Revisiting the Power Explanation
 

Jim Kelley wrote:


Total current from the two sources in
parallel into a 50 ohm load would now be 2.828 amps.

I misspoke he The current limit of two sources in parallel would be
2.828 amps, not the current into 50 ohms.

73, jk

Revisiting the Power Explanation
 

Cecil Moore wrote:

...

Will the fun never cease 8-)

http://www.ee.surrey.ac.uk/Personal/...ures/koan.html

Regards,
JS

Revisiting the Power Explanation
 

Jim Kelley wrote:
There
is nothing wrong with the proper use of superposition and interference.
Given that, what do you think the problem might be?

Please don't tell me you don't understand constructive
interference.

Quoting "Principles of Optics", 4th edition, by Born
and Wolf, page 257:
*************************************************
Suppose now that two monochromatic waves E1 and E2
are superposed at some point P. The total electric
field at P is

E = E1 + E2 (6) so that

E^2 = E1^2 + E2^2 + 2*E1*E2 (7)
*************************************************
[Note from w5dxp: Each one of those terms in
equation (7) is proportional to power which is
proportional to intensity! The last term in the
equation is certainly proportional to interference.

Resuming the quote from Born and Wolf:
*************************************************
Hence the total intensity at P is

I = I1 + I2 + J12 (8) where

I1 = E1^2 and I2 = E2^2 (9a)

are the intensities of the two waves, and

J12 = 2E1*E2 (9b) is the *interference term*."
*************************************************
As you know, the power associated with the wave is
proportional to E^2 so if E1 = E2, the power in
the superposed waves is four times the power in
a single wave. That's the nature of total constructive
interference as explained by Hecht in "Optics", 4th
edition, page 388.

Hint: When two identical EM waves are superposed
*in phase* in free space, the ratio of the E-field
to the B-field must remain equal to 377. The E-field
doubles and the B-field doubles so the (power) in the
wave quadruples to

Ptot = (E1+E2)x(B1+B2) = 4*E1xB1

Such is the nature of constructive interference. If
Keith can get two IC-706's to do that, I will believe
that superposition is valid for IC-706's.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Hi Cecil -

I'm glad to learn that you finally got yourself a decent optics text.
Now, please spend some time studying it. Take very careful note of
exactly what it says, and try to get rid of your preconceived notions.
Don't read between the lines, and don't selectively edit. If you
do, you will just end up leading yourself down another wrong path.

73 de ac6xg

Cecil Moore wrote:

Jim Kelley wrote:

There is nothing wrong with the proper use of superposition and
interference. Given that, what do you think the problem might be?


Please don't tell me you don't understand constructive
interference.

Quoting "Principles of Optics", 4th edition, by Born
and Wolf, page 257:
*************************************************
Suppose now that two monochromatic waves E1 and E2
are superposed at some point P. The total electric
field at P is

E = E1 + E2 (6) so that

E^2 = E1^2 + E2^2 + 2*E1*E2 (7)
*************************************************
[Note from w5dxp: Each one of those terms in
equation (7) is proportional to power which is
proportional to intensity! The last term in the
equation is certainly proportional to interference.

Resuming the quote from Born and Wolf:
*************************************************
Hence the total intensity at P is

I = I1 + I2 + J12 (8) where

I1 = E1^2 and I2 = E2^2 (9a)

are the intensities of the two waves, and

J12 = 2E1*E2 (9b) is the *interference term*."
*************************************************
As you know, the power associated with the wave is
proportional to E^2 so if E1 = E2, the power in
the superposed waves is four times the power in
a single wave. That's the nature of total constructive
interference as explained by Hecht in "Optics", 4th
edition, page 388.

Hint: When two identical EM waves are superposed
*in phase* in free space, the ratio of the E-field
to the B-field must remain equal to 377. The E-field
doubles and the B-field doubles so the (power) in the
wave quadruples to

Ptot = (E1+E2)x(B1+B2) = 4*E1xB1

Such is the nature of constructive interference. If
Keith can get two IC-706's to do that, I will believe
that superposition is valid for IC-706's.

Revisiting the Power Explanation
 

Cecil Moore wrote:
John Smith I wrote:
IBM extended ascii, ain't it great? grin

What is surprising is that if I simply enter a
Shift-6 and a '2', it somewhere gets changed
to that IBM extended superscript squared
character.

With an extended ascii chart (giving the decimal value of the character)
and the alt-key combined with the number pad, it is possible to enter
extended ascii. However, not all news servers will honor all extended
ascii characters and not all news readers will represent them correctly
(plus, you probably have to set the news reader to allow them in it's
settings.)

Hold down the alt key while entering 2-5-3 (253) from the numeric
keypad, release the alt key and "²" is presented--so can all extended
ascii be created in notepad, dos edit, etc. ...

JS

Revisiting the Power Explanation
 

Jim Kelley wrote:
I'm glad to learn that you finally got yourself a decent optics text.
Now, please spend some time studying it. Take very careful note of
exactly what it says, and try to get rid of your preconceived notions.
Don't read between the lines, and don't selectively edit. If you do,
you will just end up leading yourself down another wrong path.

Jim, it is obvious that you do not understand
constructive interference between coherent EM waves.

The stuff I quoted from Born and Wolf agrees with Hecht
and contradicts what you have said. In particular, equation
(7) on page 257 contradicts your earlier posting. Given
that power is proportional to E^2, please explain how the
following equation is possible in 377 ohm space in light
of your earlier posting.

E^2 = E1^2 + E2^2 + 2E1*E2

From that equation, Born and Wolf develop the interference
term which they call J12, same as Hecht's I12, same as
Dr. Best's 2*SQRT(P1*P2).

This is exactly what Hecht described in "Optics". Seems
that you don't realize that the square of the sum is
more than the sum of the squares when constructive
interference between two coherent EM waves occurs.

Two identical EM waves in free space must maintain the
377 ohm free space ratio. Therefore, if the E-field doubles,
the B-field must also double, contrary to your earlier posting
that said that voltage and current could not double
simultaneously but that is exactly what happens in a fixed
Z0 environment like free space or a transmission line.

I explained this to Dr. Best way back in 2001. That you
don't yet understand it is the cause of our many arguments.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

John Smith I wrote:
Hold down the alt key while entering 2-5-3 (253) from the numeric
keypad, release the alt key and "²" is presented--so can all extended
ascii be created in notepad, dos edit, etc. ...

I've got that chart hanging on my wall. It's just
interesting that if I type a shift-6 and then a 2,
it comes back as a superscript-2. Alt-253 doesn't
do anything in Thunderbird.
--
73, Cecil http://www.w5dxp.com

Revisiting the Power Explanation
 

Cecil Moore wrote:
John Smith I wrote:
Hold down the alt key while entering 2-5-3 (253) from the numeric
keypad, release the alt key and "²" is presented--so can all extended
ascii be created in notepad, dos edit, etc. ...

I've got that chart hanging on my wall. It's just
interesting that if I type a shift-6 and then a 2,
it comes back as a superscript-2. Alt-253 doesn't
do anything in Thunderbird.

Cecil:

Whoa! I am not arguing with you man.

I just thought I would toss that out, not everyone may be as savvy as
yourself.

This conversation holds my interest, I just "look out the windows" from
time to time, teacher used to scold me for that too ... I'll redouble my
efforts to stay focused :-)

Regards,
JS

Revisiting the Power Explanation
 

Cecil Moore wrote:
Jim Kelley wrote:

I'm glad to learn that you finally got yourself a decent optics text.
Now, please spend some time studying it. Take very careful note of
exactly what it says, and try to get rid of your preconceived notions.
Don't read between the lines, and don't selectively edit. If you do,
you will just end up leading yourself down another wrong path.


Jim, it is obvious that you do not understand
constructive interference between coherent EM waves.

The stuff I quoted from Born and Wolf agrees with Hecht
and contradicts what you have said.

Cecil - I have had Born and Wolf on my shelf for years. I use it
regularly. I understand interference. It's not difficult. I work
with it on a regular basis in fact - both optically, and at RF.

In particular, equation
(7) on page 257 contradicts your earlier posting. Given
that power is proportional to E^2, please explain how the
following equation is possible in 377 ohm space in light
of your earlier posting.

E^2 = E1^2 + E2^2 + 2E1*E2

Power doesn't interfere. It doesn't even propagate, Cecil. (You might
note the distinct absence of any descriptions of how power
propagates in the physics texts. Hopefully you'll also note the
absence of any discussion of how power constructively and
destructively interferes in Born and Wolf.) And as the above equation
points out quite plainly, electric fields interfere. Electric fields
do propagate, along with their counterpart: magnetic fields.

From that equation, Born and Wolf develop the interference
term which they call J12, same as Hecht's I12, same as
Dr. Best's 2*SQRT(P1*P2).

I think you'll find the equations to be largely the same in most
optics texts, Cecil. No need to point that out.

73, Jim AC6XG

Revisiting the Power Explanation
 

John Smith I wrote:
Whoa! I am not arguing with you man.

That's good, cuz I'm not arguing with you either.
What do we do now?
--
73, Cecil http://www.w5dxp.com