# SWR Question.

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

Not open for further replies. 1. Seems the importance of the standing-wave has been over-emphasized. One of the authors of one of my references says that a "standing wave" doesn't meet the definition of a wave at all since it doesn't transfer energy and probably shouldn't even have been called a wave.

The superposition principle gives us permission to consider the two traveling waves separately and add the results to obtain the total. There is never any reason to consider the standing wave as a stand-alone entity. It's very existence depends upon the two underlying traveling waves without which it wouldn't even exist.

Some people have gone so far as to assert that the standing wave causes the reflected wave to cease to exist and the result is a "mashed potatoes" version of energy on a mismatched transmission line. IMO, that is just another indication of the dumbing-downward spiral that is evident in the American educational system.

Mathematical curiosities do not alter or create reality.

2. The impedance seen on the transmission line is a function of the standing wave voltage and current in space, not the time variant instantaneous values of the forward and reflected wave. It is dependent on the interaction between the forward and reflected wave. This means the impedance curve follows the same shape as the standing wave. If you want to stick an impedance matching device at a point on the transmission line where the Impedance = Z you can assume an average impedance change value between min's and max's (i.e. a straight line from max to min) and use a Smith Chart to find a point of attachment.

Doing this, however, will *never* be totally accurate (except right at the nodes themselves), especially if the impedance point is near a minimum where the phase velocity, and therefore impedance, changes drastically as you move along the transmission line. The closer you are to a voltage or current min the more this will be noticed.

Whether this actually intrudes on reality will depend a lot on how "reality" is implemented. If actual physical measurement error is more than the error this phenomenon introduces, who cares? I've always wondered, however, when someone says they had to add more length or take length away from stubs or change their placement or even when trimming an antenna doesn't produce exactly the calculated results, how much of this is from assuming the impedance curve between min and max points is a straight line when it really isn't?

tim ab0wr

3. Actually, the impedance seen on the transmission line is (Vfor+Vref)/(Ifor+Iref), i.e. the total superposed phasor voltage divided by the total superposed phasor current. An impedance based only on the standing wave voltage and standing wave current would always be purely reactive because a "standing wave", as defined in The IEEE Dictionary, is incapable of delivering power to the load. The traveling wave being delivered to the load has a large effect on the impedance seen on the transmission line and furnishes all of the resistive component (in a lossless transmission line).

4. Tim, it seems to me that nobody who understands how to use a Smith chart (or the various algebraic equations) to make these types of transmission line calculations would ever assume that the impedance curve follows a straight line.

73, K5MC

5. I suspect I am not being precise.

Beta, B, the propagation constant is d(phi)/dx. Phase velocity, vp, is w/B. (where w is the angular frequency).

Thus if the phase velocity is not constant then B is not a constant either. If B is not a constant then d(phi)/dx is not a constant. This implies that "x", the distance needed to move from one value of phi to another value of phi, is not a constant. This also implies that lambda, the wavelength, is not a constant either since lambda = 2pi/B. If Beta changes as you move in space along a transmission line then so does lambda.

Since the impedance at any point on a transmission line is related to (wt-Bx), this means that it is also related to B or d(phi)/dx. This also implies that the distance needed to move from Impedance1 to Impedance2 at different points on the transmission line is a variable.

In essence, the Smith Chart makes no allowance for this at all. Almost everyone I know assumes that moving from 3.4+j2 to 4.2+j1.2 (moving from .23 lambda to .24 lambda) on the Smith Chart will require moving the same "x" distance on the transmission line as moving from .35+j1 to .4+j1.3 (.13 to .14 lambda). This is because they just use the average lambda=w/B value for the line.

This obviously cannot be true if d(phi)/dx is not a constant as you move along the transmission line. You could rewrite (wt-Bx) as [wt - (d(phi)/dx)x].

So I guess what I am saying is that d(impedance)/dx is not a constant although most people assume that it is.

Does this make any sense at all?

tim ab0wr

6. Cecil, stop and think about what you are saying. Preferably, lay it out with some math backup.

It would seem that you've now come around to the point of view that all of the power inserted into a transmission line does *not* get absorbed by the load -- only that part of the power represented by the traveling wave gets absorbed.

Is that *really* what you want to imply?

tim ab0wr

7. If most people assume that, then most people are pretty foolish. dZ is a complex number with increasing/decreasing amplitude/phase. dx is a real, linear constant number. Seems dZ/dx cannot possibly be a constant. Here's some web pages that might help: http://www.rfmwdesign.com/Smith_Chart.html

You 2 guys have made this a pissing match out of a simple question. Back off and answer the question in simple terms the man can understand which after 2 pages you haven't although others said what needed to be said without the boxing match.

K2WH

9. Cecil, you've gone back to being a troll.

The propagation constant Beta (B) = w/vp where w=angular frequency and vp is the phase velocity. If vp is a variable then Beta is a variable.

Perhaps you would like to list out all the characteristic attributes dependent on Beta.

Concentrate specifically on d(phi)/dx.

Then tell us again how dx can be a real, linear, constant number.

tim ab0wr

10. Could it be that you have gone back to ad hominem assertions? Why don't we just stick to the technical discussion?

Note that there is no 'B' in dx so 'B' is irrelevant to the value of dx. 'x' is simply the one-dimensional distance in units-of-length along a transmission line (plotted on the x axis). How can slices of delta-x, i.e. d(length) along the 'x' axis possibly be anything but real, linear, and constant? Wouldn't dx being imaginary, non-linear, and/or variable cause calculus calculations using dx to yield inaccurate results?

Last edited: Jul 29, 2008