On Sat, 05 Apr 2008 10:01:13 -0500
Cecil Moore wrote:

Roger Sparks wrote:
The overriding issue is to account for all the power, which we are having a hard time doing. The current is flowing the wrong way for the source voltage at Ps(91) so
the source is absorbing power. That negates the idea that the source
has an impedance of zero when we also assign the source a voltage.

Consider that what you are seeing is the flip side of the
interference at the source resistor. When a local source is
present, it can certainly absorb destructive interference
energy and supply constructive interference energy. The
following example has identical steady-state conditions
but brings Pfor1 and Pref1 into play for the instantaneous
values. I suspect that Pref1 is being completely ignored
in the present analysis.

Vs(t)---1WL 50 ohm---Rs---1WL 50 ohm---+j50
Pfor1-- Pfor2--
--Pref1 --Pref2


I think this would be right on the average basis. Because any sine waves of identical frequency can ultimately be added to make one wave, we can describe a single sine wave on the source side and another wave on the load/reflection side. There is no need for constructive or destructive interference as part of the final sine wave description.

On the other hand, if we want to understand how the final wave is assembled for each side of the resistor, we need the idea of constructive and destructive interference. Your pictorial showed only the single reflection, but as you have explained previously, there are many more reflections between the resistor and +j50 points until the power on the +j50 side finally stabalizes to some power level.

It seems to me like my spreadsheet found at

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

captures a description of the forward and reflected waves as a single equation for each side of the resistor. The forward wave is y*sin(t) and reflected wave is y*sin(t+90).

If we want to learn how to find out how the source load begins at 100 ohms resistive and changes to 70.7 ohms reactive, we can either notice how the peak current has shifted from resistive to reactive (45 degree) from the combined waves described on my spreadsheet, or we can add all the reflections on each side of the resistor and come to the combined wave after many additions of ever smaller reflections.

If we can't account for the power, it is because we are doing the accounting incorrectly.

Try the above example and maybe it will become clear.

Pref1 = Pfor1(rho1^2) + Pref2(1-rho2^2) + interference1

Pfor2 = Pfor1(1-rho1^2) + Pref2(rho2^2) + interference2

Interference1 and interference2 would be the combined effects of successive ever smaller reflections. Frankly, I don't see that combining the smaller reflections in this way to be of much value. It is like saying that the first reflection is special and the subsequent reflections equally special so we will give subsequent refections a group name, "interference". To me, all the reflections are "interference" and must be either added or subtracted in the same manner.

The source power doesn't appear directly in the equations
and need not be considered at all.

We have to have a starting point, which must be the source power. How could we avoid having a starting point?

Pfor1 + Pref2 + P.Rs = Pfor2 + Pref1 (all average)

I suspect the above equation will account for all the
energy components even at the instantaneous level such
that:

Pfor1(t) + Pref2(t) + P.Rs(t) = Pfor2(t) + Pref1(t)

Please note that all of these power components exist
when the two transmission lines are removed so this
analysis is probably the key to understanding what
is wrong with the earlier analysis.
--

I think this equation is missing some terms, reflections 2,3,4...n.

--
73, Roger, W7WKB