On Dec 11, 10:34 pm, Roger wrote:
Keith Dysart wrote:On Dec 9, 9:36 pm, wrote:The constantly-in-phase traveling wave concept requires the difficult-to-believe observation that a directional ammeter placed very near the end of an open transmission line will read the same current as if it were placed at the source end. Perhaps someone can perform that experiment some day, but I can not imagine how it can be done without placing a load on the line, thus invalidating the initial assumptions.The experiment will show the expected result but will not help understand why. For that, examination of the measurements and arithmetic performed by a directional ammeter is useful. Below, all voltages and currents are instantaneous. Total voltage, Vt = Vf + Vr Total current, It = If - Ir Vf = If * Z0 Vr = Ir * Z0 Substituting.... Vt = (If + Ir) * Z0 Ir = Vt/Z0 - If If = It + Ir If = It + (Vt/Z0 - If) If = (It + Vt/Z0)/2 Similarly, Ir = (It - Vt/Z0)/2 The directional ammeter measures instantaneous Vt and It, does the above arithmetic and presents If. A directional ammeter that presents a single number rather than the time varying If has probably converted the instantaneous values to RMS. Examing It and Vt at various points on the line and doing the above arithmetic will reveal why the same value for If is obtained everywhere. Directional wattmeters are more common than directional ammeters. A directional wattmeter does the above arithmetic then squares If, multiplies by Z0 and presents the results in watts. All this from just measuring Vt and It. ...KeithHi Keith,
Thanks to you and others for responding on this side issue. It was very helpful to me and resulted in a vast improvement in how I understood the theory behind directional watt meters. I had the misconception that current pickup over some lineal distance of transmission line was NECESSARY for the device to work, but now clearly understand that instantaneous measurement points suffice (and that instantaneous current measurement may be impossible).
After considerable thought, I think the math you presented above is for one of two cases of reflective waves, the reflection from a higher impedance load. When the load is less than the Zo of the line, the currents add but voltages subtract. Right?

I don't think so.
Vt = Vf + Vr, It = If - Ir, Vf = If * Z0 and Vr = Ir * Z0 are the
fundamental
equations defining forward and reverse waves.

Perhaps you arrive at two choices because sometimes Vr and Ir
are negative, which after simplification appears to give an
alternate form?

The end result is the same for both cases.

This is good. If you chase the signs, though, I think you will find
that there is only one case.

We probably should not toss Power into the mix until agreement
is reached on this. Power is fraught with issues which seriously
confuse some.

...Keith