RE: Re: NEC-LIST:Proper Antenna Patterns

At 11:39 AM -0400 10/13/01, ghagn_at_erols.com wrote:
>If an antenna in the real world is mismatched at the feed, this can
>cause currents to flow on the outside of the shield of the coax from
>the source/ sink (transmitter or receiver) to the antenna. These
>extra currents (which are usually not modeled in NEC) do contribute
>to the pattern measured....

Unbalanced (common-mode) current on the transmission line feeding an
antenna is indeed a common problem in the real world, but its cause
is symmetry violation rather than impedance mismatch, unless you
extend the definition of term "impedance mismatch" beyond its
conventional meaning, to include symmetry mismatch.

My preferred term "symmetry violation" may need clarification. A
transmission line having two terminals at its antenna can be excited
and may propagate waves in two orthogonal modes with respect to
ground: the "common mode" for which equal currents flow into the two
terminals, and the usually-desired differential mode in which the sum
of the currents into the two terminals is zero. The latter mode is
often called "balanced."

Either a balanced-mode or a common-mode wave may travel in either
direction on the line; and by introducing voltages and/or impedances
to the discussion we can further distinguish forward and reverse
waves.

The balance/symmetry/mode of the _excitation_, defined in terms of
voltage/current as I have just done, is not the same thing as as the
balance/symmetry of the _structure_ of the transmission-line. E.g.,
coaxial line is unbalanced or asymmetric in geometry, but ordinarily
we try to excite it purely in the balanced mode, so it won't radiate
or couple to external conductors.

At its antenna-connected end, a transmission line has one input
impedance for its balanced mode (e.g., 50 ohms for RG-8/U coax) and
another input impedance, not so well controlled or known because it
depends on factors outside the line itself, for its common mode.

In general, the excitation of the line is the superposition of these
two modes. Combining or resolving the modes is straightforward
algebra. (Again, there is the further resolution of waves into
forward and reverse.)

Likewise any antenna structure has balanced and unbalanced modes, and
these have distinct input impedances. Objects near what one may
regard as the antenna are, like it or not, effectively also part of
the antenna. Sometimes surrounding objects, and/or sometimes the
putative antenna itself have/has asymmetry that cross-couples the
balanced and unbalanced modes.

Matching the characteristic impedance of the balanced mode of a
transmission line to the impedance of the balanced mode of an antenna
to which the line is connected is no guarantee that unbalanced
current will not flow, and _mis_matching the characteristic impedance
of the balanced mode of a transmission line to the impedance of the
balanced mode of an antenna to which the line is connected is no
guarantee that unbalanced current _will_ flow.

A trivial example of the latter possibility is connecting a balanced
source to one end of a perfectly symmetrical parallel-wire line
having (balanced-mode!) characteristic impedance Zo = 600 ohms, and
connecting the other end of this line to the center of a perfectly
symmetrical orthogonal dipole antenna (in free space) whose
balanced-mode input impedance is 70 ohms. There's a huge impedance
mismatch but the symmetry is perfect so no common-mode current flows
anywhere.

A trivial example of the former possibility is connecting a source to
one end of a coaxial line having (balanced-mode) Zo = 70 ohms, and
connecting the other end of this line to the center of the same
perfectly symmetrical dipole antenna whose balanced-mode input
impedance is 70 ohms. What upsets the symmetry of this pretty,
nominally impedance-matched, picture is that the unbalanced or
"common" mode of the coax is excited by the asymmetric connection of
the outer or "shield" conductor of the coax to one terminal of the
antenna's feedpoint terminal-pair.

My point is that "impedance matching" (which is commonly but
sometimes erroneously regarded as a purely balanced-mode problem;
i.e., the common mode is erroneously disregarded), and the symmetry
of excitation/response, are distinct, although often coupled,
problems.

For real-world success you must consider both. Fortunately NEC does
provide us with tools for modeling both.

>So I think we need to be careful about generalizations which may
>apply to the model, and its assumptions, but which may not apply in
>a real-world implementation.

I agree, of course. I would just repeat the advice that there is
more to worry about in feeding a real-world antenna than just
conventional, balanced-mode, impedance-matching. One must also
consider the (usually undesired) excitation of the common mode.

-Chuck.

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