Green Egghead wrote:
Roy Lewallen wrote:
Green Egghead wrote:
. . .
Are there multipath solutions using circular polarization
between double side band supressed carrier components?
Sorry, I don't understand the question. What do you mean by solutions
between components? Solutions to what? Or is the question about
polarization between components? If so, what does that mean?

The original question and my answer involved only linearly polarized
fields, not circular or elliptical.

Roy Lewallen, W7EL

By "solution" I mean to the problem of recovering as much
of the transmitted signal strength as possible.
More specifically under typical receiving conditions
where polarization of that transmitted signal
is affected by reflections, atmospheric conditions or
some other cause (what would be other causes?).

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.

. . .

Please correct me where I am wrong here.
From what you wrote:

One antenna is transmitting a "horizontally" polarized
(electric) field with a time varying electric amplitude A(t):

B_h = A(t)*cos(0) = A(t)
B_v = A(t)*sin(0) = 0

where "horizontal" is represented by an angle of zero degrees
in the transmitter's coordinates, and B_h and B_v are it's
respective horizontal and vertical e-field strengths.

Similarly the other transmitting antenna is vertically polarized:

C_h = A(t)*cos(90) = 0
C_v = A(t)*sin(90) = A(t)

again where "vertical" is represented by an angle of 90 degrees
in the transmitter's coordinates.

Ok so far.


Superposing these two fields yields a 45 degree linear field
polarization (45 degrees relative to the transmitter's coordinates)
As far as the transmitter is concerned this polarization will
be the same for every point in free space. This is ignoring the
observer's relative perspective on the transmitter.


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.

Circular polarization is not due to the superposition of
two orthogonal linearly polarized fields at a receiving dipole
where one of the field's linear polarization is rotated
90 degrees with respect to the other. As you pointed out,
that's just a 45 degree linear polarization and it does
not change from one point in free space to the next.

That's right.

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.


Wouldn't the phase between the electric and magnetic
fields have to be different (other than 90 degrees)
to create a circularly polarized wave?

No. Traditionally, polarization refers only to the orientation of the
electric field. Once the phase of the E field is known, both the
magnitude and phase of the H field can be found. The ratio between the
two is called the impedance of the medium, and is dictated solely by the
nature of the medium through which it travels. In free space, the ratio
of E to H is a purely real number (about 377 ohms), so E and H are
always in phase. You can't alter that except in the field close to an
antenna (the near field).

If so can
circular polarization be described as changing more
or less than once per cycle?

No. The field rotates exactly one revolution per cycle, never any more
or less.

Any single linearly polarized field can be parametrized
into two circularly polarized fields (represented
as the superposition of two circularly polarized fields).
Therefore, any receiver with a horizontal dipole,
can be described as receiving two circularly polarized waves.
But this would be an analytical description of the receiver,
rather than a physical description of the field that was
actually sent.

The splitting of a single field into two orthogonal components such as
horizontal and vertical linear or left and right circular is a way of
describing the field itself. It's useful for such purposes as
determining what the response of a particular kind of antenna would be.

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.

Roy Lewallen, W7EL