When a molecule or atom is nonsymmetrical in its structure, it will have a preferred orientation if placed in an electric field. Such molecules or atoms are said to be polar. Polar mol­ecules or atoms cause far more loss to a radio signal than nonpolar molecules or atoms, since the application of an ex­ternal field causes the polar molecules or atoms to reorient themselves. The reorientation (or relaxation) of the dipoles will remove energy from the applied field and cause heating of the medium. This is the principle of a microwave oven. The major constituents of the troposphere, oxygen and nitrogen, are electrically nonpolar and so no absorption due to electric dipole resonance will take place. Oxygen however, is a para­magnetic molecule with a permanent magnetic moment which causes resonant absorption at particular frequencies. Water and water vapor, which both contain two oxygen atoms, are therefore polar molecules and so absorption occurs due to resonance at critical frequencies.

Oxygen and Water Vapor Resonance Lines

The specific gaseous attenuation у (dB/km) is given by

Y = Yo + Yw (dB/km) (13)

where yo and yw are the specific attenuations (dB/km) due to dry air (essentially oxygen) and water vapor, respectively. The specific attenuation needs to be multiplied by the length of the path over which it operates to arrive at total path at­tenuation. On terrestrial paths, this is simply the distance between the transmitter and receiver, L (km), and the path attenuation A (dB) is given by

A = y L = (Yo + Yw )L (dB) (14)

For earth-space paths, the situation is not so straightfor­ward, since the density and make up of the atmosphere change rapidly with height. The value of L used must be able to take account of the density and other variations along the link through the atmosphere.

Figure 3, abstracted from Fig. 3 of Ref. 14, gives the total zenith gaseous attenuation at frequencies up to 1 THz (1012 Hz) for two conditions: a standard atmosphere and a dry at­mosphere. A standard atmosphere is defined as having the following surface characteristics: pressure 1013 hPa, temper­ature 15°C, and water vapor density 7.5 g/m3. In general, the dry atmosphere curve in Fig. 3 shows the resonance absorp­tion lines of oxygen, while the standard atmosphere curve is a summation of the resonance absorption lines of water vapor and oxygen. A software code (in Matlab) that calculates the total gaseous attenuation in a line-by-line fashion up to a fre­quency of 1 THz is available from the Radiocommunication Bureau of the ITU in Geneva.

For nonzenith paths, it is necessary to know not only the specific attenuation at each point in the link but also the length of the path that has this specific attenuation. To derive the incremental path lengths, ray bending through the atmo­sphere must be considered [see Fig. 1(a)]. A full procedure to accomplish this is given in Ref. 14. In this procedure, formu­lae are given for the precise calculation of yo and yw, and the total zenith attenuation is calculated from

Az = Yoho + Yw hw (dB) (15)

where ho is the equivalent height of the dry gaseous absorp­tion and hw is the equivalent height of the water vapor ab­sorption. Typical values of ho and hw are 6 km and 2.1 km (during rainy conditions), respectively. For elevation angles between 10° and 90°, a cosecant law gives the total gaseous attenuation A, namely

A = 4^- (dB) (16)

sin p

where p is the elevation angle. For elevation angles below 10°, a more accurate formula that takes account of the real length of the atmospheric path is required (14). For most earth — space systems, gaseous absorption is not significant compared with the other impairments. It also changes very little with time and so is usually relatively easy to factor into a system design.

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