Cecil Moore wrote:

Jim Kelley wrote:

Cecil Moore wrote:

Of course, my statement is related to steady-state. I don't
see anything worth responding to, Jim. Where's the beef?


The problem is that there should only be a 1 second lapse of time
between the beginning of gozinta at 100 Joules/sec and the beginning
of comezouta at 100 Joules/sec. At what point is the additional 2
seconds worth of energy fed into the system?


During the power-on transient phase. The load rejects half the incident
power. To keep things simple, assume a very smart fast tuner. After
one second, the feedline will contain 100 joules. The load will have
accepted zero joules. After two seconds, the feedline will contain the
100 joules generated plus 50 joules rejected by the load and the load
will have accepted 50 joules. Already the feedline contains 150 joules
while the source is putting out 100 joules per second. After 'n'
seconds, the line contains 300 joules, 100 from the source and 200
rejected by the load during the power-on transient stage.

seconds forward energy reflected energy load power
1 100 0 0
2 100 50 50
3 150 50 50
4 150 75 75
5 175 75 75
6 175 87.5 87.5
7 187.5 87.5 87.5
8 187.5 93.75 93.75
9 193.75 93.75 93.75
10 193.75 96.875 96.875
n 200 100 100

After 10 seconds the source has output 1000 joules. The load
has accepted 709.375 joules. 290.625 joules are already stored
in the feedline on the way to 300 joules during steady-state.
This is simple classical reflection model stuff.

If a load in rejecting half its incident power, the steady-
state reflected power will equal the steady-state load
power. The steady-state forward power will be double
either one of those.

It really is an interesting theory. And I'm willing to concede on a
certain point here. If we were to fit a curve to the data in your far
right side column, what we have is a dispersion curve. That is a
predictable phenomenon, most easily observable on long transmission
lines. However as this is not actual data, an important column is
missing. A column marked 'energy from source' is crucial to proving
your point. Without running the experiment and taking the data we can't
really know how much energy would be in any of the columns at any given
time. When we assume what that energy might be, we run the risk of
making an ass out of u and me. Well, mostly u. :-)

73, AC6XG

Jim Kelley wrote:
A column marked 'energy from source' is crucial to proving
your point.

Jim, I was hoping you were capable of multiplying 100 joules/sec
by the number of seconds to get the total number of joules
delivered to the system over time by the source. My 1000 joules
after ten seconds is 100 joules/sec multiplied by ten seconds.
Is that math too difficult for you? :-)

Maybe you need a simpler example. Here it is:

100w SGCL source----one second long feedline----load

The SGCL source is a signal generator equipped with a circulator
and circulator load. The circulator load dissipates all the
reflected power incident upon the signal generator. The signal
generator outputs a constant 100 watts.

The load is chosen such that the power reflection coefficient
is equal to 0.5, i.e. half the power incident upon the load
is reflected and half accepted by the load.

This configuration reaches steady-state in 2+ seconds. After 2+
seconds, the forward wave contains 100 joules and the reflected
wave contains 50 joules. 50 watts is being dissipated by the
load and 50 watts is being dissipated by the circulator load.
The source has output 150 joules of energy that has not been
dissipated by the load or the circulator load. 150 joules is
exactly the amount of energy to support the energy levels of
the forward wave and the reflected wave.

What could be simpler than that if you really believe in the
conservation of energy principle?
--
73, Cecil, http://www.qsl.net/w5dxp


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Cecil Moore wrote:

Jim Kelley wrote:

A column marked 'energy from source' is crucial to proving your point.


Jim, I was hoping you were capable of multiplying 100 joules/sec
by the number of seconds to get the total number of joules
delivered to the system over time by the source. My 1000 joules
after ten seconds is 100 joules/sec multiplied by ten seconds.
Is that math too difficult for you? :-)

:-) My contention is that it's too remedial. What you require is faith,
not math. Is the source supposed to be a virtual fire hydrant of
constant energy, or is it more like a real system? You seem to be
assuming a constant 100 Joules per second input, regardless of the fact
that the impedance the source sees is changing over the interval.
That's not particularly realistic, hence a need for the empirical. But
we could assume that the source is constant, and continue.

Maybe you need a simpler example. Here it is:

100w SGCL source----one second long feedline----load

The SGCL source is a signal generator equipped with a circulator
and circulator load. The circulator load dissipates all the
reflected power incident upon the signal generator. The signal
generator outputs a constant 100 watts.

The load is chosen such that the power reflection coefficient
is equal to 0.5, i.e. half the power incident upon the load
is reflected and half accepted by the load.

This configuration reaches steady-state in 2+ seconds. After 2+
seconds, the forward wave contains 100 joules and the reflected
wave contains 50 joules. 50 watts is being dissipated by the
load and 50 watts is being dissipated by the circulator load.
The source has output 150 joules of energy that has not been
dissipated by the load or the circulator load.

You have provided a lot of detail about where it all resides and in what
proportions, but you still haven't shown how much energy a source would
actually produce under such circumstances. Further, you're assuming
that energy would move forward in a transmission line at a rate higher
than the rate at which it is provided by the source. This is highly
speculative and suspect. What we know for sure is, once steady state is
achieved, energy is absorbed by the load(s) at the same rate at which it
is generated, all the energy from the source goes to the load(s). Given
that, there's very little impetus to believe that there need be any more
than one second's worth of energy held within a one second long
transmission line. It is therefore reasonable to contend that in the
first scenario, 100 Joules of energy is held within the transmission
line as it propagates toward the load. And in this latest scenario, 50
Joules is heading toward the load, and 50 is in the path to the
circulator for a total of 100 Joules stored within the one second long
transmission line.

The way to prove that there's any greater surplus of energy held within
the transmission line would be to make the energy vs. time measurements
at each end of such a transmission line. Absent that, it's purposeful
speculation.

73, AC6XG

Jim Kelley wrote:
You seem to be
assuming a constant 100 Joules per second input, regardless of the fact
that the impedance the source sees is changing over the interval.

It's a mental exercise, Jim. I told you it was equipped with
a very fast very smart autotuner. If you are cool with a one
second long lossless feedline, you should be cool with a
very fast very smart autotuner.

You have provided a lot of detail about where it all resides and in what
proportions, but you still haven't shown how much energy a source would
actually produce under such circumstances.

It's too simple to mention. The signal generator is putting out a
constant 100 watts. Hint: multiply the watts (joules/sec) by the
number of seconds to get the total joules. Dimensional analysis
indicates the product will be joules.

Further, you're assuming
that energy would move forward in a transmission line at a rate higher
than the rate at which it is provided by the source.

Nope, I'm not. All wave energy moves at the speed of light. You
are confused. 100 joules per second is headed toward the load.
50 joules per second is headed away from the load.

This is highly speculative and suspect.

Easy to understand given your level of confusion. To get the forward
power, divide the load power by one minus the power reflection
coefficient. That's 50w/0.5 = 100 watts. That's how you calculate
forward power.

... there's very little impetus to believe that there need be any more
than one second's worth of energy held within a one second long
transmission line.

Jim, if you have 1.5 gallons in a tank with one gallon/sec flowing
in and one gallon/sec flowing out, how many gallons are in the tank?
You have to have enough energy in the feedline to support the
forward power and the reflected power. More or less than that
amount would violate the conservation of energy principle.

It is therefore reasonable to contend that in the
first scenario, 100 Joules of energy is held within the transmission
line as it propagates toward the load.

Yes, half is headed into the load and half will be rejected by
the load.

And in this latest scenario, 50 Joules is heading toward the load,

50 joules are destined for the load but 100 joules are heading
toward the load. Remember to get 50 watts into the load, you
must hit the load with 100 watts. 100 watts for one second is
100 joules, not 50.

and 50 is in the path to the
circulator for a total of 100 Joules stored within the one second long
transmission line.

Your math or model or both are faulty. The forward power must
be 100 watts to get 50 into the load. Therefore, the forward
wave energy in a one second feedline is 100 joules. The reflected
wave energy is half of that. Therefore, there's 150 joules in
the feedline.
--
73, Cecil http://www.qsl.net/w5dxp

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