On Jun 6, 4:58*pm, Roy Lewallen wrote:
This is why, for
example, a center loading coil must have more inductance than a base
loading coil to effect the same change in reactance at the base.

The following is based on a fixed length antenna.

The phase shift at the top of each coil is associated with the abrupt
shift in characteristic impedances at the coil-stinger junction
(according to W8JI). When a base section is added to a base-loaded
antenna, there is an opposite abrupt shift in characteristic impedance
at the base-coil junction. That bottom (negative) phase shift
subtracts from the (positive) phase shift at the coil-stinger junction
so more phase shift must be added through the coil to compensate for
the phase shift lost at the base-coil junction. Increasing the coil
length provides the necessary additional phase shift.

Assume a loading coil has a characteristic impedance of 4000 ohms and
the stinger has a characteristic impedance of 600 ohms at the coil-
stinger junction. Given the impedance looking into the stinger, it is
easy to calculate the phase shift at the coil-stinger junction. Let's
(for instance) say the stinger's input impedance is 0.25 - j2500 ohms.
If we normalize that impedance to the assumed Z0=600 ohms of the
stinger, we get very close to -j4.167. The impedance at the very top
of the coil is the same and if we normalize to the assumed Z0=4000
ohms of the coil, we get -j0.625 ohms. If we subtract the arctangent
of those two values, we get the phase shift: 76.5 - 32 degrees = 44.5
degrees at the top of the loading coil. We can also read that same
value from a Smith Chart.

When we go to a center-loaded coil, the calculations are complicated
by the resistive portion of the impedance, but we will find a negative
phase shift at the bottom of the coil that subtracts from the positive
phase shift at the top of the coil. Since we have reduced the total
system phase shift by moving the coil to the center of the antenna, we
need to add more length to the coil to increase the phase shift
through the coil in order to compensate for the negative phase shift
lost at the bottom of the coil.

One can emulate the loading coil problem using pieces of transmission
line with different Z0s. The basics of shortened dual-Z0 stubs are
covered he

http://www.w5dxp.com/shrtstub.htm

For instance, the following shortened stub has a resonant frequency at
which it is electrically 1/4WL long even though it is only 1/8WL long
physically because of the 45 degree phase shift between the two
sections.

-----22.5 deg 300 ohm-----+-----22.5 deg 50 ohms-----

What happens to the resonant frequency if we move half of the 50 ohm
line to the bottom?

----11.25 deg 50 ohm---+---22.5 deg 300 ohm---+---11.25 deg 50 ohm

How many degrees do we need to add to the 300 ohm line to achieve the
same resonant frequency as before?
Can anyone out there solve this problem?
--
73, Cecil, w5dxp.com