Roy Lewallen wrote:
What is the delay through a physically very small toroidal coil with the
same inductance as the solenoidal coil? Why?

A toroidal coil cannot be modeled using the Dr. Corum
formulas. But I will take a stab at the answer.

In a physically very small toroidal coil, all the
turns are tightly coupled, i.e. the flux caused by
one coil links all of the other windings so the
delay should be quite small. In any case, one
cannot use a current with unchanging phase (referenced
to the source phase) to calculate the delay through
anything. The only phase information left in a
standing wave is in the magnitude. If the current
magnitude at the bottom of the coil is 1.0, the phase
shift is the ARCCOSine of the current magnitude at
the top of the coil for a base-loaded resonant
antenna. Actual phase measurements on the current
in standing-wave antennas is meaningless. We already
know it hardly changes at all with length. EZNEC
confirms that statement.

In an air-core solenoidal coil, like the one w8ji
used, the flux linkage tends to be associated with
adjacent turns so all the flux does not link all
the coils. Tom's coil was 100 turns, 10 TPI, 2"
diameter. The first turn was 10 inches away from
the last turn. The delay through that coil calculates
out to be about 25 nS.

If we setup a 2" transmit coil and a 2" receive
coil 10 inches away in air, the energy transfer
efficiency would be very small. I don't have a
formula for such but I assume one (or more) exists.

Bottom line: There are now formulas for calculating
the Z0 and VF of large air-core loading coils which
are known to be in the family of *slow-wave* devices.

I doubt that a toroidal coil is in the family of
slow-wave devices.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com