Walter Maxwell wrote:
But Cecil, take another look at Fig 6 on page 23-5 to note that those two waves
arrive 180 out of phase at point A, which means only that the E and H fields
cancel in the rearward direction only, resulting in a Zo match to the source.
Yes, and that is exactly my point. EXACTLY the same thing happens to the E-fields
and H-fields. That means exactly the same thing that happens to the rearward-
traveling voltages also happens to the rearward-traveling currents. Two equal-
magnitude/opposite-phase voltages cancel. Two equal-magnitude/opposite-phase
currents cancel. That doesn't happen at either an open or a short. If one
looks at just the voltages, it looks like a short. If one looks at just the
currents, it looks like an open.
With both voltage and current at 0 degrees relative to
the source, all the power in the waves reflected at B are re-reflected at A and
add to the source power.
Reflected waves ALWAYS have the voltage and current 180 degrees out of phase.
"With both voltage and current at 0 degrees" implies a forward wave which is
the *EFFECT* of re-reflection, i.e. after re-reflection. The rearward-traveling
voltage and current CANNOT be in phase before the re-reflection. After the re-
reflection, they are no longer rearward-traveling so they are in-phase and forward-
traveling. It's a cause and effect thing.
1. Proper adjustment of the tuner/stub/quarter-wave-transformer CAUSES all
voltages and currents at the perfect match point to be in-phase or 180 degrees
out of phase.
2. Destructive interference between two rearward-traveling waves of equal magnitudes
and opposite phases causes the E-field voltage and H-field current to go to zero
simultaneously, i.e. the E-fields superpose to zero in the rearward direction and
the H-fields superpose to zero in the rearward direction. EXACTLY the same thing
happens to the H-fields as happens to the E-fields in the rearward direction. Neither
a short nor an open acts like that.
"... 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." From the Melles-Groit web page.
3. "... the principle of conservation of energy indicates all "lost" reflected
intensity will appear as enhanced intensity in the transmitted beam." Quoted
from the Melles Groit web page. They don't say how but they do say why. In a
perfectly matched system, all rearward-traveling energy changes direction at
the match point and joins the forward wave as constructive interference. That
constructive interference energy is equal in magnitude to the energy involved
in the destructive interference event. It's a simple conservation of energy
process.
There is no argument about what happens at a short circuit. What I am saying
is that a match point is NOT a short circuit.
In this case the match point at A is an open circuit.
Destructive interference causes the rearward-traveling voltage to go to zero.
Voltage doesn't go to zero at an open circuit. Exactly the same thing happens
to the rearward-traveling voltages and rearward-traveling currents. Voltage
goes to zero at a short-circuit. Current goes to zero at an open circuit. A
match point causes both to go to zero in the rearward direction. That means
the voltage sees a short-circuit looking rearward and the current sees an
open-circuit looking rearward.
"Consequently, all corresponding voltage and current phasors are 180 degrees
out of phase at the matching point. ... With equal magnitudes and opposite
phase at the (matching) point, the sum of the two waves is zero." _Reflections_II_,
page 23-9. This is true for both step-up or step-down impedance discontinuities.
At a perfectly matched point, the two rearward-traveling voltages are ALWAYS of
equal magnitude and opposite phase. The two rearward-traveling currents are
ALWAYS of equal magnitude and opposite phase. That's the only way complete
destructive interference of rearward-traveling waves can occur.
J. C. Slater says that's what happens in the above quote. Voltages 1/2WL apart
in time cancel to zero. Currents 1/2WL apart in time cancel to zero.
Yep, but only in the rearward direction.
The rearward direction is what we are talking about. The point is that EXACTLY
the same thing happens to the two rearward-traveling current waves as happens
to the two rearward-traveling voltage waves. A short-circuit doesn't affect
voltages and currents in the same way. An open-circuit doesn't affect
voltages and currents in the same way. A match point affects the rearward-
traveling voltages and rearward-traveling currents in EXACTLY the same way.
The re-reflection at a match point is a conservation of energy reflection where
the rearward destructive interference energy supplies energy to constructive
interference in the opposite direction. For light, the equation a
Destructive Interference Irradiance = I1 + I2 - 2{SQRT[(I1)(I2)]} (9.16)
Constructive Interference Irradiance = I1 + I2 + 2{SQRT[(I1)(I2)]} (9.15)
_Optics_, by Hecht, fourth edition, page 388
Note the similarities to equations 13 and 15 in Dr. Best's QEX article,
Part 3.
PFtotal = P1 + P2 - 2{SQRT[(P1)(P2)]} (Eq 15)
PFtotal = P1 + P2 + 2{SQRT[(P1)(P2)]} (Eq 13)
Too bad he didn't label them as Hecht did, as "total destructive interference"
and "total constructive interference" equations.
--
73, Cecil
http://www.qsl.net/w5dxp
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