NEC-LIST: Re: Which excitation should I use ?

At 4:38 PM -0400 3/14/07, Phil Ede wrote:
>...Roy followed with the comment:
>"Ironically, the pattern of an array with elements near
>anti-resonance (e.g., monopoles near a half wavelength high), is
>better when the elements are end fed with voltages... than when end
>fed with... currents"
>
>I am now looking for an explanation for this effect, and have the
>following observations....

The explanation is simple.

1. What radiates are the currents in the array elements. So, to get
the pattern you want, you must control these currents.

2. The current throughout the length of an array element must be
controlled. For an array of vertical elements, I mean the current as
a function of height in each element.

3. The distribution of current as a function of height in an element
is determined partly by any source(s) that you insert in that
element, and partly by the fields of the other elements of the array.
Superposition applies, so we may consider each of these effects
separately.

4. First let's consider the effect of a source inserted in the
element. If you excite the element at one of its natural resonant
frequencies, you will get a big response, which is just what you want
your source to accomplish. The shape of the response, i.e., the
current distribution as a function of position along the element, is
determined by the shape of the natural "normal mode" of oscillation
in the element. For an infinitely thin monopole (grounded at its
base and open at its top), the natural current distribution function
is a sinusoid having a zero-crossing at the open end and at every
_even_ whole-number multiple of one-quarter-wavelength from this end,
and having alternating positive/negative maxima at _odd_ whole-number
multiples of one-quarter-wavelength from this end.

    It's easy to make the element "ring" this way, i.e., with this
simple sinusoidal mode shape; although you could force it to ring
with another shape by inserting a funny source (a source with a
reactive Thevenin impedance or Norton admittance) in a funny place.
To keep things simple, let's rule out funny business. Let's insert
one ideal voltage source or one ideal current source at the base of
the monopole, and let the height of the monopole be a whole number of
quarter-wavelengths.

    Either type of source will excite the same sinusoidal mode shape.

5. Now let's consider the current in this monopole element resulting
from the fields of other elements, with the voltage of the source at
the base of this element set to zero if we inserted an ideal voltage
source; or, if we inserted an ideal current source at the base of
this element, with the current of this source set to zero.

    First, assume that we inserted an ideal voltage source. With its
voltage set to zero, this source is a "short circuit." So, if the
height of the monopole is an odd number of quarter-wavelengths, it is
naturally resonant at the same frequency as that of the excitation it
feels from the other elements. So this excitation will produce a big
response. Oops! We don't want _this_ response to be big. We want
it to be small, as small as possible, because we probably can't
control the magnitude and phase of this excitation. The magnitude
and phase of this excitation will be determined by many factors such
as the distances of the other elements and the currents in them,
meaning the currents as functions of height within these other
elements. Except in certain special cases, all the planets will not
be aligned, i.e., all these other factors will not be just right.
The magnitude and phase of the excitation will not be anything that
we want.

    On the other hand, if the height of the monopole is an _even_
number of quarter-wavelengths, e.g., if the monopole is one-half
wavelength tall, since this monopole is shorted to ground at its
base, this monopole is _not_ naturally resonant at the frequency of
the excitation. Therefore its response to the excitation by the
other elements will be _small_. Yes! Small is what we want.

    To summarize our findings so far: A voltage source at the base of
a quarter-wave monopole is bad; but a voltage source at the base of a
half-wave monopole is good.

    Now assume that we inserted an ideal _current_ source. With its
current set to zero, this source is an "open circuit." This array
element is open at both ends. So, if its height is an _even_ number
of quarter-wavelengths, it is naturally resonant at the same
frequency as that of the excitation it feels from the other elements.
So this excitation will produce a big response. Oops again! Bad.

    On the other hand, if the height of this element is an _odd_
number of quarter-wavelengths, this element is _not_ naturally
resonant at the frequency of the excitation. Therefore its response
to the excitation by the other elements will be _small_. Yes again!
Small is what we want.

6. Finally, to summarize our findings for voltage sources and current
sources, and for quarter-wave and half-wave monopoles, let's draw a
two-by-two truth table:

| \ Monopole height
| Source \ in wavelengths:
| type \ Quarter | Half
| ----------+---------+--------
| Voltage | BAD | GOOD
| ----------+---------+--------
| Current | GOOD | BAD
| |

Q.E.D.

-Chuck W1HIS

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