On 5 jun, 11:22, Cecil Moore wrote:
On Jun 5, 7:08*am, Keith Dysart wrote:

We need to carefully understand the meaning of the words. Power is
energy that is moving;

Correction, it must be moving past a point, not just moving laterally
from an inductance to a capacitance and back. There is zero net
average power anywhere on a wire containing a pure standing wave.
Therefore, there is zero net energy flow anywhere on a pure standing
wave, not just at the zero current and zero voltage points. The
average power in a pure standing wave is zero whether the current or
voltage is zero or not. What is important for power is the phase angle
between the net current phasor and the net voltage phasor which is
always 90 degrees for a pure standing wave. The fact that *power is a
scalar with no negative values* and *the average power is zero*, leads
one to conclude that instantaneous power is just a mathematical
curiosity. Exactly how can the instantaneous power average out to zero
average power if there are no negative values of instantaneous power?
Seems to me to be one of those numerous "undefined" or "indeterminate"
conditions that unfortunately exists in mathematics. When you solve a
quadratic equation for a resistance and get plus or minus 100 ohms, do
you actually start searching for a -100 ohm resistor? Then why, when
you know the average power is zero, do you ask us to go searching for
some negative instantaneous power that doesn't exist?

Since power is energy flow *per unit time*, I don't see how power
calculated over zero unit time can be anything more than a
mathematical curiosity existing in human brains - and unrelated to
reality. When one integrates instantaneous standing wave power over
one cycle and gets anything except zero, one needs to recognize the
error or one's ways.
--
73, Cecil, w5dxp.com

Hi. ¡Good evening (here) to all..!

We need to carefully understand the meaning of the words. Power is
energy that is moving;

Since the energy can be dissipated also transmitted, If we talk in
power FLUX terms (instead power only), I think the issue it would be a
little more understandable because surfaces may have associated
vectors (with "power moving" I believe you are thinking about power
crossing an imaginary surface)
(Note: when I spoke about "unidimensional" nature of a TL space I am
pointing to "degrees of freedom" of energy flux circumscribed to its
physical path, of course).

For the sake of example we could imaginate a coaxial TL provided with
a resistive inner conductor and perfectly conductive outer one. On
such TL perhaps we could clearly visualize power flux vector (Poynting
vector) "slanted" towards inner conductor to "see" -through simple
vectorial decomposition on (over?) the inner wire and pependicular to
it directions both = transmission and dissipative nature of
phenomenom.
At the same time I believe will be also more ease to account for net
power FLUX of opposite directions traveling waves and do not confuse
with net power being zero, leading us to the idea of zero energy
stored in a ideal resonant TL. Note: In my last mensage I forget to
clear that with "resonant line" I was speaking about a section of TL
with its ends open or shorted (or a mix) to force a "chemically pure"
standing wave :)

I believe we always must escape from words as "real" or
"true" (outside of safe environments such mathematics or digital
logic), because "she" easily leads us to the Holy Inquisition
dangers :) Let us the Wave word to be free for jointing with
standing, sine, hand, etc, etc. and do we make efforts to understand
its conceptual meaning on each context :)

73

Miguel Ghezzi - LU6ETJ