Richard Harrison wrote:

Keith wrote:
"Are you sure you want to discard all thoughts of the instantaneous?

Certainly not, but it has little application to power in transmission
line problems.

Power is the rate of transferring energy or the rate of doing work.
Electrical power is measured in joules per seconds or more succinctly in
watts.

What is the value in watts or joules per second when seconds equal
zero? I venture an answer: It is the V x I x cos. theta at that instant,
but since work is power x time, it won`t do anything for you in zero
seconds.

But then instantaneous velocity and instantaneous acceleration won't do
anything for you in zero seconds, either. And yet, for example,
inertial navigation systems successfully operate by integrating these
instantaneous values.

Back to your assertion "but it has little application to power in
transmission line problems".

It is certainly true that for RF, average power is of most interest. It
is what gets you communicating.

But if you want to understand how things work, exploring the land of
the instantaneous is quite valuable. It is instantaneous voltages which
make standing waves. It is instantaneous signals which cause distortion
in diode demodulators. It is instantaneous voltages and currents which
are added and subtracted in Bird wattmeters. It is instantaneous
voltages and currents which interact at impedance discontinuities to
do all the neat stuff. And it is instantaneous voltages and currents
which produce instantaneous power.

But I notice an instantaneous willingness to reject the value of
instantaneous power. I suspect this is because the conclusions reached
when thinking in terms of instantaneous power are inconsistent with
some of your long held beliefs and rather than re-examine these
beliefs it is simpler to just reject instantaneous power.

But to reject instantaneous power in a consistent manner, you need to
explain why you do not also reject instantaneous velocity, acceleration,
current, flow or any of the many other interesting things which are a
derivative with respect to time.

For if we accept the argument "in zero time, no energy can flow" then
we should also accept:
- "in zero time, no charge can flow" -- say bye to instantaneous current
- "in zero time, we can move no distance" -- say bye to instantaneous
velocity
- etc., etc.

When you can't find any fundamental reason that the instantaneousness
of power is different from the instantaneousness of other common
measures like velocity, current, etc., you may wish to return to the
original assertion which caused all this fuss:

Assertion A:
"In a shorted ideal transmission line which has reached steady state,
no energy can cross a voltage or current minimum because
p(t) = v(t) * i(t) and at a voltage or current minimum, the voltage
or current is always zero, so the power is always zero, so there is
no energy flow across a voltage or current minimum."

This conclusion contradicts a commonly held belief:

Belief B:
"that in steady-state, energy is flowing along the transmission line
to the end where it is reflected and travels back to the beginning."

Unless you can find an error in the logic of Assertion A, it would
seem reasonable that you re-assess your acceptance of Belief B.

Assertion A caused me to reject Belief B and the world did not
collapse:
- Bird wattmeters still give useful indications
- ghosts still occur on TVs
- echoes still occur on phone lines
- bidirectional communications still occur on two wire lines
but the simplistic explanations for these phenomena offered by
Belief B need to be re-examined. A better understanding is all
that you stand to gain by discarding Belief B.

....Keith



....Keith