Roy Lewallen wrote:
As I pointed out some time ago, the envelope of a standing wave isn't in
general sinusoidally shaped.

Assuming the source signal is sinusoidal, your above assertion
would require non-linearity in the antenna. Since antennas are
generally considered to be linear systems, would you please
explain where the nonlinearity is coming from?
--
73, Cecil http://www.qsl.net/w5dxp

Gene Fuller wrote:
I am really puzzled. I cannot see even one inconsistency in my
statements, including those you quote.

What is the problem?

You said there is phase remaining in the cos(kz) term which
is contained in the amplitude.

Then you said there is no phase information.

Those statements contradict each other.

In any case, the graph at

http://www.qsl.net/w5dxp/travstnd.GIF

proves that there is phase information contained in the
standing wave current magnitude. The arc-cosine of the
standing wave current magnitude is identical to the phase
of the traveling wave referenced to the source current.

Please note that the "experts" have been strangely silent
on the contents of that graph.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil Moore wrote:
Roy Lewallen wrote:
As I pointed out some time ago, the envelope of a standing wave isn't
in general sinusoidally shaped.

Assuming the source signal is sinusoidal, your above assertion
would require non-linearity in the antenna. Since antennas are
generally considered to be linear systems, would you please
explain where the nonlinearity is coming from?

Additional thought: Assuming the source signal is a pure sine
wave, if the standing wave current "isn't in general sinusoidally
shaped", then the antenna would have to be introducing harmonic
radiation that doesn't exist in the source signal. That fact is
easily proved with a Fourier analysis.

I wasn't aware that standing wave antennas cause radiation on
harmonic frequencies. Any standing wave current waveform that
deviates very far from a sinusoid would be illegal.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil Moore wrote:
Gene Fuller wrote:

I am really puzzled. I cannot see even one inconsistency in my
statements, including those you quote.

What is the problem?


You said there is phase remaining in the cos(kz) term which
is contained in the amplitude.

Then you said there is no phase information.

Those statements contradict each other.



Cecil,

My exact words, which you quoted, were,

The only "phase" remaining is the cos (kz) term, which is really
an amplitude description, not a phase.

If you interpreted that comment as supporting the existence of a phase
in this situation, then I cannot offer any help except to suggest you go
back and review the meaning of "not".

This has become sillier than I ever imagined possible. I am done with
this FIGHT!

73,
Gene
W4SZ

Cecil Moore wrote:
Roy Lewallen wrote:

As I pointed out some time ago, the envelope of a standing wave isn't
in general sinusoidally shaped.


Assuming the source signal is sinusoidal, your above assertion
would require non-linearity in the antenna. Since antennas are
generally considered to be linear systems, would you please
explain where the nonlinearity is coming from?

No it wouldn't, Cecil. Even you know better than that. For those who
believe Cecil, consider a lossy transmission line terminated in a short,
or open. The signal is attenuated as it goes down the line, and also
attenuated as it comes back up the line, in an exponential fashion.
The envelope is thus not sinusoidal. The signal may be sinusoidal,
but the envelope can't possibly be. Cecil's antennas may be lossless,
but most of us want our antennas to radiate energy, hopefully, as
efficiently as possible, so we have to put up with current distributions
that aren't easy either to envision or to calculate. That's why even
Cecil uses EZNEC.
73,
Tom Donaly, KA6RUH

Cecil, W5DXP wrote:
"Assuming the source signal is a pure sine wave, if the standing wave
current "isn`t in general sinusoidally shaped (as Roy said)", then the
antenna would have to be introducing harmonic radiation that doesn`t
exist in the source signal."

Standing waves are produced by forward and reflected traveling
soinusoidal waves produced by the same generator. Coherent signals on a
transmission line and antenna of the same frequency are correctly
represented by phasors.

The term phasor is preferred over vector for an arrow which indicates
phase separation and magnitude of an electrical unit. Phasors are used
to represent sinusoidal voltages and currents. They are also used to
represent reactances and impedances.

Like vectors, phasors can be "added" by the head-to-tail method or by
the component method.

If a phasor represents an alternating current:
I = Io cos omega t,
then the sum of the two phasors representing forward and reflected
sinusoidal components is another sinusoid of the same frequency.

Point is the components are amenable to phasor representation. All the
old authors do it. This amenability is proof the standing wave is a
sinusoid too.

Best regards, Richard Harrison, KB5WZI

Gene Fuller wrote:
The only "phase" remaining is the cos (kz) term, which is really
an amplitude description, not a phase.

Yes, there it is again, you said there is phase information
in the amplitude description and you were right.
--
73, Cecil http://www.qsl.net/w5dxp

On Wed, 17 May 2006 16:19:17 GMT, "Tom Donaly"
wrote:

Cecil's antennas may be lossless,

Hi Tom,

Even more amazing is that they are linear transmission lines.

73's
Richard Clark, KB7QHC

Tom Donaly wrote:

Cecil Moore wrote:
Assuming the source signal is sinusoidal, your above assertion
would require non-linearity in the antenna. Since antennas are
generally considered to be linear systems, would you please
explain where the nonlinearity is coming from?

No it wouldn't, Cecil. Even you know better than that. For those who
believe Cecil, consider a lossy transmission line terminated in a short,
or open. The signal is attenuated as it goes down the line, and also
attenuated as it comes back up the line, in an exponential fashion.
The envelope is thus not sinusoidal.

An attenuated (damped) sinusoidal signal is still sinusoidal, Tom.
The fact that such a signal doesn't generate harmonics proves
that it is sinusoidal. If it were not sinusoidal, it would
by definition, be generating harmonics. Are you really asserting
that a damped sinusoidal signal generates harmonics? That's the
only way to prove it has gone nonsinusoidal.

All non-sinusoidal waveforms contain harmonics of the fundamental
frequency. Every competent engineer in the world is aware of that
technical fact. If the source signal to an antenna is a pure single-
frequency sine wave, and if the standing wave current is non-
sinusoidal, then the antenna has necessarily introduced harmonics,
i.e. the antenna is non-linear.

W7EL is simply mistaken when he says the standing wave current
waveform is not sinusoidal. If the standing wave current waveform
ever was nonsinusoidal, the antenna would, by definition, be
non-linear and be generating harmonics not present in the source
waveform.

Seems you guys need to review your Math 202 course covering Fourier
transforms.
--
73, Cecil http://www.qsl.net/w5dxp

Richard Harrison wrote:
If a phasor represents an alternating current:
I = Io cos omega t,
then the sum of the two phasors representing forward and reflected
sinusoidal components is another sinusoid of the same frequency.

Point is the components are amenable to phasor representation. All the
old authors do it. This amenability is proof the standing wave is a
sinusoid too.

The absence of harmonic frequencies generated by the antenna
is also proof that the standing wave is a sinusoid. All
nonsinusoidal waveforms contain harmonics.
--
73, Cecil http://www.qsl.net/w5dxp