Roy Lewallen wrote:
At HF considerable fading, including selective frequency fading, is
caused by polarization shift. But it's not easy to create a receiving
antenna that's circularly polarized when a ground reflection is involved
(because ground reflection characteristics are functions of both
reflection angle and polarization), and even more difficult to do it in
more than one direction. If you can build the antenna, it should reduce
polarization shift fading. You still have the problem of fading due to
multipath interference.

To get a circularly polarized field (again, relative to the
transmitter's coordinates irrespective of any receiver)
feeding the two linearly polarized antennas in quadrature
would be equivalent to:

B_h = A(t)*cos(0) = A(t)
B_v = A(t)*sin(0) = 0
and
C_h = A(t+90)*cos(90) = 0
C_v = A(t+90)*sin(90) = A(t+90)

Where A(t+90) represents the signal A(t) shifted
90 degrees relative to the carrier frequency.

Signal A(t) is not equal to A(t+90) at the every point in
free space and so they will interfere. This would create
a spatially and temporally changing carrier amplitude?

Yes, that's correct.

So I don't understand how two same frequency carriers
where one is 90 out of phase with the other creates a
circularly polarized wave since their resultant is not
in the polarization plane but along the direction of
the field's propagation.

Here's your error. In free space in the far field, there is no tilt in
the E field in the direction of propagation; the field is what we call a
plane wave. At any instant, the E field is oriented normal to the
direction of travel. If you look at a circularly polarized wave at a
fixed location, you'll see it rotate in the plane normal to the
direction of propagation. If you freeze the wave in time, you'll see
that the field orientation is a rotating vector, again rotating in a
plane normal to the direction of propagation. Think of the path of an
airplane propeller as the plane flies.

I don't yet see how the B_h and C_v signals, A(t) and A(t+90),
(which appear serially on the feed line as a superposition)
get physically split into their respective h and v dipoles
(I can see that if they are, circular polarization results).

Besides the 90 carrier phase shift and the 90 angular shift
of the crossed dipoles, I figure there has to be one more part
that splits the orthogonal signal components in the feed line
into their respective dipoles (it would be a waste of energy to
send the B_h component through the vertical dipole).

Is this why circularly polarized antennas like this one
seem to have a vertical and horizontal radiator combined?
http://www.ccbroadcasters.com/images/antenn3.jpg
That's what had me thinking that circular polarization
had something to do with the E and H field phase difference
since it looks like a horiz loop integrally combined with a vert dipole.


What amount of radio signal attenuation is typically
attributed to polarization mismatches?

I commonly see fades of 20 - 30 dB on 40 meters which I can reverse by
switching between horizontal and vertical antennas -- that is, at the
bottom of the fade I can switch to the other antenna and restore the
signal. So it's mainly due to polarization shift. On line of sight
paths, I believe the attenuation can be quite severe. I don't know what
proportion of the frequency selective fading you hear on distant AM
signals is due to polarization shift and how much to multipath interference.

. . .

There should be some good explanations (and undoubtedly also some bad
ones) on the web, and the topic is covered to some extent in most
electromagnetics texts.

Thanks for your experienced help getting through these rough parts for me.
I'll keep studying.