Last modified February 9 1998
E-mail: demerson@nrao.edu
In general, when a linearly polarised wave propagates through the ionosphere, apart from attenuation of the wave, two major effects take place:
How important these effects are depend on the parameters of the ionosphere and the frequency. To a good approximation, above 100 MHz Faraday rotation occurs only for propagation along the magnetic field, (i.e. longitudinal propagation) while ellipticity is only introduced by propagation perpendicular (i.e. transverse) to the magnetic field.
Below is a screen dump of a Mathcad order-of-magnitude calculation of how elliptical a linearly polarised wave can become in propagating through the ionosphere. Extreme assumptions (i.e. exactly transverse propagation, and initial polarization vector 45 degrees to the magnetic field) have been made, so the results are likely to be upper limits of what's encountered in practice. Parameters for a "normal" undisturbed ionosphere have been assumed.
| One-way distance through a uniform ionosphere, propagation normal to the magnetic field, in which a linearly polarised wave, E-field 45 degrees to the magnetic field lines, will become elliptically polarised to the indicated degree. | ||||
|---|---|---|---|---|
| AR is the Axial Ratio of the polarization. | ||||
| 50 MHz | 144 MHz | 432 MHz | ||
| Circular: (AR=0 dB) |
100 | 2800 | 76000 | (km) |
| AR=6 dB | 70 | 1700 | 45000 | |
| AR=10 dB | 49 | 1000 | 30000 | |
| AR=20 dB | 14 | 400 | 10000 | |
These are fairly extreme values; Propagation along the field lines introduces no ellipticity, to a good approximation. If the E-field of the wave propagating across the magnetic field is polarised parallel to or perpendicular to the magnetic field, NO ellipticity is introduced. If the propagation is not quite perpendicular to the magnetic field, then Faraday rotation will cause the major axis of the ellipse to rotate, in the normal way. If the Faraday rotation is an exact multiple of half-turns, then the ellipticity will cancel out exactly. This factor alone will limit how elliptical a wave can become, especially if Faraday rotation of several turns is involved. You never get more ellipticity than can be built up in a quarter-turn of Faraday rotation.
So, the general conclusion is that at 432 MHz there will never be significant ellipticity introduced by the ionosphere. At 144 MHz 20 dB axial ratios may be common, but 6 dB axial ratio will almost never happen (although maybe it could approach that at very low elevation angles exactly perpendicular to the magnetic field?) At 50 MHz, high ellipticity, even perfectly circular polarization, should be common.
This doesn't take account of other extreme conditions, where major ionospheric disturbances may temporarily give extreme electron densities. I believe the numbers should be representative of a "normal" ionosphere.
I thank Kurt Weiler, K7BLT, and John Regnault, G4SWX, for pointing out errors in an earlier set of calculations.
The mathcad sheet is available as a postscript file which has higher print quality, but is included here also as a ".gif" file which may be more convenient for some viewers.