TEST BANK FOR Antennas for all Applications By John D. Kraus Converted
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Exam (elaborations)
Exam (elaborations) TEST BANK FOR Antennas for all Applications By John D. Kraus (Solution Manual)-Converted
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---159November 20212021/2022
- Show that the directivity D of an antenna may be written 
( ) ( ) 
( ) ( ) 
∫∫ Ω 
= ∗ 
∗ 
π 
θ φ θ φ 
π 
θ φ θ φ 
4 
2 
max max 2 
, , 
4 
1 
, , 
r d 
Z 
E E 
r 
Z 
E E 
D 
Solution: 
av U 
D U max (θ ,φ ) 
= 
, 2 
max max U(θ ,φ ) = S(θ ,φ ) r , = ∫∫ Ω 
π 
θ φ 
π 4 
( , ) 
4 
U 1 U d av 
U(θ ,φ ) = S(θ ,φ )r2 , ( ) ( ) 
Z 
S E E θ φ θ φ 
(θ ,φ ) , , 
∗ 
= 
Therefore 
( ) ( ) 
( ) ( ) 
∫∫ Ω 
= ∗ 
∗ 
π 
θ φ θ φ 
π 
θ φ θ φ 
4 
2 
m...
-
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