The Dark Side of the Conjugate Match

Discussion in 'General Technical Questions and Answers' started by KL7AJ, Mar 12, 2010.

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  1. W8JI

    W8JI Ham Member QRZ Page


    I've given this some thought and I think I see what confuses people about behavior of inductors and tank circuits. Some seem to assume phase delay is caused by transmission line effects inside a typical tank, or the tank is a transmission line that conveys energy from tube to the load.

    They don't realize that magnetic flux links all turn in an inductor, and so long as turn-to-turn flux coupling is high what happens at one terminal of a inductor pretty much follows at the other so far as current.

    While everything, even one inch of lead from a tube anode to the tube connector on top of the tube, does behave like a transmission line the effect is very small compared to the lumped effects in well-designed systems. The extreme exception would be a strip line amplifier, where matching is indeed done with multiple transmission lines.

    In other words if I take a well-designed inductor with tight flux coupling and apply a voltage to one terminal, with the return through "ground", chassis, or groundplane, current rises and falls in virtual unison at each end of the inductor. The reactance slows the rise of current considerably, but does so at BOTH terminals in near unison.

    So we have a capacitor shunting the input of a tank, which slows voltage rise but does not delay current rise (it actually speeds it up). Then we have the tank inductor which at both terminals has current rise slowly through that path, which delays current rise in the loading capacitor.

    The energy storage in this system is very high, because capacitors store and release energy back and forth with the inductance.

    This stored energy dominates the system, with the tube just tugging a little bit on the tank for a fraction of every RF cycle. The "real" energy is normally small, perhaps 10% or less of the stored energy caused by loaded Q of the tank.

    Since the predominant energy is stored energy and the tube tugs such a small amount of energy compared to stored energy, we pretty much can just view the normal tank as a source without transmission line effects, that's what we want to use!!

    Using something else like a transmission line model with standing waves just over complicates the problem, and is not a good tool for describing on the system works.

    73 Tom
  2. KL7AJ

    KL7AJ Ham Member QRZ Page

    Like a lot of other aspects, it's a matter of degree. Unless an inductor is infinitely small, it's going to have some transmission line properties, (no matter how infinitesimal) as well as lumped constant properties. A helically wound vertical is particularly complex to analyze because you have a coil which is partly lumped and partly radiating. A true lumped constant would have equal current in every part of the coil...which is probably as good a test for "lumpedness" as any.

  3. W5DXP

    W5DXP Ham Member QRZ Page

    Adjacent turn coupling is high. Coupling from turn #1 to turn #100 in the 10 inch long coil that you tested is virtually non-existent. According to the Hamwaves inductance calculator, the the velocity factor of your coil is ~0.14. If the current was following the wire without any adjacent turn coupling, the velocity factor would be ~0.057. The inductive coupling between the turns causes a reasonable ~2.5 times increase in the velocity factor of the coil.

    Your 3 ns "measurement" requires an unbelievable increase of ~17 times in the base velocity factor. Note that the 2.5 times increase in the velocity factor is reasonable given the coupling from one turn to the two adjacent turns. The coupling falls off extremely rapidly past the adjacent turns. An increase of 17 times in the base velocity factor is simply impossible.

    You are quoted on the Hamwaves inductance calculator web page, under "What is the problem with other inductor calculators?", as complaining about the accuracy of the other inductance calculators. Why not just accept the Hamwaves calculator results? Your coil has an axial propagation factor of 2.122 radians per meter at 4 MHz which prohibits your coil from having a 3 ns delay as reported on your web page. The Hamwaves inductance calculator indicates a delay of ~21.5 ns which is a lot more believable than 3 ns.

    In the argument concerning reflected energy being incident upon the load-line, that very small effect in that one inch of wire is all important. It means that the source cannot respond instantly to the load change and must necessarily wait for the feedback from the load to arrive back at the source. It means that all changes in the source load-line due to a change in the load is because of feedback from the load in the form of reflections, i.e. the source has to wait for feedback from the load to know how to adjust its load-line. It's a very simple concept, based on the existing laws of physics. Any other explanation involves instant faster-than-light feedback from the load.

    Here is the crux of your misconception. You are testing the coil in an environment which is almost pure standing wave current. No matter what the delay through the coil or how many degrees the coil occupies in the antenna, the relative current phase doesn't change between the bottom of the coil and the top of the coil just like the relative current phase doesn't change through out all 90 degrees of a 1/4WL lossless stub. You can use exactly the same measurements that you used on your coil to prove that the current at one end of the stub has the same phase as the other end of the stub 90 degrees away. It does not mean that current is flowing through the stub at faster than the speed of light.

    The phase of the current is almost the same in a monopole from the feedpoint to the top of the monopole. If you cannot measure the phase shift in a 1/4WL monopole, why would you think you can measure it in a coil in the middle of a monopole?

    Tom, we need to over-complicate the problem so you (and W7EL) will understand your measurement errors. If you take a 1/4WL monopole and measure the phase of the currents at the 1/3 and 2/3 points, it will be almost exactly the same. Why are you surprised to measure the same conditions in a loading coil that replaces 1/3 of a 90 degree monopole?

    FP----------x----------y---------- top of monopole

    Let me repeat. You will measure virtually the condition in the currents at points x and y even though we know that is 30 degrees of the antenna. We can replace that 30 degrees of antenna with a loading coil and obtain the same results.

    Here is what happens in a loading coil in a standing wave antenna:

    Pure standing wave current doesn't flow. Therefore there is almost no difference in current phase anywhere along a standing-wave antenna like a 75m mobile loaded antenna. Standing wave current phase cannot be used to measure current delay through a coil or through a wire. You need to use traveling wave current for that purpose.
    Last edited: Sep 26, 2010
  4. W8JI

    W8JI Ham Member QRZ Page

    An on-line calculator proves two totally independent people's real measurements wrong. One was measured with a coil and a load resistor at the far end, not a resonant antenna at all, yet years later standing waves in an antenna are blamed for the results.

  5. W5DXP

    W5DXP Ham Member QRZ Page

    What is really amazing is that you choose not to investigate the discrepancy between your and Roy's conclusions vs what the most sophisticated impedance calculator indicates. What are the odds that you and Roy share the same misconception in interpreting your measurements? It's certainly NOT zero. Your picture is on the Hamwaves inductance calculator page along with your request for a more accurate calculator. They gave you one and now you protest that it is not accurate?

    Tom, the SWR in your coil/resistor circuit was sky high. You used a 50 ohm source. What would have been the forward and reflected power readings on a Bird wattmeter? They would have been almost the same if you had bothered to measure them. What was the impedance of your coil/resistor combination? R + jX was no doubt sky high. The reflection coefficient from such a load is very close to 1.0. If you don't believe that, calculate the reflection coefficient. Here is the equation for almost all of the current in your test system referenced from the source terminal.

    Itot = Vmax*sin(kx)*cos(wt) where x is the distance away from the source.

    At any point x, [Vmax*sin(kx)] is the amplitude term. cos(wt) is the phase term. The relative phase doesn't vary with x and doesn't change appreciably anywhere up and down the circuit! The same thing is essentially true for the current on a standing-wave antenna. You and W7EL made the same conceptual blunder because neither one of you understand the implications of using current that doesn't change phase to try to calculate the delay through a loading coil. No matter what the actual delay through the loading coil, you and Roy will always measure close to zero phase shift whether it is through the coil or through a 37 degree long piece of wire. See below.

    As you can see, the phase of Itot has nothing to do with the x position on the wire so the phase of Itot is the same no matter where it is measured. Therefore, the current you were using is useless for relating phase to delay since, at any point in time, the phase is the same throughout the circuit.

    Here is a challenge for you. Re-run the experiment except this time change the coil to one large loop of wire about 25 feet long. Now there is no turn-to-turn coupling yet your results will be the same. You will detect almost zero phase shift in that 25 feet of wire even though 25 feet of wire at 4 MHz is known to be about 37 degrees long. How does the current jump instantly, at faster than light speed, from one end of a 25 foot piece of wire to the other end? Why can't you measure any phase shift in 37 degrees of wire? See the above Itot equation.

    In your coil measurement methodology, you assumed the lumped-circuit model which presupposes faster-than-light travel in the RF energy. The lumped-circuit model presupposes zero reflections which will probably be your next argument. In order to measure the actual delay, you would have to eliminate (or minimize) the reflected current in the circuit. Here is what you would have to do to actually measure the delay through the loading coil. For your coil, change the 4000 ohm values to ~4600 ohms, the ~Z0 of your coil predicted by the Hamwaves inductance calculator.


    You have already admitted that reflections can occur when the load is one inch away from the source. Your test coil was ten inches long. I suspect the physical distance around your test loop was ~20 inches. The problem with both yours and Roy's conclusions from your measurements is that you assumed the lumped-circuit model which ignores reflections and presupposes faster-than-light propagation of RF signals. Your presumptions were wrong and you paid for it with misconceptions based your measurements. Your measurements were correct - there is no appreciable phase shift in standing-wave current. Your conclusions were wrong based on misconceptions, i.e. that the phase shift in standing wave current can be used to predict the delay through a loading coil. It cannot.
    Last edited: Sep 26, 2010
  6. W5DXP

    W5DXP Ham Member QRZ Page

    I forgot to add: It wasn't your and Roy's measurements that were wrong, It was your conclusions drawn from the measurements that were wrong. The standing-wave current phase on each end of a coil simply doesn't yield valid calculated results for the delay through the coil or even through a wire.

    To W7EL's credit, I cannot find anywhere that he supports your 3 ns delay through a 100 turn air-core loading coil. He correctly reports a negligible phase shift in the (standing wave) current through a loading coil. Nowhere that I can find does he assert that the phase shift in the current measurements are related to the delay through the coil. All he does below is report valid measurements. What he doesn't say below is that your interpretation of the measurements is technically valid. Perhaps W7EL agreed with your conclusions about the measurements, but he avoids saying so on this web page.

    In fact, Roy earlier agreed that there is no appreciable phase shift in the current from the feedpoint to the top of a 1/4WL monopole, whether a loading coil is present or not. In any previous argument about such, Roy deliberately retreated to a physically small ferrite toroidal inductance to prove his point. The Hamwaves inductance calculator doesn't cover ferrite inductances. To the best of my knowledge, W7EL knew better than to attempt to prove his point using a large 100 turn, air-core loading coil as his example.

    Perhaps you should check with W7EL to see if he agrees with your 3 ns delay through your 75m air-core loading coil. I'm willing to bet Roy doesn't agree with that 3 ns delay that you allegedly "measured". I'll bet that he only agrees with your phase shift measurements which are unrelated to the delay through the coil.
  7. W5DXP

    W5DXP Ham Member QRZ Page

    A few more thoughts:

    That was the experiment in which you reported a 3 ns delay through a 100 turn loading coil based on the non-changing phase in standing-wave current. The Hamwaves inductance calculator indicates that the delay through that coil at 4 MHz is close to 21.5 ns which is ~31 degrees at 4 MHz.

    If the coil is 31 degrees and there are a couple more degrees in the wiring, that circuit is ~1/3 wavelength long, i.e. it is a distributed network. For certain parameters, the lumped-circuit model will give erroneous results in a circuit that is 1/3 of a wavelength long.

    In terms of classical logic, what you have done is called Petitio Principii, begging the question and assuming the proof.

    If you instead assume the circuit is 1/3WL long at 4 MHz and make the appropriate measurements, you will see that the circuit is indeed close to 1/3WL long. But you cannot prove it using standing-wave current which shifts phase hardly at all except at the current nodes where it shifts by 180 degrees. In order to detect the phase shift through the coil you must eliminate (or at least reduce) the reflections in the network and use traveling wave current for the phase measurement.
  8. WR9H

    WR9H Ham Member QRZ Page

    Hello Cecil,

    I think your arguments are interesting but esoteric. My suggestion, to you, is this: set up the coil experiments and "see what you get".

    These experiments would not be terribly complex and the results, if posted, would be interesting.

    Here's my suggestion for another experiment: connect a mismatched load to a transmitter BUT design a device (perhaps lumped reactances) that absorb the reflected wave BEFORE it reaches the transmitter. What would the transmitter do?

    My prediction: burn out the finals, or if using hollow state, produce high plate currents! Here goes: the miss-matched load is the "problem" not the reflected wave!!

    Now play nice...hihi!

  9. W5DXP

    W5DXP Ham Member QRZ Page

    Herb, this argument started about seven years ago. Over the years, I have posted the results of many experiments and many simulations using EZNEC - all to no avail. Years ago, I posted my ~23 ns delay measurement for my 75m Texas Bugcatcher coil tested on 4 MHz. I used a 100 MHz dual-trace scope for the measurements so they were not extremely accurate but the delay was certainly nowhere near the 3 ns reported by w8ji. Those postings are hopefully archived on Google groups r.r.a.a. Here are a couple of web pages that resulted from my experiments and simulations:

    The most convincing argument is the current through a monopole. Points x and y are the center 1/3 of the monopole.

    FP----------x----------y----------top of monopole

    According to EZNEC, the phase of the current changes by one degree between x and y for a thin wire yet we know that there is 30 degrees of antenna between points x and y. So how can the phase measurement in a monopole be used to calculate the delay in the wire? Hint: It cannot. If it cannot be used to calculate the delay in the the wire, how can it possibly be used to calculate the delay in the loading coil that replaces the wire? It also cannot be used for such but that is exactly what w8ji and w7el did and reported their results as valid delay measurements.

    I told the two of them seven years ago that they needed to use traveling wave current instead of standing wave current and w7el said, "Current is current, there's no difference" even though the equations for the two types of current are quite different.

    Traveling wave current = Imax*cos(kx+wt)

    Standing wave current = Imax*cos(kx)*cos(wt)

    If we replace the x to y wire length in the diagram above with a loading coil, we get approximately the same phase readings as the 30 degrees of wire. How can anyone say there is negligible delay through the loading coil when we know there is a 30 degree delay through the wire it replaced and the phase measurements are essentially the same in both cases?
  10. K4VLF

    K4VLF Ham Member QRZ Page

    Cecil, experiments for reflection time measurements:

    It would seem fairly easy to setup your favorite CW generator, to a TL, to a electronically switchable load (FETs?) .

    Connect good digitizing scope to load and generator.

    1) Enable generator at T zero and trigger scope. See load voltage increase at T zero + prop delay.

    2) Change load at T one and trigger scope again. Verify voltage change at CW source at T one + prop delay.

    If needed, add the tuner function in the equation. And if a CW signal makes measurements painful, just use the first half cycle from a good rf generator.

    Would not this simple test show that it is the reflected energy is causing a change at the generator (which is what I think are trying to prove).

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