becomes a straight line. As the destination of the radio signal is an unknown factor, the only solution is to modify the earth's curvature SO that the radio signal becomes a straight line. Thus, after changes, the new model of the above stated actual scenario would look like the one shown in Figure 3.40. The amounts by which the curvatures of the radio signal and the earth surface are changed in order to make the radio signal a straight line is called the 'k-factor'. It is defined as the ratio of the effective earth radius to the actual radius of the earth: (3.17) Transmission Network Planning and Optimisation Figure 3.39 Microwave path Reff. Figure 3.40 Microwave path where R is the radius of the earth. The microwave signal varies with climatic conditions, with the variation of any one or all factors like pressure, temperature and humidity. These factors vary with height. This will result in a variation of the radius of the radio signal and hence the k-factor. Thus, the k-factor varies with the changes in height. Thus, with every small variation of height (dh), there will be small variations of refractivity (dn), which will result in a variation in the radius of the microwave signal. This is represented mathematically as (3.18) where RMW is the radius of the microwave signal and dn/ dh is the vertical gradient of the refractive index. This expression is valid when the angle of launch of the microwave signal is zero degrees (to horizontal) and refractivity is unity. Hence the k-factor is dependent upon the refractive index gradient and is mathematically represented (3.19) (3.20) In standard atmospheric conditions, the refractive index gradient is 40 N/km. The radius of earth is approximately 6400 km; putting these values in the above equation (3.21) Microwave Link Planning Figure 3.41 First fresnel zone This means that (for standard atmospheric conditions), to find the effective radius of the earth, the radius of the earth should be multiplied by 1.33. This introduces a bulge on the surface of the earth, the curv