# SWR Question.

Discussion in 'General Technical Questions and Answers' started by KD8GFC, Jul 17, 2008.

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1. ### AB0WRHam MemberQRZ Page

Cecil,

You are trying to sound very learned and knowledgeable but what you are saying makes no sense at all. If y=f(x) then (d/dx)f(a) = (dy/dx)(a) -- the slope of the line defined by f(x) at position "a" on the x-axis. Neither dx or x are "constant" nor is dy a constant.

If you would have answered the questions I asked you this would be obvious by now.

If d(phi)/dt = (-2pi/T)

then dt = (-T/2pi)d(phi)

If v = dx/dt

then, substituting for dt you get:

v = dx/[(-2pi/T)d(phi)] = (-w)/[d(phi)/dx]

So you now have v, i.e. phase velocity, based on the slope of the phase vs distance function. Since we know that phase velocity, v, changes from a max to a min as you move along the transmission line from node to node with a ratio equal to VSWR^2 , then we also know that d(phi)/dx must also change as you move along the transmission line.

If d(phi)/dx changes as you move along the line then the amount of "x" movement needed to effect a specified amount of phase angle change also changes based on your position on the line.

Before you tell me again that I am missing a simple mathematical point you *NEED* to be able to show me where my math above is wrong. If you can't do that then stop telling me I am missing a simple mathematical point. You tried doing that with my math in the complex plane and wound up with egg on your face. If you can't show me where my math above is wrong you run a very real risk of doing the same thing with this analysis.

See my answer to Mickey on this subject. You are not just arguing with me but with Dr. John D. Kraus whose math I am paraphrasing.

tim ab0wr

2. ### W5DXPHam MemberQRZ Page

You are trying to force 'x' to be a function of 'phi' when it doesn't even meet the definition of "function".

The point that you continue to miss is that phi is the dependent variable and x is the independent variable, i.e. phi varies with x, not vice versa. You are turning cause and effect upside down. This is such a basic mathematical principle that, if you don't get it by now, you are unlikely to get it at all. Length and time are primary elements in space-time calculations. Phi is the dependent result.

Paraphrasing what you have said: The amount of time movement needed to effect a specified amount of phase angle change also changes based on your position on the time line. Does that really make any sense to you? Phase angle is a function of time. Time is NOT a function of phase angle. Increments of time do not change length with phase angle. Neither do increments of length.

Mathematical functions must meet certain defined requirements. It can be easily proven that phase angle is a function of the length 'x'. It can just as easily be proven that 'x' is NOT a function of phase angle. Math 101

Last edited: Jul 31, 2008
3. ### K5MCHam MemberQRZ Page

I believe I understand what you are saying here, Tim, but it's my opinion that you are adding an unnecessary layer of complexity by suggesting that B is not the "actual" phase constant. Mathematically, the instantaneous velocity of the constant phase point P of the total instantaneous voltage wave can be derived without taking the viewpoint you seem to suggest. (And I'm reasonably sure that the vast majority of professional engineers who work, write, or teach in this subject area agree with my viewpoint rather than yours.)

If you are suggesting (or still suggesting) that there are inherent errors in using a Smith chart and slotted line in solving the classic transmission line problems (determining the impedance of an unknown load, designing a stub tuner, etc.) because engineers fail to consider the fact that the phase velocity of the total instantaneous voltage wave (and current wave) is not constant, then I do disagree with you on that point.

73, K5MC

4. ### AB0WRHam MemberQRZ Page

Mickey,

B is the average value of phase velocity. Insofar as the "average" is a "constant" then B is a constant. The "average" certainly shouldn't be expected to change when using a fixed component. That doesn't mean that phase velocity is constant on a transmission line. If phase velocity isn't constant then the distance you need to move on the transmission line to effect a specified phase change (which implies a specified impedance change) is different at different points on the transmission line.

The derivation used to arrive at this is probably irrelevant.

The Smith Chart and slotted lines work fine. As I said before the problem is the *implementation* of the results obtained from these tools. If the Smith Chart says you need to move from .13lambda to .14lambda for stub 1 location and from .23lambda to .24lambda for stub 2 location and you assume that this implies moving the same "x" distance on the transmission line (i.e. B is a constant that applies everywhere on the transmission line) then it is quite likely that your implementation will not give exactly the results you expect. I've seen a lot of people just shrug and say "well, my measurements must have been off and I'll just make an adjustment" when, in fact, part of the reason the measurements were off is because they didn't realize they had a built-in "off factor"!

tim ab0wr

5. ### AB0WRHam MemberQRZ Page

No, Cecil, phi is a function of x. The amount that phi changes for a change in x is d(phi)/dx. The amount of change in phi for a change in x does *NOT* have to be a constant.

Phi *does* vary with x, Cecil! What do you think the term "Bx" in (wt-Bx) is? The *amount* of change in phi for a change in x *is* d(phi)/dx.

If I want a change in phi of pi/16 radians I might have to move delta_x=1 in one spot on the transmission line and delta_x=2 in a different spot on the transmission line because d(phi)/dx is not the same everywhere.

You are being a troll again, Cecil -- pure and plain.

No, that is NOT what I have said. You are being a troll again making up your own strawmen to argue with. How do you get a change in "time" out of d(phi)/dx?

It's *YOUR* strawman, does it make sense to you?

You are a troll that has gone back to living only on the Real axis.

I'll ask again: in the term e^j(wt-Bx) what do you think the term "Bx" is? (hint: it has the same dimensions as "wt").

The amount of time needed to effect a specified change in phase angle *is* dependent on the speed at which the phase angle is changing in time, Cecil. That "speed" is defined as "w" (omega).

What do you suppose the relation d(phi)/dt represents, Cecil?

What is the definition of a function, Cecil? (hint: single output to a single input)

If I give you the relation: y-x=0, which is the independent variable and which is the dependent variable?

tim ab0wr

6. ### K5MCHam MemberQRZ Page

Tim, the Smith chart and slotted line do work for the classic transmission line problems and the results obtained from these tools are valid. There's no built-in "off factor" in the implementation of these results.

I guess we will have to agree to disagree. Without sounding too sarcastic (I hope), I think you should submit your ideas here to a professional journal. Perhaps you are correct and I am all wet.

73, K5MC

7. ### W5DXPHam MemberQRZ Page

Yes, now you are getting it exactly as I have been saying all along. phi is a function of x. x is NOT a function of phi, as you implied (without realizing it?). Your artificial constant amount of change in phi is bogus smoke and mirrors since phi never undergoes a constant amount of change during a delta-x. It is the independent variable x that undergoes a constant amount of change using the rules of ordinary calculus. Perhaps you have invented a new version of calculus where the previous rules don't apply.

The fact that an artificially constant delta-phi results in a ever-changing delta-x is completely irrelevant since phi is not the independent variable. You can just as easily say a constant delta-sin(x) results in an ever-changing delta-x. It is just meaningless drivel. You have a habit of taking an obscure irrelevant tidbit of math and blowing it out of all proportion while violating the rules of classical math. I wish you wouldn't do that.

Yes, you got it. Now please stop implying that x is a function of phi. Delta-x --> dx in the limit, is a constant since x is the independent variable. When you artificially suggest that delta-phi --> d(phi) in the limit is the new-and-improved actual constant, you are in violation of the rules of mathematics since phi is the dependent variable. It is an example of trying to pull the wool over the eyes of the uninitiated using mathematical smoke and mirrors. You did the same thing in the past when you tried to get away with dropping the e^jwt terms thus completely ignoring the instantaneous values when the IEEE definition requires instantaneous values.

EXACTLY! - and that's why x is NOT a function of phi as you imply (without realizing it?) If x were a function of phi, as you imply, x would be multiple-valued in violation of your own above statement.

With this last posting, you have just admitted that most of your other postings are invalid (without realizing it?) How did you ever expect to get away with violating the rules that you just posted?

Last edited: Jul 31, 2008
8. ### AB0WRHam MemberQRZ Page

"phi never undergoes a constant amount of change during a delta-x."

What in holy blue blazes do you think I've been saying, Cecil?

This means that d(phi)/dx is not a constant!

You are still trolling, Cecil. Why don't you stop?

Answer the question: If y-x=0 what is the independent variable and what is the dependent variable?

You have not shown in any manner that my math is wrong, Cecil. Without showing how the math is wrong, there is *NOTHING* in my posts you can say is invalid. You've done nothing but troll the forum and beat a strawman to death.

Answer the following questions. They are simple math and math relations.

Is the statement: d(phi)/dt = (-2pi/T) wrong?

Is the statement: dt = (-T/2pi)d(phi) wrong?

Is the statement: v = dx/dt wrong?

Is the statement: v = dx/[(-2pi/T)d(phi)] wrong?

Is the statement: v = (-w)/[d(phi)/dx] wrong?

If you can't show where any of the statements are wrong, then how can you claim what I have said is invalid?

You are still trolling, Cecil, nothing more. Show me the math that shows I am wrong.

tim ab0wr

9. ### WA0LYKHam MemberQRZ Page

Mickey, some time back you said the following:

If the Vmin points are more sharply defined than the Vmax points, then the only conclusion you can arrive at is that the phase velocity has a different value as you approach each of these points. When you also assume that the phase determines the impedance seen at that point, then the impedance change per given distance must also vary as you approach each of these points. A Smith chart simply doesn't take this into account which means it is only an approximation.

The only other conclusion that can be arrived at is that the instantaneous phase velocity DOES NOT have a relationship to the change in impedance as you move from point to point. That is, that the instantaneous phase velocity is not related to the impedance change per given distance measurement. This would require the impedance to be related to some other variable whose phase velocity is constant and would result in the same change in impedance for each equal distance measurement. However, this would also make finding Vmax and Vmin equally easy when using a slotted line. A Smith chart would be absolutely accurate if this conclusion is correct.

Jim
WA0LYK

10. ### WA0LYKHam MemberQRZ Page

If the change in delta-phi is not constant with constant increments of delta-x then simple logic dictates that constant increments in delta-phi WILL result in non-constant changes in delta-x. It is as simple as that.

Figure it out symbolically on your own. If you have the following points, x=1, phi=1 and x=2, phi=4 and x=3, phi=9, what is the value of x when phi =1 and when phi=2 and when phi=3?

The relationship only implies what you want it to imply. It makes neither constant increments of delta-x or constant increments of delta-phi incorrect.

Jim
WA0LYK