On Sat, 05 Jun 2004 10:14:09 -0500, Cecil Moore wrote:
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.
Snip
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.
Sorry, Cecil, in spite of their similarity with Hecht's, these equations are
totally invalid. Steve derived them from his Eq 9, which is also totally invalid
for use with reflected power. This equation is correct and valid when there are
two separate and individual sources. But here there is only one source, the
transceiver. When connecting two batteries in series Eq 9 works, because there
is enough energy there to support the additional current demanded with the
increased voltage. But not when the transceiver is the sole source of power.
With the transmission line system Steve's voltage V2 comes from the same source
as V1. The problem is that when the total forward power resulting from the
addition of reflected power and source power the total forward power is never
absorbed in the load, the power resulting from the reflection is subtracted from
the total power. This limitation does not occur when there are two separate
sources to maintain the increased current.
Because Steve used Eq 9 in an invalid way to derive Eqs 10 through 15, all of
these derived equations are also invalid. Try Eq 13 for example. It says 75 w
plus 8.33 w = 133.33 w, as you well know. This is absurd!
In addition, because the powers don't add up correctly using V1 and V2 at zero
phase relationship, he concocted the ruse that they must add vectorially, and he
goes through several values of phase relationships to show what the forward
power would be with the various phases. This is poppycock, because the phase
relationship between the source (V1) and re-reflected voltage (V2) is ALWAYS
ZERO on lossless lines.
His initial problem is that he misinterpreted Eq 6 in Part 1 to yield the
forward voltage Vfwd, where it actually yields the voltage E of the standing
wave at any point on the line, where the point on the line is determined by the
'L' term in the exponents on the right-hand side of the equation. In other
words, the summation of terms on the right-hand side of his Eq 6 does not equal
forward voltage Vfwd, as it indicates incorrectly, but instead equals the
voltage of the standing wave.
In addition to other errors, the entire right-hand column of page 46 is invalid.
Walt
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