Owen Duffy wrote:
Walter Maxwell wrote:
It appears to me that even with all the successive posts on the
subject of power in the standing wave, you all seem to be missing the
ingredient that proves why there is no useable power in the standing
wave. It is because the current and voltage in the standing wave are
90° out of phase. Multiplying E x I under this condition results in
zero power.

I am trying to make sense of this and the first issue is what you mean by
the term "standing wave".

Walt is right.
Let's look at an arbitrary example of forward and reflected
voltage and current instantaneous phasors at one point on a
particular line.

Vfor = 100v at 45 degrees, Ifor = 2 amps at 45 degrees

The forward voltage and forward current are in phase.

Vref = 100v at -45 degrees, Iref = 2 amps at 135 degrees

The reflected voltage and reflected current are 180 degrees
out of phase.

Now calculate the total voltage and total current.

Total voltage = 2*100cos(45) = 141.4v at 0 deg

Total current = 2*2sin(45) = 2.83a at 90 deg

For a pure standing wave, the instantaneous voltage is
*always* 90 degrees out of phase with the instantaneous
current. There are no V*I*cos(A) watts in a pure standing
wave. There are only V*I*sin(A) VARS.

However, the VARS in the standing wave require energy
which can be converted to watts by I^2*R losses.
--
73, Cecil http://www.w5dxp.com