On Mar 5, 8:06 am, Cecil Moore wrote:
....blah, blah...

So consider the case of a section of lossless uniform transmission
line of characteristic impedance R0, which I write as R instead of Z
since it of course must be real-valued, connected between two sources
S1 at end 1 and S2 at end 2. These sources each have source impedance
R0: they are perfectly matched to the characteristic impedance of the
line. The line is long enough that we can observe any standing waves
that may be on it. (For believers in directional couplers, that can
be short indeed, but it does not need to be short.) Source S1 is set
to output a sinusoidal signal of amplitude A1 into a matched load, on
frequency f1. Similarly S2 outputs a sinusoidal signal A2 into a
matched load at frequency f2, which is distinct from f1.

It is easy to show mathematically, and to measure in practice, that
the amplitude of the frequency f1 is constant along the line, and
similarly that the amplitude of the frequency f2 is constant along the
line. That is to say, there is no standing wave at either frequency.
Energy at f1 travels on the line only in the direction from S1 to S2,
and vice-versa for f2.

That says to me that the energy on the line at f1 is absorbed entirely
by source S2, and the energy at f2 is absorbed entirely by S1, with no
reflection at the boundaries between S1 and the line, and the line and
S2.

At this point, I leave it as an exercise for the reader to interpret
or explain exactly what is meant by "absorbed by." This may involve
understanding that in a Thevenin or Norton simple model of each
source, the energy delivered by the voltage or current source at any
moment in time may not equal that which it would deliver into a
matched load at the same point in the cycle...

Cheers,
Tom

K7ITM wrote:
So consider the case of a section of lossless uniform transmission
line of characteristic impedance R0, which I write as R instead of Z
since it of course must be real-valued, connected between two sources
S1 at end 1 and S2 at end 2. These sources each have source impedance
R0: they are perfectly matched to the characteristic impedance of the
line. The line is long enough that we can observe any standing waves
that may be on it. (For believers in directional couplers, that can
be short indeed, but it does not need to be short.) Source S1 is set
to output a sinusoidal signal of amplitude A1 into a matched load, on
frequency f1. Similarly S2 outputs a sinusoidal signal A2 into a
matched load at frequency f2, which is distinct from f1.

What you have described is a system with two sources which
are incapable of interfering with each other because they
are not coherent. Note that this example bears zero resemblance
to a system where the sources are coherent, i.e. frequency-
locked and phase-locked and therefore, capable of interference.

It is easy to show mathematically, and to measure in practice, that
the amplitude of the frequency f1 is constant along the line, and
similarly that the amplitude of the frequency f2 is constant along the
line. That is to say, there is no standing wave at either frequency.
Energy at f1 travels on the line only in the direction from S1 to S2,
and vice-versa for f2.

Obviously true for non-coherent sources.

That says to me that the energy on the line at f1 is absorbed entirely
by source S2, and the energy at f2 is absorbed entirely by S1, with no
reflection at the boundaries between S1 and the line, and the line and
S2.

Obviously true for non-coherent sources.

Unfortunately, "non-coherent sources" is not the subject of
this discussion. The rules change between non-coherent, non-inter-
fering sources and coherent, interfering sources. I suggest you
reference the "Interference" chapter in "Optics", by Hecht.
--
73, Cecil http://www.w5dxp.com

On Mar 5, 1:27 pm, Cecil Moore wrote:
The rules change between non-coherent,
non-interfering sources and coherent, interfering sources.

And exactly which part of "linear system" do you fail to understand?

K7ITM wrote:
On Mar 5, 1:27 pm, Cecil Moore wrote:
The rules change between non-coherent,
non-interfering sources and coherent, interfering sources.

And exactly which part of "linear system" do you fail to understand?

When two equal amplitude coherent signals are superposed,
the resulting power density can be four times the power
density of one of the single waves due to constructive
interference.

That is not true for two equal amplitude non-coherent
waves of different frequencies. The interference term
averages out to zero so there are no bright rings and
dark rings.

I'm surprised you don't know that.
--
73, Cecil http://www.w5dxp.com

On Mar 5, 5:25 pm, Cecil Moore wrote:
K7ITM wrote:
On Mar 5, 1:27 pm, Cecil Moore wrote:
The rules change between non-coherent,
non-interfering sources and coherent, interfering sources.

And exactly which part of "linear system" do you fail to understand?

When two equal amplitude coherent signals are superposed,
the resulting power density can be four times the power
density of one of the single waves due to constructive
interference.

That is not true for two equal amplitude non-coherent
waves of different frequencies. The interference term
averages out to zero so there are no bright rings and
dark rings.


Yes, yes, you've posted all that a billion times before in this NG.
Now, exactly what part of "linear system" do you fail to understand?

(I might also ask why you're going to so much trouble to be
disagreeable with something that agrees with what you were
posting...but I think I already know the answer to that one.)

K7ITM wrote:
Now, exactly what part of "linear system" do you fail to understand?

Have you stopped beating your wife?
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
K7ITM wrote:
Now, exactly what part of "linear system" do you fail to understand?

Have you stopped beating your wife?

(I might also ask why you're going to so much trouble to be
disagreeable with something that agrees with what you were
posting...but I think I already know the answer to that one.)

Tom, we were getting along quite well before you asked
your leading question, obviously designed to elicit
anger, not just once but twice.
--
73, Cecil http://www.w5dxp.com

K7ITM wrote:
And exactly which part of "linear system" do you fail to understand?

I understand the meaning of your question now and
here is one for you:

Exactly which part of a constant, average, steady-state
condition of destructive interference do you fail to
understand?

Given two coherent signals interfering whose results are
10 watts of constant, average, steady-state destructive
interference, how do you propose to accomplish that
outcome when the signals are not coherent?
--
73, Cecil http://www.w5dxp.com

K7ITM wrote:
On Mar 5, 1:27 pm, Cecil Moore wrote:
The rules change between non-coherent,
non-interfering sources and coherent, interfering sources.

And exactly which part of "linear system" do you fail to understand?

Tom, I am ready to eat crow and apologize to you on this
one. My false statement above was a rash assumption based
on my aversion to instantaneous values.

Last night, while puppy siting my girlfriend's dog in
a Walmart parking lot, I realized that the power density
(irradiance) equation as presented by Hecht and others
does work at the instantaneous level. Mea Culpa.

The difference between coherent and incoherent signals
is not in the rules but in the timing. Keith and I
were making essentially the same mistake. Thanks for
making me think this one through.
--
73, Cecil http://www.w5dxp.com