Where D(2,N) is the directivity indB, and the radiation pattern power in aspecific direction is Pd(2,N), which isnormalized by the total integrated radiatedpower. Another important concept is thatwhen the angle in which the radiation isconstrained is reduced, the directive gaingoes up. For example, using an isotropicradiating source, the gain would be 0 dB bydefinition (Figure 2(a)) and the powerdensity (Pd) at any given point would be thepower in (Pin) divided by the surface areaof the imaginary sphere at a distance Rfrom the source. If the spacial angle wasdecreased to one hemisphere (Figure 2(b)),the power radiated, Pin, would be the samebut the area would be half as much, so thegain would double to 3 dB. Likewise if theangle is a quarter sphere, (Figure 2(c)), thegain would be 6 dB. Figure 2(d) shows apencil beam. The gain is independent ofactual power output and radius (distance) at which measurements are taken
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