On Nov 13, 8:25*pm, Owen Duffy wrote:
If for example, the feedpoint Z of a 0.6 wave vertical over four quarter
wave radials was 150-j500, your tapped coil matching network can be
designed using bulk standard circuit theory to transform 150-j500 to 50
+j0, and nowhere do you use the missing 54° in those calcs.

That's because the lumped-circuit model assumes that all signals
travel instantly at faster than light speeds through the coil. At
instant, faster than light speeds, the coil cannot possibly occupy any
degrees of the antenna. When the real-world speed of light limit is
taken into account by using the distributed network model, the degrees
occupied by the coil falls out as part of those real-world
calculations. The lumped-circuit model is simply flawed for the
purpose of trying to determine the degrees occupied by the coil. I am
finishing up an article on this subject. At 3.5 MHz, the velocity
factor of the 100 turn, 10 inch long coil is 0.04, which makes the
coil occupy 26.4 degrees when used for a 3.5 MHz mobile antenna.

The "Axial Propagation Factor" from the Hamwaves Inductance Calculator
at:

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

can be used to determine the number of degrees occupied by a loading
coil. For the above coil at 3.5 MHz, the axial propagation factor is
1.8118 radians/meter. Multiplying by 1.4554 converts it to degrees/
inch. The coil is 10 inches long so: 1.8118(1.4554)(10) = 26.4 degrees
occupied by that loading coil at 3.5 MHz.

We can model a transmission line as lossless, but none exists in
reality.

We can model a loading coil that occupies zero degrees of the antenna,
but none exists in reality.
--
73, Cecil, w5dxp.com