I won't believe your theory, Yuri, until you and Cecil take the
time to present it in terms of field theory. Since you guys have taken
EM classes in college you should have no trouble doing this, right?

Please reference Chapter 1 of _Fields_and_Waves_... by Ramo,
Whinnery, and Van Duzer. Start with equations 1.18 (4)&(5)
and 1.22 (1) & (2). Also _Antenna_Theory_ by Balanis, equations
4-81 and 10-1 and one other that I cannot locate right now. :-)
The one I cannot locate is the simplified one for a 1/2WL dipole.
--
73, Cecil http://www.qsl.net/w5dxp

I don't have Ramo et al's book, but I do have Balanis' book. I think
anyone who wants to understand equation 4-81 should read the whole
section: 4.5.6 where he makes it clear these equations are
approximations that are pretty good under some circumstances
and lousy under others. The standards he judges them on
are the techniques of Integral Equations and Moment Method
which he explains in another part of the book. He doesn't say
a single thing about a "cosine law" for a real antenna, as Yuri
does.
I think I'll keep my EZNEC.
73,
Tom Donaly, KA6RUH
(P.S. I looked, in Balanis, for a section on inductively loaded
antennas and couldn't find one. That doesn't mean it doesn't exist.
If anyone knows where to look in that book for information on such
I'd be obliged for the information.)

Tdonaly wrote:
He doesn't say
a single thing about a "cosine law" for a real antenna, ...

I didn't say a single thing about a "cosine law" either.

If anyone knows where to look in that book for information on such
I'd be obliged for the information.)

Information on inductively loaded antennas seems to be sadly lacking.
But I have found one in _Antennas_ by Kraus & Marhefka, third edition.
I trust that will be a good enough reference for everyone.

On page 823 under "23-13 TRAPS", what he says about traps is not relevant.
But what he says about traps on half their resonant frequency is absolutely
choice.

"At frequency F1, for which the dipole is 1/2WL long, the traps introduce
some inductance so that the resonant length of the dipole is reduced."

On the next page, the current distribution is shown for the trapped dipole
on 1/2 the trap's resonant frequency. Needless to say, it clearly shows
a current drop through the inductive trap.

And talking about phasing using coils: "A coil can also act as a 180 degree
phase shifter as in the collinear array of 4 in-phase 1/2WL elements in Fig.
23-21b. ... THE COIL MAY ALSO BE THOUGHT OF AS A COILED-UP 1/2WL ELEMENT."

Emphasis mine. Now you guys can stop pulling our legs and confess that it
was all a joke.
--
73, Cecil http://www.qsl.net/w5dxp
"One thing I have learned in a long life: that all our science, measured against
reality, is primitive and childlike ..." Albert Einstein



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Tdonaly wrote:
"He doesn`t say a single thing about a "cosine law" for a real
antenna...."

Like Cecil, I didn`t either, but I am surprised a challenge exists to
sine or cosine current distribution which most serious antenna authors
assume and illustrate.

If the projected height of of a sine wave is cast upon a circle, its
amplitude is completely described by the projection of the radius on the
diameter of the circle.

A sine wave amplitude is the vertical or "y" value of the (x,y)
coordinates of the tip of a radius vector rotating counter-clockwise in
a circle of unit value.

The angle considered is that made by the radius vector with the "x"
axis.

Antenna discussions often use cosine waves. These are identical to sine
waves except that they are displaced by 90-degrees, or 1/4-cycle, or pi
radians (all different names for the same thing). When sine equals +1,
the cosine equals 0-degrees, and it is about to go negative. This is
because the sine starts at a value of zero at zero degrees. At the same
0-degree start, cosine is +1.

There is no difference between a sine and a cosine wave except for
90-degrees phase lead of the cosine wave. The sine of an angle is the
same as the cosine of (that angle minus 90-degrees). Example: sine of
90-degrees = 1.
Cosine of 0-degrees = 1 also, etc. etc. etc.

Ed Laport in "Radio Antenna Engineering" says on page 19:

"The principles of the electrically short antenna are better understood
from Fig.1.1, in which the natural sinusoidal current distribution along
a straight uniform section quarter-wavelength vertical is used for
reference. A straight uniform vertical antenna with a height of 20
degrees would have the relative current distribution shown for the sine
curve above the 20-degree level A."

And in John Devoldere, ON4UN`s now famous Fig 9-22:

"Short loaded verticals with their current distribution." Note the
cosines given for each antenna height demarcation.

Best regards, Richard Harrison, KB5WZI