On Dec 9, 9:36 pm, Roger 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.

....Keith