On Jun 4, 12:26*pm, K1TTT wrote:
this becomes MUCH harder to analyze. the transmission line case is
easy because the equations collapse to a single linear dimension, so
you can write your simple standing wave equation with a single sin(kx)
term. in a solenoid, especially a finite length solenoid, and double
especially because the length may be an appreciable fraction of a
wavelength, there is no such simple representation for the fields.

Well maybe it is much harder using Maxwell's equations but maybe there
is a simple representation. See what you think about this idea. At the
following web site is an impedance calculator that will yield the
characteristic impedance and velocity factor of a loading coil so the
coil can be analyzed the same way as a transmission line. (We also can
model the whip using EZNEC and, like a transmission line stub, equate
the feedpoint impedance to the impedance of a lossy open-circuit
stub.) We know the Z0 of the whip will be a few hundred ohms.

http://hamwaves.com/antennas/inductance.html

The velocity factor of the specified coil can be calculated from the
axial propagation factor in radians per meter.

So please assume a frequency of 4 MHz and a typical six inch long
bugcatcher loading coil with a Z0 of 3800 ohms and a VF of 0.024. All
losses in/from the coil can be lumped together as if they were normal
transmission line losses. The electrical length of the coil can be
calculated from the physical length and VF. I don't see that it is all
that "MUCH harder to analyze" than a transmission line example with
the same amount of losses.
--
73, Cecil, w5dxp.com