 transmission formula as in Equation 27.12, where P is The mismatch between two elliptically polarised waves is given received power in watts, P is transmitted power in watts, G is the by Equation 27.15, where R is given by Equation 27.16 and R by gain of the transmitting antenna in the direction of the receiving Equation 27.17. R is the transmit antenna axial ratio, and R is the antenna, G is the gain of the receiving antenna in the direction of receive antenna axial ratio. Wavelength: centimeter millimeter sub-millimeter 100um d8/km 150mm/h 0.1g/m3 0.25mm/h 10' GHz Figure 27.12 Atmospheric and rainfall attenuation versus frequency. (A: rainfall at 0.25, 25 and 150mm per hour; B: fog at 0.1 gram per m³; C: molecular absorption by water vapour and air) Terrestrial line of site propagation 27/11 1 + R 2 R r 2 + RR cos 20 (27.15) 10800 1 + R t 2 ) (1 + R, r 2 ) 10400 10000 R 1 - = + 1 (27.16) (27.17) R r = rr + 1 Equation 27.13 assumes free space conditions, however absorp- tion occurs due to rain and fog and also water vapour and oxygen in the air, as shown in Figure 27.12. It will be noted that the first water absorption band occurs at 2.45GHz, a phenomenon that is put to good use in microwave ovens. The attenuation figure taken from this graph must be added to the figure calculated from the Friis formula. Although v.h.f., u.h.f. and microwave point to point communica- tions is frequently referred to as 'line of sight', the change in the refractive index of the atmosphere with height does in fact cause Surface refractivity (NS) radio waves to be bent in the same direction as the earth's curvature. This in effect extends line of sight, and the relationship between the surface refractivity and the effective earth's radius is shown on Figure 27.13. The refractive index of air does in fact depend on Figure 27.13 Atmospheric surface refractive index versus atmospheric pressure, water vapour pressure and temperature and effective earth radius all these factors vary. An average effective earth radius factor of 1.33 or '