### Attenuation at VHF in propagation through the Ionosphere

Darrel Emerson, June 1 1998

The following equation gives the value of "typical" daytime
attenuation in passage through the ionosphere. It is taken from
*Radio Wave Propagation* by Lucien Boithias, published
by North Oxford Academic. The attenuation is in dB, and as seen
decreases as the square of frequency f. The attenuation depends
on the slant distance through the ionosphere, which is mainly a
function of takeoff angle from the earth's surface. The slant distance
is a weak function of the assumed height h of the absorbing
ionospheric layer and of the earth radius R, because of the
earth's curvature. Strictly this relation is only valid for frequencies
higher than about 50 MHz.

The height h of the absorbing layer is assumed to be 100 km

and the radius R of the earth, in km, is taken as:
The attenuation A in dB, as a function of frequency f (MHz) and of
takeoff angle phi, is then given by:

The attenuation according to this relation is plotted here for frequencies from 30 MHz to
about 1000 MHz, for takeoff angles of 0, 15, 30 and 90 degrees.

The above equation and plot are for typical daytime conditions.
During night-time hours, typical attenuations are a factor of
10 to 30 lower.

I thank John Regnault, G4SWX, for drawing the above reference on
*Radio Wave Propagation* to my attention.

Link to Darrel Emerson's
homepage

Link to *Elliptical Polarization in the Ionosphere*