Cecil Moore wrote:
Tom Donaly wrote:

We're talking about the envelope, Cecil, what are you talking about?
Since you've become so enamored of math all of a sudden, go ahead and
plot the current envelope on a length of very lossy transmission line
and tell me, with a straight face, that it follows a sine
function. On the other hand, don't bother. I know it's too hard
on your head, but it's an interesting exercise for everyone else.


The envelope of an unattenuated sine wave is a straight line, Tom.
Is a straight line sinusoidal? Give us an everloving break! You
can fool half the people half the time but please stop trying to
fool all the people all the time.

Here is an example that should put an end to your foolishness.

100W-----50 ohm coax------50 ohm load dissipating 50 watts

Please explain how the 3dB attenuation in the coax causes
nonsinusoidal signals in the system. Proof of nonsinusoidal
signals would be the generation of harmonics. We are all
awaiting your reinvention of the laws of physics.

Nice try, but you still keep conflating time with distance.
If any of the lurkers on this newsgroup want, they can
consider a dipole somewhat shorter than 1/2 wavelength. According to
one of Cecil's sources, Balanis, the current distribution on such
a wire resembles a triangle. Now, it's true you can do a Fourier
analysis on this triangle, but you won't come up with frequencies.
You will come up with an infinite group of sine and cosine waves
with units of cycles/meter (as opposed to cycles/second). What earthly
use are units of cycles/meter? Does Cecil have a radio that can tune in
cycles/meter? On the other hand, if you could measure the current and
turn it into a voltage so an oscilloscope could show it, you would see
a nice sine wave everywhere except at the ends of your antenna. And the
units would be in cycles per second. Cycles per meter, phaseless
phasors... you sure have a vivid imagination, Cecil.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
According to
one of Cecil's sources, Balanis, the current distribution on such
a wire resembles a triangle.

It only resembles a triangle. It is actually part of a
cosine waveform. From cos(80) to cos(90), the cosine
function is close to a straight line but it is *NOT*
a straight line. Assuming the current distribution is
a triangular is only an approximation with a known error.
The current distribution acutally remains a cosine function
but assuming a straight line simplifies the math and doesn't
cause an unacceptably large error.

It is akin to the approximation that A = sin(A) when
A is very small. It is *ONLY* an approximation with limited
accuracy.

cos(80)=0.17365, cos(85)=0.08716, cos(90)=0

0.17365/2 = 0.08682 which is an error of 0.4% when one assumes
a triangular function.
--
73, Cecil http://www.qsl.net/w5dxp