Superposition
 

K7ITM wrote:
On Nov 17, 4:03 pm, Cecil Moore wrote:
The waves are launched by the external reflection from a
Z0-match and the internal reflection from the load.

So the waves are going opposite directions along the line??

No, all reflections travel toward the source and
therefore, are traveling in the same direction.
Their Poynting vectors are all toward the source.
Given the following Z0-match impedance discontinuity
in a transmission line with the source to the left
and the load to the right:

Z0-match
------Z01---+---Z02------
Pfor1-- Pfor2--
--Pref1=0 --Pref2

The power reflection coefficient is
rho^2 = [(Z02-Z01)/(Z02+Z01)]^2

Pref1 is a combination of two reflected waves

1. P1 = Pfor1(rho^2) "the external reflection from the
Z0-match"

2. P2 = Pref2(1-rho^2) "the internal reflection from
the load"

Pref1 = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Pref1 equals zero at a Z0-match so P1+P2 and A=180 deg.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Antonio Vernucci wrote:
The extra power measured at the receiver is obviously "created" at the
expense of power taken away from other regions of the space (according
to the transmit antenna pattern).

Too fundamental to deserve further discussions!

Almost everyone knows what occurs in free space -
constructive interference in the direction of
greater gain and destructive interference in the
direction of lesser gain. But my posting was not
about free space. I thank you for your input so
far but please now extend those EM wave concepts
to transmission lines.

Everyone doesn't agree that constructive and
destructive interference also happens at a Z0-
match point in a transmission line with reflections.
That is the topic that needs "further discussions".

Just as constructive interference functions to
increase antenna gain in one direction while
destructive interference functions to decrease
antenna gain in another direction, in a transmission
line at a Z0-match point, constructive interference
functions to increase the energy flow toward the
load while destructive interference functions to
decrease the energy flow toward the source.

Antonio, please don't bow out now. You are apparently
one of the few posters who fully understands interference.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Sun, 18 Nov 2007 12:05:05 -0500, "Stefan Wolfe"
wrote:


"Richard Clark" wrote in message
.. .
On Sun, 18 Nov 2007 00:16:47 -0500, "Stefan Wolfe"
wrote:

Let's rewind up that list of charades to revisit:
Well, power is a vector quanity subject to the rules of vector
math.
and ponder the implication of a negative power, for simplicity:
P1 = 50W @ 90deg
P2 = 50W @ 270deg
what does the math reveal?

I am not trying to define power as negative with respect to zero
Negative with respect to zero? What about with respect to positive?
Or even a smaller negative! How about half negative (only 90 degrees
shift instead of 180)?
What happened to:
Well, power is a vector quanity subject to the rules of vector
math.

I was so wanting to see your solution, much less how:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)
migrated into the negated sine in:
= (50 - 0) + (50 - 0) - 2SQRT P1*P2 sine(A)


Oh God this is getting frustrating!

You are lagging the community by at least 8 to 10 postings.

http://math2.org/math/integrals/more/restrig.htm

1. See top equation. THE INTEGRAL OF A COSINE IS A SINE.

What you published above is not the integral of the system and it has
problems even in isolation.

I added a minus
sign, I shouldn't have BUT IT DOESN'T MATTER.

As so many previous mistakes don't matter either. I also note (and I
am full aware of the math) that YOUR reference (see top equation)
solves with a constant added - as it should if this were a legitimate
exercise.

My students didn't get full credit for discarding constants,
especially when they didn't have the vaguest notion of how these
constants contribute to the outcome.

Let me guess, you will say "it doesn't matter" with emphasis. :-)

I think you are marginalizing your credibility with each succeeding post in
which you dispute freshman caluclus fundamentals. Depending upon your
education base, this could be quite a blow to you. I thought you knew
math...maybe it was just me getting the wrong impression. Are you pulling
our legs?

Well, I did think I had mined this troll to completion, but another
round may yet bring more fascinating entries.

73's
Richard Clark, KB7QHC

Superposition
 

Just as constructive interference functions to
increase antenna gain in one direction while
destructive interference functions to decrease
antenna gain in another direction, in a transmission
line at a Z0-match point, constructive interference
functions to increase the energy flow toward the
load while destructive interference functions to
decrease the energy flow toward the source.

I cannot follow your reasoning as I cannot understand what is a "Z0-match
point".

In my understanding:
- if the transmission line end is mismatched, in no point impedance can be equal
to Z0.
- conversely if the transmission line end is matched, impedance is equal to Z0
in all points. But there is no reflected wave and hence no energy flow toward
the source

Then, your "Z0-match point" must be something else which I cannot figure out.

73
Tony I0JX

Superposition
 

Tony, I0JX wrote:
"Then, your "Zo-matchpoint" must be comething else which I cannot figure
out."

I`ll guess with Tony that in a made-up case of a 50-ohm antenna and a
50-ohm transmitter connected by a 1/2-wavelength of 300-ohm twinlead, we
have a Zo-match to 50-ohms because the twin-lead, mismatched at both
ends, still looks to source and load like 50-ohms.

Best regards, Richard Harrison, KB5WZI

Superposition
 

Antonio Vernucci wrote:
I cannot follow your reasoning as I cannot understand what is a
"Z0-match point".

A Z0-match is defined in my ARRL Antenna Book.

Then, your "Z0-match point" must be something else which I cannot figure
out.

Here is an example of a Z0-match to 50 ohms at point '+':

XMTR--50 ohm coax---+---1/2 WL 300 ohm feedline---50 ohm load

The SWR on the 300 ohm feedline is 6:1. The SWR on the 50
ohm coax is 1:1. What happens to the energy and momentum
of the reflected waves on the 300 ohm feedline? Seems
obvious that there is destructive interference toward
the XMTR and constructive interference toward the load.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Sun, 18 Nov 2007 14:28:09 -0500, "Stefan Wolfe"
wrote:

BTW the constant you saw has
nothing to do with the equation at hand since we assume zerop power for that
component at t = 0.

An unemphatic "it doesn't matter!" :-)

I could have made C =100,

Hmmm, 0 is as good as 100?

what must the value of C
be in this equation? Ha!

You are right, you have been away from math class too long. The value
of the added C as the result of integration is unknown by definition.
This constant is, after all, from your own reference supplied by you.
Plugging in any value (including your fudge factor of 0) plucked from
the air is invalid. Hardly the best way to demonstrate the
conservation of energy (power, karma, the trade balance, or
what-have-you).

73's
Richard Clark, KB7QHC

Superposition
 

A Z0-match is defined in my ARRL Antenna Book.

Sorry, I have that book, but I do not remember where it is.

Here is an example of a Z0-match to 50 ohms at point '+':

XMTR--50 ohm coax---+---1/2 WL 300 ohm feedline---50 ohm load


OK, understood.

The SWR on the 300 ohm feedline is 6:1. The SWR on the 50
ohm coax is 1:1. What happens to the energy and momentum
of the reflected waves on the 300 ohm feedline? Seems
obvious that there is destructive interference toward
the XMTR and constructive interference toward the load.

I am not sure on whether I am able to correctly interpret your statement. My
understanding is:

- reflected power does not reach the transmitter, as it is fully reflected back
toward the load
- such re-reflected power reaches the load, where it is partially absorbed (thus
contributing to the total power delivered to the load) and partially reflected
back once more

Probably this is what you call destructive interference at the trasmitter and
constructive interference at the load.

The fact that reflected power is fully re-reflected to the load does not seem to
be appreciated by everyone. Many people still attribute their transmitter power
transistors failure to reflected power burning them. The failure is instead
clearly due to malfunctioning or poor design of the SWR protection circuit that:
- does not keep the collector voltage within its maximum allowable value when
load impedance is too high
- does not keep the collector current and the junction temperature within their
maximum allowable values when load impedance is too low

73

Tony I0JX

Superposition
 

Cecil, W5DXP wrote:
"Antonio, please don`t bow out now."

Why is a principle so trivial as superposition worth a thread in this
newsgroup?

Best regards, Richard Harrison, KB5WZI

Superposition
 

Richard Harrison wrote:
Why is a principle so trivial as superposition worth a thread in this
newsgroup?

Because most of the posters to this newsgroup do not
know what happens to the energy in the waves during
superposition inside a transmission line. They seem
to understand superposition in free space but not
inside a transmission line. Maxwell's laws are the
same for EM waves in free space and inside a
transmission line.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Sun, 18 Nov 2007 16:10:57 -0500, "Stefan Wolfe"
wrote:

When integrating the actual equation at hand over its limits,
the value of the constant does not matter because it always subtracts out.

This is simply leaning on the Xerox to resuscitate a doomed method. We
only have to consider that if this "logic" were applied to the actual
equation (again, from you):
Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)
= (50 - 0) + (50 - 0) - 2SQRT P1*P2 sine(A)
That all terms would be rendered 0. After all, the two leading terms
are constants too.

Will we hear another chorus of "it doesn't matter?" :-)

You are simply compounding errors.

73's
Richard Clark, KB7QHC

Superposition
 

On Sun, 18 Nov 2007 17:40:53 -0500, "AI4QJ" wrote:

This is funny.

A chorus indeed.

73's
Richard Clark, KB7QHC

Superposition
 

On Sat, 17 Nov 2007 21:46:30 -0500, "Stefan Wolfe"
wrote:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Hi Dan,

Now let's return to this equation.

It is drawn from the classic optics formula for finding the Intensity
of radiation at a point in space that is illuminated by two sources.
The intensity is a function of illuminators and their relative (at
that point) phase.

Phase can also be thought of as distance (which returns us to the
point in space). As each path has a different length; then relative
phase, their difference in length, is simplified by casting out all
full cycles to leave only the remnant, or partial cycle. Of course,
keeping count of the complete angular distances can be preserved,
nothing will change in the result.

A is a single value (as a point in space is 1D) and is expressed as
that relative phase. A, thus in the world of all possible variations,
can be any single value between 0 and 2·Pi radians. It follows that
the cosine operation then renders a single value between +1 and -1.

If you were to integrate this over some portion of time, or for all
time; then it wouldn't change the answer one iota. The intensity of
interference at a fixed spot in space from fixed illuminators does not
change with time.

If you were to integrate this over some portion of space, or for all
space; then you would come up with different solutions. Across all
space the intensity would become the sum of the two sources'
illumination.

There is no necessity of changing cos(A) to -sin(A) + C at all. There
is no issue of unknown constants, the original intensities do not
disappear.

However, Integration does not resurrect Cecil's sucker punch. There
is no missing power (energy, calories, what-have-you) as the question
was tailored to an illusion that too many bought into.

Lest we go 'round the mulberry bush on that again, please respond to
my critique posted some time ago if you fault IT.

73's
Richard Clark, KB7QHC

Superposition
 

On Sun, 18 Nov 2007 20:22:21 -0500, "AI4QJ" wrote:

point to me to where it is?
It is my first post to this thread, at level 2, responding directly to
Dave.

2. You are saying that A is not a function of time. OK, OF COURSE that
changes the appearance of the curve I was using. Still, the total energy
expended over one cycle (can be thought of as phase angle - distance, not
time), 0 to 2pi radians, is = zero

As always, engineering is done by strict language. Look at your own.
"Expended" energy is power. Integration of power over time will never
result in no power unless no energy was "expended."

(It is still valid to integrate and
cancel out C ;-)) Over the full cosine power cycle, energy is still
conserved, however the model is totally different.

The model never changed, the consideration of superposition (partial
solutions) may momentarily suspend us, but upon its completion the
complete solution resolves to exactly what I've posted. Hence, there
is no "missing" power (energy, etc.).

Why didn't you mention
that A was not a function of time before?

Consider the genesis of the formula. It informs us all that this is a
point location solution of total illumination from two remote sources.
There is no need for me to create a shopping list of all the things
this formula is NOT a function of.

I am only trying to show conservation of energy which must hold true for any
of these power formulas to be correct. And this equation still shows
conservation of energy being true, even if A is the phase angle.

If it is any different from what is not already in my post, feel free
to elaborate.

73's
Richard Clark, KB7QHC

Superposition
 

On Sun, 18 Nov 2007 21:36:37 -0500, "AI4QJ" wrote:


"Richard Clark" wrote in message
.. .
On Sun, 18 Nov 2007 20:22:21 -0500, "AI4QJ" wrote:

point to me to where it is?
It is my first post to this thread, at level 2, responding directly to
Dave.

I can only handle one issue at a time (regarding what you said, it IS
possible to have a zero net energy expenditure as long as energy that was
sent out was received back again at a later time or at a different place;
that is what the sine/cosine functions essentially tell you, whether they
are functions of time or distance):

Hi Dan,

Well then, your concept of expended is quite different from most and
flexible to the point of not really meaning much. So what is the
point in using the word?

Regarding:

"Neither of these artificial conditions actually exist in the reality
of superposed waves, and that is the con. The group has been fixated
on the separate artificial environments with their partial solutions
as though they actually exist independent of the reality of the
superposed, complete solution."

This is a bit philosophical for me but let me say that I believe that a
square wave is definitely the sum of superimposed odd harmonics in
accordance with Fourier. I believe each of the superimposed waves exists
independently. If you do not believe me, just ask anyway who lives next door
to a CB'er with a linear amp and transmits over modulated square waves (due
to saturating his amplifier). The square waves exist but so do the component
waves. I am not sure if this is related to what you are saying but it seems
to be the same thing.

I believe that cupiditas is the root of evil; however, both of our
beliefs have nothing to do with partial solutions of Superposition
posing as real world entities.

73's
Richard Clark, KB7QHC

Superposition
 

On Nov 18, 7:22 am, Cecil Moore wrote:
K7ITM wrote:
On Nov 17, 4:03 pm, Cecil Moore wrote:
The waves are launched by the external reflection from a
Z0-match and the internal reflection from the load.

So the waves are going opposite directions along the line??

No, all reflections travel toward the source and
therefore, are traveling in the same direction.
Their Poynting vectors are all toward the source.
Given the following Z0-match impedance discontinuity
in a transmission line with the source to the left
and the load to the right:

Z0-match
------Z01---+---Z02------
Pfor1-- Pfor2--
--Pref1=0 --Pref2

The power reflection coefficient is
rho^2 = [(Z02-Z01)/(Z02+Z01)]^2

Pref1 is a combination of two reflected waves

1. P1 = Pfor1(rho^2) "the external reflection from the
Z0-match"

2. P2 = Pref2(1-rho^2) "the internal reflection from
the load"

Pref1 = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Pref1 equals zero at a Z0-match so P1+P2 and A=180 deg.
--
73, Cecil http://www.w5dxp.com

Ah, finally you get around to telling us the setup.

So to get to the conditions in the original posting, we must have a
total power coming into that Z01:Z02 junction exactly equal to the
power leaving it. For example, if Z01 = 50 ohms as implied by your
numbers, and Z02 = 100 ohms, barring stupid math errors, I make out
that the left-to-right power on the Z01 line is 450 watts, and the
right-to-left power on the Z02 line is 56.25 watts, for a total of
506.25 watts. Since you've only accounted for 171 watts, the
remainder must be going off to the right from that junction. Change
the phases, and the power will split differently.

This seems to all agree with standard superpostion. So what the heck
was the point of the original posting in this thread?

Or, why do I even bother reading these things in the first place,
since they all turn out to be pretty boring?

Once again, we see that everything interesting going on in the system
is happening right at the discontinuity where waves arrive and are
reflected. Same in a Wilkinson combiner, same in a "magic T" (which I
suppose the Wilkinson is, if you look at it the right way), same as in
a resistive combining network (if you account for power dissipated in
the resistors), ...

Superposition
 

AI4QJ wrote:
. . .
This is a bit philosophical for me but let me say that I believe that a
square wave is definitely the sum of superimposed odd harmonics in
accordance with Fourier. I believe each of the superimposed waves exists
independently. If you do not believe me, just ask anyway who lives next door
to a CB'er with a linear amp and transmits over modulated square waves (due
to saturating his amplifier). The square waves exist but so do the component
waves. I am not sure if this is related to what you are saying but it seems
to be the same thing.

This is indeed a philosophical question. A consequence of superposition
is that there's *no possible way* to tell if a particular square wave is
made from separately generated sinusoids, a single step, or combinations
of any of an infinite number of other possible periodic waveforms. With
the proper sorts of filters, you can take the square wave apart into any
of those infinite sets of functions, "proving" the "independent
existence" of each. Sinusoids are mathematically convenient, but they're
by far not the only choice.

Roy Lewallen, W7EL

Superposition
 

Richard Clark wrote:
However, Integration does not resurrect Cecil's sucker punch. There
is no missing power (energy, calories, what-have-you) as the question
was tailored to an illusion that too many bought into.

There's no illusion and no missing power, just interference
at a point balanced by the opposite kind of interference
somewhere else - just following the conservation of energy
principle. It was a rhetorical question.
--
73, Cecil http://www.w5dxp.com

Superposition
 

K7ITM wrote:
This seems to all agree with standard superpostion. So what the heck
was the point of the original posting in this thread?

Some posters deny that destructive interference is associated
with zero reflected energy toward the source when a Z0-match
exists. If you are not one of those posters, the thread was
not aimed at you.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Antonio Vernucci wrote:
- reflected power does not reach the transmitter, as it is fully
reflected back toward the load

The re-reflection is associated with destructive interference
toward the source and an equal magnitude of constructive
interference toward the load. The energy in the canceled
reflected waves is redistributed to a region that allows
constructive interference to occur, i.e. in the opposite
direction to the direction of reflected wave cancellation
toward the source.

Probably this is what you call destructive interference at the
trasmitter and constructive interference at the load.

At a Z0-match *point*, destructive interference *toward* the
transmitter and constructive interference *toward* the load.

It is akin to the passive elements of a Yagi causing
destructive interference to the rear and constructive
interference toward the front. What is the front/back
ratio of a Z0-match? :-)
--
73, Cecil http://www.w5dxp.com

Superposition
 

"Cecil Moore" wrote in message
et...
Richard Harrison wrote:
Why is a principle so trivial as superposition worth a thread in this
newsgroup?

Because most of the posters to this newsgroup do not
know what happens to the energy in the waves during
superposition inside a transmission line. They seem
to understand superposition in free space but not
inside a transmission line. Maxwell's laws are the
same for EM waves in free space and inside a
transmission line.
--
73, Cecil http://www.w5dxp.com

Superposition
 

"Sal M. Onella" wrote in message
...

"Cecil Moore" wrote in message
et...
Richard Harrison wrote:
Why is a principle so trivial as superposition worth a thread in this
newsgroup?

Because most of the posters to this newsgroup do not
know what happens to the energy in the waves during
superposition inside a transmission line. They seem
to understand superposition in free space but not
inside a transmission line. Maxwell's laws are the
same for EM waves in free space and inside a
transmission line.
--
73, Cecil http://www.w5dxp.com



Sorry for the blank post, above, -- double-click-itis set in.

I like 90% of these technical discussions. I'm a curious person by nature
but I don't always know what doors to pull open, so it's nice when a good
door is held open for me.

73
"Sal"
(KD6VKW)

Superposition
 

Sal M. Onella wrote:
I like 90% of these technical discussions. I'm a curious person by nature
but I don't always know what doors to pull open, so it's nice when a good
door is held open for me.

It stands to reason that if interference is associated
with a redistribution of EM wave energy in free space,
essentially the same thing could happen in a transmission
line. Incidentally, interference is also associated with
the feedpoint impedance of a standing wave antenna. If
the feedpoint impedance of a dipole is 50 ohms, that's
a Z0 match to 50 ohm coax for an antenna supporting an
SWR far in excess of 1:1.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Nov 18, 7:40 am, Cecil Moore wrote:
Just as constructive interference functions to
increase antenna gain in one direction while
destructive interference functions to decrease
antenna gain in another direction, in a transmission
line at a Z0-match point, constructive interference
functions to increase the energy flow toward the
load while destructive interference functions to
decrease the energy flow toward the source.

Correction. The Z matching device functions to increase the energy
flow toward the load and decreases the energy flow toward the source.
Interference is just the mathematical description of the resulting
spacial distribution.

73, ac6xg

Superposition
 

Jim Kelley wrote:
Correction. The Z matching device functions to increase the energy
flow toward the load and decreases the energy flow toward the source.
Interference is just the mathematical description of the resulting
spacial distribution.

The decrease to zero in reflected energy flow toward the source
is known as "total destructive interference" in the noun version
of the word as used by Hecht. The increase in energy flow
toward the load is known as constructive interference. One need
not refer to superposition as the cause of interference since
the interference *event* implies superposition of two (or more)
coherent waves as the *cause* of the interference *process*.

I am using "interference" as a noun synonymous
with an "interference process" event, not as in "interference
rings". The Z0-matching event cannot occur without an interference
process (event). "Total destructive interference" as defined
by Hecht is *necessary and sufficient* for a Z0-match to occur,
i.e. if total destructive interference exists toward the source,
a Z0-match has been achieved.

From Websters: "interference - n. the *process* in which
two coherent EM waves combine to reinforce or cancel each
other." The reinforcing or canceling can be partial or total.
Thus, I am using Hecht's noun definition of "interference"
which "yields a resultant irradiance that deviates from the
sum of the component irradiances". Reinforcement or cancellation
is the *result* of that *process*. Superposition is the *cause*
of that *process*.

The *result* of the interference *process* is sometimes wave
cancellation if the appropriate conditions exist. That's
what happens at a Z0-match.

The interference pattern of an antenna is the *result*
of the interference *process*. Hecht says interference
"corresponds" to the "interaction" of two or more
coherent EM waves "yielding a result ...". He clearly
considers interference to be in the cause and effect
chain of events, as do I.
--
73, Cecil http://www.w5dxp.com

Superposition
 

"Antonio Vernucci" wrote in message
...
................
If you instead put your receiver/antenna in a point where the two waves
have equal amplitude and same phase, your receiver will measure 200
joules/s (i.e. four times the power produced by each wave alone, not just
two times).
.....................
73

Tony I0JX

You know that can't be right, because combining two antennas gives 3 db
gain. For example, if you connect them in series, you will get twice the
voltage, but the impedance also doubles.

Tam

Superposition
 

Richard Clark wrote:
On Sat, 17 Nov 2007 17:16:11 -0500, "Stefan Wolfe"
wrote:

snip


Then I am sure you will agree that using terms like "taking Cecil's sucker
bait" is not the type of "strict language" and "solid logic" appropriate in
a technical forum.

In fact, it is in the strictest language par excellence! Strict
allows for no wiggle room, nothing nebulous. You completely
understood what it meant and technical forums are assaulted with a lot
of bankrupt theories- sometimes innocently offered, but not in this
case. You might complain of style, but not substance.

That made me think of a paper that I read a few years ago that summarized:

"There would appear to be the possibility of a potential correlation..."


Talk about going out on a limb!

- 73 de Mike N3LI -

Superposition
 

Tam/WB2TT wrote:
"Antonio Vernucci" wrote in message
...
...............
If you instead put your receiver/antenna in a point where the two waves
have equal amplitude and same phase, your receiver will measure 200
joules/s (i.e. four times the power produced by each wave alone, not just
two times).

You know that can't be right, because combining two antennas gives 3 db
gain. For example, if you connect them in series, you will get twice the
voltage, but the impedance also doubles.

The constructive interference in free space occurs before
the antennas, not after them. Such is the nature of
constructive interference which very few posters fully
understand. My original posting was designed to expose
the beauty of constructive interference. Instead, I
was accused of diverting the issue or worse.

But it's simply a fact of physics - total constructive
interference between two equal amplitude waves results
in four times the amplitude of each wave. Of course, the
result somewhere else is total destructive interference,
i.e. complete absence of energy.

No one can fully understand what happens at a Z0-match
point without an understanding of interference.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Jim Kelley wrote:
Correction. The Z matching device functions to increase the energy
flow toward the load and decreases the energy flow toward the source.
Interference is just the mathematical description of the resulting
spacial distribution.

The decrease to zero in reflected energy flow toward the source
is known as "total destructive interference" in the noun version
of the word as used by Hecht. The increase in energy flow
toward the load is known as constructive interference. One need
not refer to superposition as the cause of interference since
the interference *event* implies superposition of two (or more)
coherent waves as the *cause* of the interference *process*.

I am using "interference" as a noun synonymous
with an "interference process" event, not as in "interference
rings". The Z0-matching event cannot occur without an interference
process (event). "Total destructive interference" as defined
by Hecht is *necessary and sufficient* for a Z0-match to occur,
i.e. if total destructive interference exists toward the source,
a Z0-match has been achieved.

From Websters: "interference - n. the *process* in which
two coherent EM waves combine to reinforce or cancel each
other." The reinforcing or canceling can be partial or total.
Thus, I am using Hecht's noun definition of "interference"
which "yields a resultant irradiance that deviates from the
sum of the component irradiances". Reinforcement or cancellation
is the *result* of that *process*. Superposition is the *cause*
of that *process*.

The *result* of the interference *process* is sometimes wave
cancellation if the appropriate conditions exist. That's
what happens at a Z0-match.

The interference pattern of an antenna is the *result*
of the interference *process*. Hecht says interference
"corresponds" to the "interaction" of two or more
coherent EM waves "yielding a result ...". He clearly
considers interference to be in the cause and effect
chain of events, as do I.

Cecil,

You are waaay too concerned with philosophical words like *cause*,
*process*, *result*, and *event*.

There is no justification for saying that interference causes
superposition or that superposition causes interference or any such
combinations. Causality is a very important concept in physics, but it
has no useful meaning in this situation.

The way a physicist solves problems like this is to set up the equations
in terms of generic sinusoidal functions with variable parameters. Then
the boundary conditions of the problem are applied to determine
precisely what the parameters must be. That's it. No worries about *why*
something is happening or what is causing what. Those items are
impossible to define in any case.

If you were to read Born and Wolf you would find that they deal with the
multiple interference problem (antireflective glass) in exactly the same
manner. They never even mention constructive or destructive interference.

There is a reason physicists use this type of problem solving method. It
works for a entire range of boundary conditions. Try using your
constructive/destructive interference technique when the problem is not
quite so simple. For example, 3D problems when the incidence angles are
not so tidy, materials with absorption, or multiple films such as those
used in *real* AR coatings. You might muddle through with some generic
concept of constructive/destructive interference, but you won't be able
to get a quantitatively useful answer.

By the way, Born and Wolf must have been pretty well connected. It
appears that they copied the multiple reflection lattice diagram from
your web page. 8-)

73,
Gene
W4SZ

Superposition
 

Tam/WB2TT wrote:
"Antonio Vernucci" wrote in message
...
...............
If you instead put your receiver/antenna in a point where the two waves
have equal amplitude and same phase, your receiver will measure 200
joules/s (i.e. four times the power produced by each wave alone, not just
two times).
.....................
73

Tony I0JX

You know that can't be right, because combining two antennas gives 3 db
gain. For example, if you connect them in series, you will get twice the
voltage, but the impedance also doubles.

If you supply your power to two identical antennas instead of one, each
antenna gets half the power. If there's no mutual coupling between the
antennas (seldom actually true), then each then produces 0.7071 times
the field strength that the original antenna did, because each is
getting half the original power. At the points where the fields from the
two antennas completely reinforce, the sum of the fields is 0.7071 +
0.7071 = 1.4142 times the field produced by the original antenna. This
is a field strength gain of 3 dB compared to the original antenna, and
it's a field strength gain, as Antonio says, of 2 (6 dB) compared to the
field produced by each of the two antennas.

Your comments about impedance and voltage makes me wonder if maybe
you're confusing feedpoint voltage with field strength. If you connect
two antennas in series and supply the same total power as you did with
one, both the current and the voltage of each will be 0.7071 times the
values the single antenna had. Again, though, all this assumes no mutual
coupling between the antennas, which is seldom true.

Roy Lewallen, W7EL

Superposition
 

Cecil Moore wrote:


Hecht says interference
"corresponds" to the "interaction" of two or more
coherent EM waves "yielding a result ...".

I know from corresponding with you for many years that what someone
says, and what you understand them to say are not necessarily the same
thing. In instances such as this you apparently take whatever meaning
you wish from the words. Interference is not the particular kind of
"process" that you have in mind. There are many meanings to the words
'interaction' and 'process'. In the case of wave interference , the
words do mean that waves are 'doing things' to other waves.

73, ac6xg

Superposition
 

Cecil Moore wrote:


The constructive interference in free space occurs before
the antennas, not after them. Such is the nature of
constructive interference which very few posters fully
understand. My original posting was designed to expose
the beauty of constructive interference.


Cecil,

That's the best line of the month. Can you help out with the Hollywood
writer's strike? Leno and Letterman need some help.

73,
Gene
W4SZ

Superposition
 

Gene Fuller wrote:
There is no justification for saying that interference causes
superposition or that superposition causes interference or any such
combinations.

That's really good because I didn't say anything like that.
Please don't try to imply that I did.

Superposition can occur with or without interference.

Interference can occur with or without wave cancellation.

If you were to read Born and Wolf you would find that they deal with the
multiple interference problem (antireflective glass) in exactly the same
manner. They never even mention constructive or destructive interference.

I've moved and can't find my Born and Wolf but Hecht certainly
holds constructive/destructive interference in central
position in his classic book. He devotes an entire chapter
to interference.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Gene Fuller wrote:
Cecil Moore wrote:
The constructive interference in free space occurs before
the antennas, not after them. Such is the nature of
constructive interference which very few posters fully
understand. My original posting was designed to expose
the beauty of constructive interference.

That's the best line of the month. Can you help out with the Hollywood
writer's strike? Leno and Letterman need some help.

It's in Born and Wolf, Gene. Too bad you missed it.
Two one watt coherent waves combine with total
constructive interference to a four watt wave.
Of course, somewhere else they combine with total
destructive interference to a zero watt wave so the
average power remains at two watts.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Jim Kelley wrote:
In the case of wave interference , the
words do mean that waves are 'doing things' to other waves.

Thanks Jim, that is exactly what I have been saying
for years. For ideal non-reflective thin-film coatings
on glass, waves are indeed doing things to other waves,
i.e. canceling them.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Jim Kelley wrote:

In the case of wave interference , the words do mean that waves are
'doing things' to other waves.

That should read "In the case of wave interference , the words don't
mean that waves are 'doing things' to other waves."

Thanks for pointing out the typo, Cecil.

73, ac6xg

Superposition
 

Roy Lewallen wrote:
At the points where the fields from the
two antennas completely reinforce, the sum of the fields is 0.7071 +
0.7071 = 1.4142 times the field produced by the original antenna. This
is a field strength gain of 3 dB compared to the original antenna, and
it's a field strength gain, as Antonio says, of 2 (6 dB) compared to the
field produced by each of the two antennas.

That's an example of constructive interference.

At the points where the fields from the two antennas
are equal and 180 degrees out of phase, the sum of the
fields is zero. That's the necessary destructive
interference on the flip side of the coin that satisfies
the conservation of energy principle.

Essentially the same thing happens at a Z0-match in
a transmission line.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Jim Kelley wrote:
That should read "In the case of wave interference , the words don't
mean that waves are 'doing things' to other waves."

If waves are not 'doing things' to other waves, how
are reflected waves eliminated by thin-films on glass?
What happens to the reflection from the thin-film
which has a reflectance of 0.01? If something is
not done to that real reflection, it must still be
there, but we can see that it is not there.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
There is no justification for saying that interference causes
superposition or that superposition causes interference or any such
combinations.

That's really good because I didn't say anything like that.
Please don't try to imply that I did.

Superposition can occur with or without interference.

Interference can occur with or without wave cancellation.


Cecil,

Your exact words we

The decrease to zero in reflected energy flow toward the source
is known as "total destructive interference" in the noun version
of the word as used by Hecht. The increase in energy flow
toward the load is known as constructive interference. One need
not refer to superposition as the cause of interference since
the interference *event* implies superposition of two (or more)
coherent waves as the *cause* of the interference *process*.


# Is this not written in English?

# Is there some other interpretation of *cause* in the last sentence?

# Just what do you mean by, "superposition of two (or more)
coherent waves as the *cause* of the interference *process*"?

# Are you playing some sort of word game by using *event* and *process*?

# Do you have a reference for the rules of that word game?


73,
Gene
W4SZ

Superposition
 

Cecil Moore wrote:
Gene Fuller wrote:
Cecil Moore wrote:
The constructive interference in free space occurs before
the antennas, not after them. Such is the nature of
constructive interference which very few posters fully
understand. My original posting was designed to expose
the beauty of constructive interference.

That's the best line of the month. Can you help out with the Hollywood
writer's strike? Leno and Letterman need some help.

It's in Born and Wolf, Gene. Too bad you missed it.
Two one watt coherent waves combine with total
constructive interference to a four watt wave.
Of course, somewhere else they combine with total
destructive interference to a zero watt wave so the
average power remains at two watts.

Cecil,

Sorry. I missed it because it is not there. They don't say any such thing.

73,
Gene
W4SZ