# SWR Question.

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

Not open for further replies. 1. Perhaps I overlooked it, but I don't remember where you explained the meaning of "phi" and "T" in your earlier comments. Please describe exactly what those terms represent.

73, K5MC

2. Jim, I am not questioning the fact that the phase velocity of the total instantaneous voltage wave varies just as Kraus (third edition, 1984) illustrates in Figure 10-44 on page 442 in his electromagnetics textbook. Indeed, I have derived the detailed equations (at least, for the special case I've mentioned several times now) that provide the numerical values of phase velocity that Kraus hints at.

The problem I have with you here (and, apparently, Tim) is the suggestion that the Smith chart doesn't take this mathematical detail (phase velocity of the total wave) into account and, therefore, the results obtained from the Smith chart are only an approximation. If you will review the fundamental equations that Smith used to develop his chart, I believe you will find the complex algebra and other details are quite in order.

73, K5MC

3. By mathematical x,y axis convention, x is the independent variable, y is the dependent variable.

But you know that's the wrong question. The real generalized question is:

If y = fun(x), which is the dependent variable?

That's probably true, Tim, but I have shown that your math is irrelevant and meaningless. Let's get down to the basics of math.

Given: y = fun(x) for any function other than y equal x,

Observation: If delta-y is kept constant, then delta-x is not constant.

Is the observation true? Of course, it is trivially true. Is the observation meaningless? Of course, it is completely meaningless.

The fact that if delta-phi is constant, then delta-x is not constant, is trivially true for all possible cases (except for the one impossible case, phi=x).

4. I think we are talking by each other. I'll repeat, I have not said that a slotted lines and Smith Chart don't work or have errors. It is transferring the results from the two into real world implementations where the errors occur.

Mickey, you said yourself that you use the null points on the slotted line because they are "sharper".

What does "sharper" mean?

I suspect that it means the voltage rate of change per distance, i.e. dv/dx, is higher at a null. Since dv/dx is also related to the phase change per distance that implies that the greater dv/dx is then the greater d(phi)/dx is also.

If someone were to tell you to move .1radians in phase at a peak on the slotted line (instead of v volts) then how far would you have to move in millimeters? If someone were to tell you to move .1 radians in phase at a null on the slotted line (instead of v volts) then how far would you have to move in millimeters?

If a slotted line measured phase instead of voltage I suspect this would all be common knowledge.

If the two movements on the slotted line are not equal then why would anyone expect them to be equal on any physical transmission line with a standing wave?

tim ab0wr

5. Bzzztttt! That statement is easily proved to be false.

1. Vmin is MOST sharply defined when Vmin=0

2. When Vmin=0, the phase velocity is a constant ZERO at every point on the transmission line.

6. It isn't that the Smith Chart is an approximation for lambda but it is an approximation for "x" if a constant, average B value is assumed during implementation, The Smith Chart doesn't include anything to use as far as "d(phi)/dx" is concerned. The only measurement it provides is in fractional lambda.

That's ok as far as it goes. .1lambda will always be .1lambda. If, however, .1lambda is 10mm in one spot and 90mm in another (e.g. an SWR of 3 with a phase velocity ratio of 9) then the Smith Chart can't be used to determine that implementation detail. And that is where implementation errors come from.

tim ab0wr

7. Correction: It is as simple-minded as that. It is also completely irrelevant and meaningless. Let me paraphrase for you using y=sin(x):

If the change in delta-sin(x) is not constant with increments of delta-x, then simple logic dictates that constant increments in delta-sin(x) WILL result in non-constant changes in delta-x. Whooopppeeee! Will wonders never cease?

So what? That statement is trivially true for every possible case for every possible function in the world (except for the function, y=x).

Why are you guys trying to sell fool's gold as real gold?

8. It means that the slope of the total voltage is maximum at the zero-crossing point and minimum at the peak value point. In a transmission line where SWR is not infinite, the voltage maximum and voltage minimum do NOT occur at the same time. Therefore, one cannot draw any conclusions about phase of the actual wave when dealing only with the envelope of the wave.

9. "convention?" What does "convention" have to do with it?

The basic definition of a function is that one input provides one output.

If I have y-x=0 then *either* can be defined as the independent or dependent variable. If I put in y=1 I get out x=1. If I put in x=1 then I get out y=1.

If I do dy/dx I get 1. If I do dx/dy I get 1.

Now, tell me again which is the dependent and which is the independent variable?

It's not just "probably true" Cecil. It *is* true. If you can't show where my math is wrong then it is only irrelevant and meaningless *to you*. You are using the Argumentative Fallacy of Dysphemism to try and make ithe math "sound" like something that it is really *not*. And that's because you don't understand enough of it to even show *where* it is wrong, let alone irrelevant and meaningless.

trivally true?

You are using the argumentative fallacy of Dysphemism, Cecil -- using descriptive words to make something appear to be worse or more evil than it actually is.

The truth is the truth. Whether it is trivial or not is purely a subjective matter.

The fact that if you hold delta_phi constant then delta_x is not constant is exactly what I've been saying for the past three pages.

You can't expect to move 5mm at a node and 5mm in-between nodes and expect to see the same amount of change in voltage, phase, or impedance on a line with an SWR. What you will see for a constant interval of "x" *is* dependent on where that constant interval is taken.

tim ab0wr

10. Cecil,

Do you see the word "approach" in LYK's posting?

Since when does "approaching" vmin mean the same as "equaling" vmin?

In fact, your argument is a non-sequitur -- that means it doesn't even address the subject at hand.

Vmin is only zero for an open, a short, or a pure reactance. For these standing waves, d(phi)/dx is not even defined at the minimum point since the minimum point is a point of discontinuity in the function.

You seem to be hopelessly lost in this discussion, Cecil. Perhaps you should take a deep breath and re-evaluate what you are actually trying to say. You seem to be trying to prove everyone's math is wrong but you can't and you just keep getting wound tighter and tighter. You are going to burst if you keep it up.

tim ab0wr