# 217 beam solid angle weve already stated that the

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2.1.7 Beam solid angle We’ve already stated that the beam solid angle is always given by = 4 π/D regardless of the beam shape. This can be proven by expressing the total radiated power as an integral and invoking the definition of directivity: P t = integraldisplay P d = integraldisplay D ( θ,φ ) P t 4 π d Here, P t is a constant (the total radiated power) that can be canceled from both sides of the equation, leaving the identity: 4 π = integraldisplay D ( θ,φ ) d 32

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otherwise appear as an additional source in the transmitter circuit. The total power delivered to the antenna by the transmitter to the transmitting antenna is then P t = 1 2 | I 1 | 2 R 1 where R 1 = Z 11 is the radiation resistance. Coupling cannot be neglected in the receiver circuit, of course, since that is the only thing driving a current. The power delivered to the receiver under matched load conditions,

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