TEST BANK FOR Antennas for all Applications By John D. Kraus Converted
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Exam (elaborations) TEST BANK FOR Antennas for all Applications By John D. Kraus (Solution Manual)-Converted
- Exam (elaborations) • 159 pages • 2021
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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...
Exam (elaborations)
Exam (elaborations) TEST BANK FOR Antennas for all Applications By John D. Kraus (Solution Manual)-Converted
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ago
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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