NEC-LIST: MININEC Shows Standing Waves at Resonance on Twinline

Chuck Counselman and R. P. (Bob) Haviland,

Thanks for replying to my problem regarding standing waves at
resonance on twinline.

I'll reply to Chuck Counselman first.

Let me comment on the side issue. I said in my original message that
"the propagation of information (i.e., group velocity) in a conductor
is a few percent slower than the free-space speed of light...". Chuck,
your reply was:

   "This is not what you asked about, but I believe I detect a
    misconception or two here. I'll stick out my neck and hope that
    I'm _helping_ by commenting:

    (1) If the conductor is perfect, then wave propagation along it is
    at the speed of light in vacuuo.

    (2) Group velocity is irrelevant here. It's phase velocity that
    matters. The dipole resonance you're dealing with is a
    single-frequency, continuous-wave, phenomenon. Group velocity
    would matter if, e.g., we were discussing the time taken for a
    _pulse_ to propagate some distance.

    (3) Perhaps you're thinking of the well-known fact that a
    "half-wave" wire dipole resonates at a frequency slightly lower
    (by a few percent, depending on wire diameter) than the frequency
    for which the wire length equals one-half wavelength in vacuuo.
    This effect is due to the lumps of excess capacitance at the open
    ends of the wire, where the E-field "fringes", i.e., spreads out
    from the end of the wire radially in three dimensions, rather than
    in two dimensions in the plane perpendicular to the wire. BTW, if
    the resonance-frequency reduction _were_ due to a modification of
    phase velocity along the wire, the necessary modification would be
    an increase, not a decrease."

In a second message, Chuck, you wrote:

    "BTW, if the resonance-frequency reduction _were_ due to a
     modification of phase velocity along the wire, the necessary
     modification would be an increase, not a decrease. I think I got
     that backward. Sorry."

Reply to (1): I will tentatively accept your statement. I have tried
to find a resource that definitively states this, but so far no
luck. I would guess that your statement applies to a single thin
straight conductor having no self capacitance. However, when you have
two (or more) parallel conductors, distributed self capacitance and
mutual inductance will cause the propagation of energy along those
conductors to travel at less than the speed of light. For example, one
table says that an open wire line (twinline) with either 1/2 inch or 1
inch spacing using #18 conductors has a velocity factor of 95% (i.e.,
the signal or energy is propagated at 95% of the speed of light.

Reply to (2): I'll agree with you. For a single frequency transmission
or for transmission in a non-dispersive medium, the group and phase
velocities are identical. However, I really was referring to phase
velocity.

Reply to (3): Again, I agree with you except that the capacitance and
inductance are distributed all along the wires, including the
ends. This means that one cycle is completed in a distance shorter
than it would for a wave in free space. Hence, it is the same as I
said in my reply to (1).

Chuck, now I'll reply to your comments on the "real problem" (viz., standing
waves at resonance on twinline). Your comments were:

  "Here's your problem, I believe. MININEC can not accurately model a
   parallel-wire transmission line, or "twinline," with such close
   spacing between the wires. It's been five years since I used
   MININEC, but I think I recall that the practical lower limit for
   the center-to-center spacing is about three times the wire
   diameter. (Perhaps someone can refine this estimate.)

   I suggest doing the following little experiment with MININEC, which
   I remember finding very instructive. Define a parallel-wire
   transmission line of length somewhat greater than a half
   wavelength, so that you'll be able easily to see the standing-wave
   pattern. Put a source at one end and a resistive load (not an
   antenna) at the opposite end. (You can halve the number of
   segments required and cut execution time by using a perfectly
   conducting ground plane and modeling one wire of the twinline
   rather than both wires.)

   Observe the standing wave pattern with different values of load
   resistance, to find the characteristic impedance of the
   line. Compare this value with what the usual formula gives.

   Hope this helps."

Chuck, I am aware that MININEC has a problem with closely-spaced
wires. It declares them to be "crossed" and issues a warning. Thus, I
tried not only the setup I described (i.e., 0.3 cm diameter wires (d)
with a center-to-center spacing (D) of 0.36 cm, corresponding to Z0 =
74.68 ohms) but many other setups with wider spacings (up to D = 6.0
cm, corresponding to Z0 = 447.59 ohms). All showed basically the same
strange results (standing waves at resonance). With D = 6.0 cm and d =
0.3 cm, the ratio D/d = 20 should not be a problem for MININEC.

I like your idea of using a resistive load instead of a dipole. I will
try a variety of setups (sets of frequencies, sets of resistances, and
sets of spacings) to see what happens.

Now let me reply to Bob Haviland. Your message was: "I have never used
this version of MiniNEC, but with the older versions twinline seems
to give wrong answers with the feed system you have used. I have found
it necessary to use two sources of opposite sign in the twinline one
segment from the short segment representing the short at the line
terminals. If you try this, I would like to know the results."

Bob, I'm puzzled by this. The current magnitude and phase just on
either side of the current source looks OK. That is, the magnitudes
are identical and the phases differ by 180 degrees as you would
expect.

Now a question for anyone: Would I be able to eliminate the short wire
that connects the start of the twinline? My understanding of MININEC
is that a current source (or a voltage source) is mathematically
inserted at a point (at the junction of two current segments, which is
why I segmented the short wire into 2 segments so that the current
source would be mathematically at the center of that wire and would
allow me to maintain a balanced but oppositely-phased currents on the
two sides of the twinline). I would prefer to specify the positive
terminal of a current source be connected to the start of one of the
parallel wires and the negative terminal of the same current source be
connected to the start of the other parallel wires; however, I don't
think MININEC will allow me to do that. Does anyone have some thoughts
about this and about the standing wave problem I have? Thanks.

(-: Jerry R. Ehman :-)
Received on Wed Jun 17 1998 - 09:41:13 EDT