Here's a post of mine from the thread titled 'colinear connundrum'
from a
few years ago. Perhaps it will shed some light on the subject :

Gray Frierson Haertig wrote:
"One of the classic implementations of the collinear uses parallel
resonant circuits as the phase inverting means between separate
elements---."

I`ve discussed the if and how a parallel resonant circuit can
replace a
short-circuit 1/4-wave stub as a phase inverter, and never been
satisfied either.

If considered as two terminal devices, a 1/4 wl stub, parallel
resonant
LC circuit and an insulator are equivalent, at least for steady state
AC. Understanding the difference requires a slightly more elaborate
model for the stub or LC circuit. The model must account for charge
accumulation, or common mode current on the device. Classic network
theory can be used if a third, or 'common mode center tap' is added to
the device model.

Consider the parallel resonant LC circuit with the center of the
inductor (or capacitor) grounded. The impedance between the two 'hot'
terminals will be very high as in the two terminal case. The ground
connection introduces a new constraint. The voltage on a 'hot'
terminal
is now constrained to be equal in magnitude and of opposite polarity
from the other 'hot' terminal. This is not the case for the two
terminal
device model.

The three terminal device (center tap grounded) can be used as a
polarity reversing 1:1 transformer by connecting one 'hot' terminal to
a
ground referenced source and driving a load with the other terminal.
Of
course the same effect could be accomplished without the capacitor if
the center tapped inductor (autotransformer) had suitable properties.

Note that if the two 'hot' terminals are shorted the impedance (common
mode) to ground is zero.

Observe:
The differential mode impedance between 'hot' terminals is very high
(ideally infinite).
The common mode impedance to ground is zero.
The voltage on the 'hot' terminals respect to ground is of equal
magnitude and opposite polarity.

But, as Gray noted, a perfect parallel resonant circuit is an
insulator.
So is the perfect short-circuit 1/4-wave stub.

Now look at a 1/4 wl shorted stub far removed from ground. Viewed as
a
two terminal device it behaves similar to a parallel resonant LC
circuit. If the two open 'hot' wires are shorted, the stub looks like
a
1/4 wl long wire. The impedance with respect to ground is
approximately
36 ohms, which is very small compared to the nearly infinite
differential impedance. Think of it as a single 1/4 wl counterpoise;
adding a second colinear 'radial' results in an even lower ( 36/2
ohms) 'virtual ground' impedance.

Thus the 1/4 wl stub behaves similar to the parallel resonant LC
circuit
with the grounded center tap. The common mode behavior of the
freespace
1/4 wl stub provides the low impedance 'virtual ground'. Of course
suppressing the common mode resonance by coiling the transmission line
or applying a common mode choke has the effect of inserting a high
impedance in series with the 'ground' connection.

In reality, the common mode impedance to ground of an isolated LC
circuit is not infinite. Both the inductor and capacitor have
capacitance to space which will provide some 'grounding' effect. At
MF
through VHF, the components would generally need to be physically very
large to have a usefully low common mode impedance to ground however.


The opposite terminals of the parallel resonant circuit and the
opposite
terminals of the short-circuit stub are out of phase, in either
case.
They are equivalent.

Coupling between the elements exists in an ordinary dipole, even
though
the elements are end-to-end. There must be enough coupling to
complete
the transmission circuit, else the antenna wouldn`t work.


Turns out the mutual impedance between two isolated colinear dipole
elements is of the wrong polarity for parasitic operation as a
broadside
array. As you might expect, the mutual impedance between elements is
dominated by end to end capacitance which is wrong for broadside gain.
The Yagi configuration has a natural tendency to provide broadside
gain,
while the colinear does not.


I think equivalence is the key. If one works, the other must work
too.


As long as they are truly equivalent for the case being considered.
Failing to consider common mode impedances is unfortunately a very
common practice and will often lead to incorrect conclusions. The
devil
is often in the details.

bart
wb6hqk