Bob Dixon wrote:
Here's a related question:

WHY do parasitic elements work the way they do?

Let's consider a two-element yagi with a driven element and a parasitic
"reflector", ie a parasitic element longer than a half wavelength.
(We could make the same arguments in reverse for a "director".)

The driven element radiates an electromagnetic field, some of which
impinges on the reflector. This causes a current to flow in the
reflector, and a voltage to appear across it. Since it is longer than a
half wavelength, it acts inductive, and the current LAGS behind the
voltage.

The reflector then radiates its own electromagnetic field in all
directions, some of which heads back toward the driven element.
(For simplicity, we ignore the mutual impedance effects and the new
current which is induced in the driven element.)

You also need to ignore the fields from all other elements if present.
They can have a major impact on the overall field to the rear which the
reflector must attempt to cancel.

If the fields from the reflector and driven element are to be in phase
in the direction from the reflector towards the driven element, then the
radiated field from the reflector must be advanced in phase by how much
it lost traveling from the driven element to the reflector, plus another
same amount as it travels back. So the phase of the field radiated by
the reflector LEADS the phase of the driven element significantly.

But the purpose of the reflector isn't to make a field which reinforces
the driven element's field in the forward direction, but to make a field
which cancels it in the reverse direction. For this to happen most
effectively, the phase lag of the reflector current (relative to the
driven element current) and the distance between reflector and driven
element should add to 180 degrees. In practice, both the phase and
magnitude of the current induced in the reflector change with element
length. And in general, the farther you get from self-resonance, the
smaller induced current. So as you adjust the element length, by the
time you reach the optimum phase angle of induced current, its magnitude
is too small for good cancellation. A compromise is inevitably reached,
resulting in an acceptable but far from perfect front/back ratio.

Now the question is (assuming this is all right so far):
How do we explain the phase of the field radiated from the reflector, in
terms of the phase of the current and voltage in the reflector?

The magnitude and phase of the field are directly related to the
magnitude and phase of the current. The incremental longitudinal voltage
in the element can be ignored in calculation of fields. While it's
possible to base the field calculation on the longitudinal voltage
rather than the current, I don't believe I've ever seen this done.

Roy Lewallen, W7EL