W5DXP wrote:
wrote:
Let me make it simpler then: the lamp cord from the wall to the table
lamp; lamp off and lamp on. Most lamp cord looks like twin-lead; some
have said it is approximately 100 Ohms but for the purposes of
discussion feel free to assume any convenient Z0 for the cord.
I don't think you understand the problem. That lamp cord is about
0.0000005 wavelength at 60 Hz. Any reflected wave effects are completely
negligible. It's like expecting reflections due to resistor leads at
HF RF. They are theoretically there but usually too small to measure.
While the standing wave will be difficulty to observe, none of
the equations related to ideal transmission lines require a
minimum length. The reflected voltage and power can be trivially
calculated just as it is for RF. Let me do it for you.
120 Volt RMS line, open circuit, assume 100 Ohms for the lamp cord:
Vf = 60V RMS, Vr = 60 V RMS
Pf = 36 W,
Pr = 36 W
And if it is not an RF transmission line?
If it is a DC circuit? Say your phone line when on hook?
If it is a lamp cord?
The transmission line has to be a non-negligible percentage of a
wavelength for one to have to switch from circuit math to
transmission line math.
But you can switch early if you wish and should still get
reasonable results.
What's the wavelength of DC? What's the
wavelength of voice audio? What is the wavelength of 60 Hz?
If the phone line is an appreciable percentage of a wavelength,
there will be reflections (echoes) as anyone doing a transcontinental
phone call can attest. Echo cancellation is big business with the
telephone companies. Your theory would make telephone line echoes
impossible for long unterminated lines. It is known that unterminated
telephone lines result in the largest magnitude of echoes.
Of course, we were discussing sinusoidal steady state for which
there will be no echoes. Echoes only happen when the line energy
state is changing.
It just occurred to me that you can revolutionize the telephone
industry if you are right. You could patent your idea of no
reflected energy on a long unterminated telephone line and sell
it to the telephone companies for millions of dollars. Just have
every intercontinental telephone line unterminated by using
high impedance receivers on each end. Since no reflected energy
could cross the voltage minimum point, echoes would be eliminated
without the expensive echo cancellation equipment.
Unfortunately, such a situation only occurs when the line is in
steady-state which means no information could be sent, which would
render the line economically unviable.
Please, replace wall outlet with lamp cord to table lamp.
Are you capable of measuring the 0.0001 degrees of phase shift
between the forward wave and reflected wave? Your measuring
instrument needs to be about plus or minus 0.0000001 degrees
to get an accurate measurement.
Don't need to measure phase shift to obtain forward and reflected
voltages and powers.
But I think I understand the technique. Whenever the theory would
produce answers with which you might be uncomfortable, rather than
producing those anwsers and attaining a better understanding of the
viability of the theory, you prune the problem space to which the
theory applies. Ergo, not for DC, not for 60 Hz, not for lamp cords,
not for step functions. But the math from the theory works just fine
in all these situations. Try it.
....Keith