On Apr 9, 12:59*pm, Cecil Moore wrote:
Keith Dysart wrote:
Cecil Moore wrote:
There is no capacitance or inductance in the source to
store energy.

"In" is an oxymoron for the lumped circuit model.
The lumped reactance exists *at* the same point as
the source because everything is conceptually lumped
into a single point.

In the real world, circuits are never single points
and there exists a frequency at which distributed
network effects cannot be ignored. In reality,
distributed network effects occur for all real
circuits but they can often be ignored as negligible.

The two inches of wire connecting the source to the
source resistor has a characteristic impedance and
is a certain fraction of a wavelength long. If it is
not perfectly matched, reflections will occur, i.e.
there will exist forward power and reflected power on
that two inches of wire.

It was your Fig 1-1, made of ideal elements with none
of these issues.

For the 1/8WL
shorted line, there appears to be 125 watts of forward
power and 25 watts of reflected power at points on each
side of the source.

Not if there is no transmission line.

Aha, there's your error. What would a Bird directional
wattmeter read for forward power and reflected power?
Consider that short pieces of 50 ohm coax are used
to connect the real-world components together.

It would read something completely different if it was
calibrated for 75 ohms, though the difference between
Pf and Pr would be the same.

But that is not the circuit of your Fig 1-1.

Or chose any characteristic impedance and do the math.
You will discover something about the real world, i.e.
that you have been seduced by the lumped circuit model.

It was your circuit; Fig 1-1.

Perhaps. *But I don't need more examples where the
powers balance. I already have the one example where
they don't.

And that one example is outside the scope of the
preconditions of my Part 1 article. Let me help you
out on that one. There are an infinite number of
examples where the reflected power is NOT dissipated
in the source resistor but none of those examples,
including yours, satisfies the preconditions specified
in my Part 1 article. Therefore, they are irrelevant
to this discussion.

As long as you agree that the imputed energy in the
reflected wave is not dissipated in the source
resistor; and only claim that the imputed average
power in the reflected wave is numerically equal
to the increase in the dissipation.


But there are no component powers in the source. It
is a simple circuit element.

No wonder your calculations are in error.
Perform your calculations based on the readings of
an ideal 50 ohm directional wattmeter and get back to us.

Well there's a plan. Measure everything in a
circuit with a directional wattmeter. You first.
Start with Fig 1-1.

But you'll have to choose the calibration impedance.

I'd suggest 100 ohms for the section between the
source and the source resistor because the source
resistor and the line initially present a 100 ohm
impedance and you would not want any reflections
messing up the measurements.

Hint: Mismatches cause reflections, even in real-world
circuits. The reflections happen to be *same-cycle*
reflections. The simplified lumped circuit model, that
exists in your head and not in reality, ignores those
reflections and thus causes confusion among the
uninitiated who do not understand its real-world
limitations.

We should explore this new world. Please discard your
voltmeter, ammeter, oscilloscope, .... All you need
is a Bird wattmeter.

...Keith