Notes5

# Notes5 - Notes#5 ECE594I Fall 2009 E.R Brown Free-Space...

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Notes #5, ECE594I, Fall 2009, E.R. Brown 94 where the subscript "t" is for transmitting, P rad is the total radiated power, P in is the power used to drive the transmitting antenna (in the matched case, equal to P rad ), θ t and φ t are the spherical angles in the spherical coordinate system centered at the transmitting antenna, τ (r) is the power transmission function including all attenuation effects, and r is the distance (i.e., the “range” between transmitter and receiver. In writing (3) it is understood that F t is taken in the direction ( θ t , φ t ) pointing towards the receiver, which is not necessarily the direction of the maximum of F t . Substitution of (3) into (2) yields the relationship p r r t t t r t in eff rec r r F F G P A P ε τ π φ θ = ) ( 4 ) , ( ) , ( 2 (4) This can be simplified further in terms of the (ostensibly) known parameters of the receiving antenna using the relationships, 2 eff r rec r r rec out / A 4 G P D G P P λ π = (5) where P out is the power delivered to the load of the receiving antenna. Substitution of (4) into (5) yields p t t t r r r t r in out r F F G G r P P λ = ) ( ) , ( ) , ( 4 2 1 (6) the expression commonly known as Friis' formula after its originator. It effectively treats the
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Notes5 - Notes#5 ECE594I Fall 2009 E.R Brown Free-Space...

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