Dave Shrader wrote:

If dV/dt = 0 then I must have maximum voltage. This has meaning.

You must be into this new math. What is the slope of a point
when dt=0 = the width of a point? :-) Is that point flat, pointing
up, or pointing down? :-)
--
73, Cecil http://www.qsl.net/w5dxp



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Tdonaly wrote:
Cecil seemed to indicate that he thought delta t going to zero meant that
t was perpetually zero.

If delta-t ever gets to zero, time stands still. All you can allow
delta-t to do is to approach zero. Once it reaches zero the ballgame
is over. Limit delta-t to a minimum of a yoctosecond and everything
will be perfectly OK.
--
73, Cecil http://www.qsl.net/w5dxp


Are you trying to start an argument? I wrote "going to zero," not
"at zero." Besides, what the hell is a yoctosecond? All this was
argued over and discussed in the 18th century. You and Richard
Harrison are beginning to sound like Bishop Berkeley.
73,
Tom Donaly, KA6RUH

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

Tom Donaly wrote:
"You and Richard Harrison are beginning to sound lke Bishop Berkeley."

We are in good company. Terman says on page 84 of his 1955 opus:
"In these equations Zo = sq rt Z/Y is termed the "characteristic
impedance" of the line. In the case of radio-frequency lines, Zo can
nearly always be assumed to be a pure resistance, as discussed on page
88."

When Terman says SWR = Emax / Emin, it makes no difference whether you
use instantaneous values or rms values, so long as you are consistent,
the ratio is the same.

Some complained that nobody provided a trustworthy VSWR related to
power. Bird Electronic Corporation does:

VSWR = 1+sq rt (reflected pwr/forward pwr) over 1-sq rt (reflected
pwr/forward pwr).

Millions of conversions have proved this VSWR from measured powers
relation.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
For the power sine wave, though the fact that a minus times a minus is a
plus results in 2x the voltage frequency, dP/dt=0 at maxima.

Alternatively, from amplitude modulation, the product of two sine waves
produces a sum and difference frequency. When the two sine waves have
the
same frequency (as they due for the voltage and current contributing to
the power), the result is a double frequency sine wave and a 0 frequency
difference which is the DC or average power.

A question raised in this thread is, how can energy, which is joules per
second times seconds, be zero when the number of seconds is zero? The
answer seems obvious. Zero times anything is zero.

Exactly. And when the voltage or current is always zero, so must be the
power.

....Keith

Keith wrote:
"---you need to explain why you do not reject instantaneous velocity,
acceleration, ---."

I don`t reject instantaneous anything including power. Instantaneous
power is not particularly useful in working with radio transmission
lines.

Like infinity, the infinitesimal is unmeasurable. Like infinity, the
infinitesimal is useless in calculations. The idea of the infinitesimal
is useful in perceiving targeted values approached as a variable
approaches a limit.

A differential "d" is an infinitesimal smaller than a difference. "dy"
is the differential of y. "dx" is the differential of x. "dt" is the
differential of t. The ratio "dy/dx" is a slope defined at a point and
is equal to the limit as x goes to zero of the ratio delta y over delta
x.

The basis of differentation is superfluous to this discussion, but Keith
asks, why not reject things which are a derivative with respect to time
including acceleration.

Acceleration may be a good example. Calculus can give the rate at which
a variable varies. On the other hand, it can give a function if the rate
of change is given.

Velocity is the variable in acceleration. Assume velocity is increasing
and you have a definition of the function. For a given velocity the
acceleration can be determined, and for a given acceleration, the
velocity can be determined.

My point, repeated again, is that when delta time is zero, no distance
is traversed, not that acceleration and velocity are zero.

Power x time = energy. Thast`s how the electric power company calculates
your bill. If no time elapses during which power is available, no energy
is consumed.

Best regards, Richard Harrison, KB5WZI

On Sun, 24 Aug 2003 08:40:44 -0400, wrote:

For the power sine wave, though the fact that a minus times a minus is a
plus results in 2x the voltage frequency, dP/dt=0 at maxima.

Alternatively, from amplitude modulation, the product of two sine waves
produces a sum and difference frequency. When the two sine waves have
the
same frequency (as they due for the voltage and current contributing to
the power), the result is a double frequency sine wave and a 0 frequency
difference which is the DC or average power.


Hi Keith,

The two statements above are in not about the same thing within the
context of the subject.

The products of two sine waves as you describe are non-linear and are
not found on the Smith Chart, nor in the transmission line. [Except
insofar as it is forced deliberately (and that has yet to be revealed
by any correspondent), or through negligence of line maintenance with
corrosion products and dissimilar metals interfaced.]

73's
Richard Clark, KB7QHC

Richard Harrison wrote:
Standing waves are perceived only by using a sensor which does not
discriminate by direction and accepts power traveling in both directions
at the same time. There actually is no abatement of power in either
direction.

Sadly for ham radio, this fact of physics has been known to man for 300
years. How can a "technical" hobby be 300 years out of date?
--
73, Cecil http://www.qsl.net/w5dxp



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wrote:
But if you want to understand how things work, exploring the land of
the instantaneous is quite valuable.

OTOH, if you want to understand how EM waves work, exploring the discoveries
of the past 500 years in the field of optics is quite valuable - discoveries
that you have officially discounted when you reject the total knowledge base
embodied in the field of optics. Seems my "sin" is pretty small compared to
yours. :-)
--
73, Cecil http://www.qsl.net/w5dxp



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Richard Harrison wrote:
Standing waves are perceived only by using a sensor which does not
discriminate by direction and accepts power traveling in both directions
at the same time. There actually is no abatement of power in either
direction.

Sadly for ham radio, this fact of physics has been known to man for 300
years. How can a "technical" hobby be 300 years out of date?
--
73, Cecil http://www.qsl.net/w5dxp

Larding it on a little thick are we, Cecil?
73,
Tom Donaly, KA6RUH