Superposition
 

Hi Dave,

Your analysis, or critique rather, has been misdirected. In fact,
everyone has been suckered. Not unusual given the problem was crafted
to be disingenuous. It is, after all, this group's form of "Three
Card Monte." Can you pick the card that is the one-eyed Jack?

With a little re-ordering here....

On Sat, 17 Nov 2007 16:08:04 +0000, Dave wrote:

Wave#3 = Wave#1 superposed with Wave#2
Wave#3 is the only thing real here.

These two waves superpose to V = 92.38v and I = 1.85a
Note: P = 171 joules/sec
Superposition is a process that gives us a solution to a system that
exists, not a figurative one. However, the process of superposition
requires the suspension of reality to perform computation, and to
render the solution that is real.

yes, lets say source S1 supplies a voltage V1 into a load L1, where L1
is a pure 50 Ohm resistance.
Dave, herein lies everyone's presumption, and one that has been
"suggested" originally. What you "interpret" does not exist
independently. In fact, S1 has no independent existence (neither does
the other source). This is the artificial contrivance of partially
solving a superposition problem.

Let's simply look at these "suggestions:"
Wave#1: V = 50v at 0 deg, I = 1.0a at 0 deg, P = 50 joules/sec
In the reality of two waves, this artificial condition is arrived at
only through removing the second wave from the reality. And like
wise:

Wave#2: V = 50v at 45 deg, I = 1.0a at 45 deg, P = 50 joules/sec
In the reality of two waves, this artificial condition is arrived at
only through removing the first wave from the reality.

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.

You have changed the circuit.

Of course he has. That is the allowed method of computing
superposition (he has in fact not done the full method of
superposition analysis - but that is immaterial to the discussion
except only to note that Cecil's posts are often rife with error).

The egregious error is found he
*During each second*, Wave#1 supplies 50 joules of energy
Wave #1 is not independent in reality, so the statement is wrong. What
is provided (50 joules) is only a partial solution in the method of
computing the superposition which for that computation, suspends
reality to examine the separate constituents in an artificial
environment.

73's
Richard Clark, KB7QHC

Superposition
 

Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate

Superposition
 

Dave wrote:
Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate
0 Infinity
is interpreted as zero times infinity

Superposition
 

Dave wrote:
Since you have changed the circuit source 1 is connected to, you should
not be surprised it supplies a different power.

But these are not "sources" per se, they are EM
waves with a fixed constant energy content. EM waves
simply cannot, willy-nilly, increase their energy
content. The actual source could conceivably be
light-years away so it would take light-years to
increase the energy content of the EM waves.

So please tell us how a 50 watts/unit-area wave can
increase its energy content to 85.5 watts/unit-area
while being light-years away from any source.
--
73, Cecil http://www.w5dxp.com

Superposition
 

K7ITM wrote:
In typical Cecil fashion, you trimmed out the only part I really cared
about having you answer: "Assuming the two "waves" existed
independently at some points in space, you'll have to first tell us
_exactly_ what was done to combine them into one wave."

They were confined to a transmission line. Coherent
waves traveling in the same direction in a transmission
line are forced to also be collinear. Unlike space, a
transmission line forces collinearity upon the EM waves.
But the same thing happens at a 1/4WL thin-film non-
reflective coating on glass. Assuming one brings the
Poynting vectors into collinearity, one can see what
is happening at http://www.w5dxp.com/thinfilm.gig
--
73, Cecil http://www.w5dxp.com

Superposition
 

Richard Fry wrote:
The physics of EM radiation.

It seems strange to me that people who know that
antenna gain in one direction comes at the expense
of gain in another direction cannot carry that
concept over to transmission lines. Constructive
interference in one direction means destructive
interference in another direction. That's what
creates the radiation pattern for antennas. It
is also exactly the same thing that routes
energy toward the antenna instead of toward the
source in a Z0-matched transmission line.

--
73, Cecil http://www.w5dxp.com

Superposition
 

Tom Donaly wrote:
Hiding behind authority again, Cecil? Using a few carefully edited
quotes from Hecht doesn't prove anything. Ian hit the nail on the
head: Vague philosophical arguments using second and third order
abstractions that you can't prove to have any connection to reality
aren't going to convince anyone.

The void technical content of your objection is noted, Tom.
Why don't you present some theory and math that prove me
wrong instead of just waving your hands and uttering ad
hominem attacks?
--
73, Cecil http://www.w5dxp.com

Superposition
 

"Richard Clark" wrote in message
...
On Sat, 17 Nov 2007 12:02:26 -0500, "Ralph Mowery"
wrote:

You can come up with a lot simpler example that at first might look like
a
paradox. Consider two DC current sources of 1 amp each. Each current
source will deliver 50 W to a 50 Ohm resistor. Now connect the two
current
sources in parallel, and the resultant 2 amps will deliver 200W to the
same 50 Ohm resistor. There is nothing wrong here.

Tam

Wouldn't you have to double the voltage to get the 1 amp from each source
to
flow ?

Hi Ralph,

That is one of the usual properties of a current source.

73's
Richard Clark, KB7QHC

If you want to drive 1 amp into a 100K resistor, make sure the current
source can develop 100,000 Volts!

Tam

Superposition
 

On Sat, 17 Nov 2007 13:52:54 -0500, "Tam/WB2TT"
wrote:

Wouldn't you have to double the voltage to get the 1 amp from each source
to
flow ?

Hi Ralph,

That is one of the usual properties of a current source.

73's
Richard Clark, KB7QHC

If you want to drive 1 amp into a 100K resistor, make sure the current
source can develop 100,000 Volts!

Hi All,

It is with some reflected amusement that I pause here to relate a
story. I was once tasked to calibrate an HP precision current source.
I had faithfully connected my standard shunt and voltmeter to do just
this, and the source performed exactly as specified (HP equipment that
wasn't broke, always did). I then disconnected the leads and was
immediately bit. The source performed exactly as specified!

73's
Richard Clark, KB7QHC

Superposition
 

Tom Donaly wrote
So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would go to
zero.
____________

As the number of radiators in a given array never can reach infinity,
neither will the input power for a given peak ERP from that array ever go to
zero. Obviously there are practical limits as well.

But this does not change the realities that...

1) other things equal, the greater the number of discrete radiators in an
array, the less input power is needed for that array to produce a given peak
ERP, and

2) the peak free-space, far field produced by a given ERP is the same for
all combinations of antenna gain and antenna input power producing that ERP.

This has been proven in commercial FM and TV broadcast systems for many
decades.

RF