On Thu, 11 Mar 2004 09:52:28 -0600, Cecil Moore
wrote:
Walter Maxwell wrote:
Cecil Moore wrote:
So you disagree with "Wave Mechanics of Transmission Lines, Part 3:"
by S. R. Best, QEX Nov/Dec 2001?
Cecil, are you saying you believe the total nonsense in Steve's Part 3?
No, Steve assumes the existence of forward and reflected energy waves.
I also assume the existence of forward and reflected energy waves and
think their existence can be proven. I assume that you agree with Steve
that forward and reflected energy waves exist. If I understand Gene
correctly, he believes that reflected energy waves do not exist in
a matched system even though there is a mismatch at the load.
I probably should have said: "So you disagree with the very existence
of reflected energy waves which is assumed by S. R. Best in his QEX
Nov/Dec 2001 article.
Cecil, it's not whether reflected waves exist that's wrong with Steve's paper,
it's his misuse them that's wrong, and it's the misuse that is 'total nonsense'.
Since Steve's article asserts the existence of forward and reflected
energy waves, it cannot be "total nonsense". In fact, Steve's equation
for total forward power yields the correct answer. In a matched system,
Ptotal = P1 + P2 + 2*SQRT(P1*P2)
indeed yields the correct result given that:
P1 = Psource(1-rho)^2 = Psource times the power transmission coefficient
P2 = Pref(rho)^2 = Preflected times the power reflection coefficient
Cecil, your equations for P1 and P2 yield absurd answers if you plug the numbers
into them. The value for P1 should read "Psource (1 - rho^2) = ..., and the
value for P2 should read "P2 = Pref (rho^2). Beega difference! Then the value
for Ptotal will be correct.
Steve's problem was that he did not recognize (actually denied) the role
of interference, destructive and constructive, and therefore left out half
of the explanation.
Exactly!!! And it's the correct interference relationship I present in QEX and
Reflections that he insists is incorrect. In much earlier emails with Steve he
told me that using my statements appearing there he could prove me technically
incompetent. He simply would not accept any of my pleadings with him to see the
correct application of the interference between reflected waves that achieves
the impedance match.
In optics, 2*SQRT(P1*P2) is known as the "interference term"
and equal magnitudes of interference happen on both sides of the match point. In
a perfectly matched system, at the match point, there exists total destructive
interference toward the source, i.e. zero reflections, and total constructive
interference toward the load, i.e. all the energy winds up flowing toward the load.
The following two problems are virtually identical. 'n' is the index of
refraction.
air | glass
Laser-------------|---------
n=1.0 | n=1.5
XMTR---50 ohm coax---75 ohm load
The magnitudes of the reflection coefficients are identical at |0.2|
The solutions to those problems are virtually identical.
air | 1/4WL thin-film | glass
Laser-------------|------------------|-----------
n=1.0 | n=1.225 | n=1.5
XMTR---50 ohm coax--x--1/4WL 61.2 ohm coax--75 ohm load
Optical physicists fully understand what happens with the Laser. It is explained
on the Melles-Griot web page and in _Optics_, by Hecht. From the Melles-Griot web
page: http://www.mellesgriot.com/products/optics/oc_2_1.htm
"Clearly, if the wavelength of the incident light and the thickness of the film
are such that a phase difference exists between reflections of p, then reflected
wavefronts interfere destructively, and overall reflected intensity is a minimum.
If the two reflections are of equal amplitude, then this amplitude (and hence intensity)
minimum will be zero. In the absence of absorption or scatter, the principle of conservation
of energy indicates all "lost" reflected intensity will appear as enhanced intensity in the
transmitted beam."
No one in his right mind can successfully argue against this. Anyone who would
argue against this is either of closed mind or an ignorant moron.
This fits perfectly with Reflections II, chapter 23: "Therefore, while reflection
angles for waves reflected at the input mismatch (point x above) are 180 deg for voltage,
and 0 deg for current, the corresponding angles at the input for the waves reflected
from the output mismatch (75 ohm load above) are reversed, 0 deg for voltage and 180
deg for current. Consequently, all corresponding voltage and current phasors are 180
deg out of phase at the matching point. ... With equal magnitudes and opposite phase
at the same point (point x, the matching point) the sum of the two waves is zero."
I'm glad you find that Chapter 23 fits, because I've known all along that it
fits perfectly with Melles-Griot. Steve (Best), on the other hand says Chapter
23 is totally wrong. You might also note that Chapter 23 is identical with my
paper in QEX in the Mar/Apr 1998 issue, which Steve also disputes in all three
parts of his QEX article.
That is a perfect description of total destructive interference. I have your reference,
J. C. Slater's book, _Microwave_Transmission_, on order.
You might find Slater (1943) difficult to obtain. I can email you a copy of the
pertinent part if you wish.
Walt, W2DU