Re: NEC-LIST: Negative driving point impedances in phased arrays

>I'm looking for good conceptual explanations (potentially backed up by
>models) for when negative driving point impedances (or negative power)
>occurs in a phased array.
>
>There are lots of generalized statements that this occurs (and, in fact,
>some fairly unexceptional appearing systems wind up with a "negative
>element"), but not a whole lot of simple qualitative explanations of when it
>occurs.
>
>One can look at a two element system (say a couple of dipoles less than 0.25
>wavelength apart) and come up with some ratios of feed currents that result
>in power fed from one element to another. This implies that you've got some
>reactive power circulating in the system (since it's obviously not
>radiated...).
>
>Is it related to superdirectivity, i.e. you've scanned into the invisible
>region? Off hand, I'm not sure, because you can have superdirective arrays
>(that is, the phase advance is more than the spacing of the elements) that
>don't have negative power on some elements.
>
>Jim Lux
>
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>NEC-List_at_robomod.net
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Jim, negative input impedances frequently occur in phased array (MF
broadcast) antenna systems. Another example is given in my chapter
on VLF, LF and MF Antennas [1], pp. 614-615. This is because you are
using multiple fed the antenna system. --- two or more sources.

For antenna systems comprising two elements closely spaces one can
visualize what is happening by considering the mutual impedance
between the elements --- the CFA is one of those antenna types ---
but you get the same result for two closely spaced electrically small
dipoles with quadrature feed --- see below:

Coupled Antenna Elements: When two near by antennas (or antenna
elements) are used in an antenna system, the driving-point impedances
of each antenna element depend on the self-impedance of that antenna
and in addition upon the mutual impedance between that antenna
element and the other, c.f. Figure. If r = current ratio I1/I2, where
in general r is a complex number, then

V1/I1 = Z11 + 1/r Z12

V2/I2 = rZ21 + Z22

Figure Mutual impedances between antennas and antenna elements.

where Z12 = Z21 is the mutual impedance between the antenna elements,
and Z11 and Z22 are approximately equal to the self- impedance of the
antenna elements.

It is seen that the input impedances V1/I1 and V2/I2 are dependent on
the current ratio r, and r is a complex number, and so the operating
impedances can be quite different from the self impedances of the
elements.

For the CFA the driving impedance of the disc element is negative,
the driving impedance of the cylinder element is positive, for the
case where the cylinder phase referenced to the disc is - 90 degrees.
The cylinder is the better radiator. If you reverse the phase
relation you radiate nothing, since you are trying to get back more
power than you are delivering. Interesting.

For antenna systems employing one source a negative input impedance
means something is wrong.

John S. (Jack) Belrose

-- 
_____________________________________________
John S. (Jack) Belrose, PhD Cantab, VE2CV
LIFE SENIOR MEMBER of the IEEE
TA ARRL
Fellow Radio Club of America
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Athlone Fellow
Radioscientist Emeritus Researcher
Communications Research Centre Canada
PO Box 11490 Stn. H
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