attachment containing the significant material in the post is the more alluring and enticing, “Looking Inside the Antenna Tuner.”    

Walt,

Although not directly related to the topic of your post, I've always been a  bit baffled over the power transfer from a solid-state amplifier into a transmission line and what occurs when a reflected wave travels back from a mis-matched load to it's solid-state, fixed output Z source.  I understand the mechanics of a complex network placed anywhere on the line, including a network placed either at the load or at the transmitter (e.g., Johnson Matchbox in the shack).

But in the case of a solid-state transmitter with broadband amplifier and no internal ATU, what happens to the reflected wave on a 50-ohm lossless line?  What I see is a wave traveling back from the load to the fixed output Z of the source generator.  If that Z looking back into the transmitter is 50 ohms, then all reflections would absorbed by the source (e.g., a classic generator).  Is a fixed-solid stage output not a classic generator, but something more complex and that complexity may change with perhaps...class of amplifier (e.g., push-pull B, or C)? 

So then, exactly what does the reflection see in this circumstance and what is the nature of the mechanics causing it?  Many Tnx!

Paul, W9AC

[W2DU]

Sorry Paul, I don't know the answer to your question, as I'm not knowledgeable concerning solid-state RF amps. The most I know about their operation is that they contain a fold-back circuit that reduces their output in proportion to the amount of reflected power incident on its output. Simply a protective device.

Wish I could help.

Walt

[WA1GFZ]

A solid state amp can do a number of things with reflected energy. Say you reflect a high voltage. This can take out the finals when a high voltage pulse lands on the collectors or drains. When the voltaghe is higher than the device ratings the part can short. If you reflect a low impedance back at a solid state final the output power can go higher increasing the current above the device ratings. A high impedance reflected back reduces the output power. I"ve run my class e rig into an open many times withiout effect. Once a tree took my antenna down. I didn't notice the swr was pegged and took out a final after keying it a number of times. The tuner was flashing over so suspect there was a high voltage reflected.

[KA2QFX]

From a mind's eye perspective it's convenient to think of a mistmatched transmission line as have two sets of independant I and E waves traveling in different directions. And in fact the source and reflected waves are not imaginary.  But at any single point on the line all these waves do sum up to a single voltage and current whose magnitudes determine the observed impedance and whose phase angle determines the observed reactance.  Once this conceptualization takes hold it is easier to see why a VSWR bridge will read differently at different points on the line, or change with line length, as was described.  Different directional couplers will have more or less success at dealing with changes in line impedance but that's a subject for another thread. 

An enjoyable little piece of software, TLDetails http://www.ac6la.com/tldetails.html , that I highly recommend, will enable you to see just such changes in impedance on mismatched lines as well as the associated loss due to SWR, etc. 

For those who haven't read Walt's book on transmission lines, it's a must have on every ham's bookshelf.

73,
Mark

[W2DU]

Thank you for the nice words concerning my book, Mark, but if you review it carefully, you'll find that it disagrees with one of the statements in your post above.

It is true, as you said, that line impedance and phase angle change along a mismatched transmission line. But it is not true that the SWR bridge will read differently at different positions along the line. Except for a small, gradual change due to line attenuation, the SWR doesn't change along with the change in line impedance along the line. On lossless line there is absolutely no change in SWR along the line. Nor does the SWR change with a change in line length, although line impedance and phase do change with different line lengths. 

Sorry to have to tell you this,  Mark, but this misconception is prevalent, and it is one of the misconceptions that certain chapters in my book clarifies.

Thanks again for saying my book should be on every ham's bookshelf. Your assessment is greatly appreciated.

Walt

[G3UUR]

Paul, no active devices generating RF power behave like ideal Thevenin sources. The impedance seen by any reflected waves that can only ever vary the collector or plate voltage will be dependent on the collector or plate resistance of the device, the conduction angle and how hard the device is driven if it’s operating in a linear mode. Consequently, the source impedance for the outgoing wave will be quite different to what the reflected wave sees.

Walt, I think there have been many reported cases of amateurs putting two SWR bridges in-line at the same time and getting different indications. They don’t realize that production variations and calibration differences will cause variations in the SWR indicated by the bridges. Also, some bridges don’t have a constant Zo through them and upset the SWR on the line slightly anyway. The hybrid form of SWR pick-up (the type using two transformers) can also degrade the SWR presented to any amplifier or a second bridge quite badly if the transformer inductance is insufficient for the frequency involved. I’ve seen several designs where the transformers appear to work perfectly in the pick-up, but present an unacceptable reactance in shunt with the transmission line and mess up the SWR. I think Mark may have been influenced by hearing about some some of these cases.

Dave.   

[w9ac]

Paul, no active devices generating RF power behave like ideal Thevenin sources. The impedance seen by any reflected waves that can only ever vary the collector or plate voltage will be dependent on the collector or plate resistance of the device, the conduction angle and how hard the device is driven if it’s operating in a linear mode. Consequently, the source impedance for the outgoing wave will be quite different to what the reflected wave sees.

Dave, many thanks for this clarification.

Paul, W9AC

[KA2QFX]

Walt,
You and I do not disagree at all on the consistency of the standing waves being constant along the line (allowing for a minute line loss).  But I can assure you there are plenty of poorly implemented SWR bridges out there which do not function well when the apparent line impedance shifts due to the mismatch. Which is to say there directional isolation stinks.
Plenty of hams have fallen prey to such erroneous readings, making it difficult to dispel the myths so prevalent in this hobby. I make a lot of ferrite RF transformers for various applications, many of them have been used in a Breune "type" of bridge arrangement.  I have discovered that many manufacturers  using a single I transformer will add the E component at the center tap of the I transformer, saving them a second variable cap.  The interaction between forward and reflected voltages summed at the opposite ends of the transformer leads to a lot of error when the SWR exceeds about 2:1.  I prefer separate transformers and cap voltage dividers whenever possible.

The worst I've seen are "Radio Shack" type bridges using long coupling rods parallel to the line, with a diode at one end and a resistor at the other.  The coupling varies wildly with frequency and they rarely look like a 50 ohm section. Well, maybe @ 27 MHz. 

The prevalence of this junk helps support many misconceptions, as you well know.  One of my pet peeves is the confusion between duplexer and diplexer.  The merchants at the flea markets sell these VHF/UHF splitters with "DUPLEXER" right on the packaging.  How can you argue with that? 

Many thanks for your contribution to the art Walt.

Regards,
Mark

[W2DU]

Right  on, Mark,

What needs to be emphasized here is that there is a big difference between no-change in SWR along the line versus an apparent change due to faulty SWR indicators. Sad, but true.

Walt