The normalized far-zone field pattern of an antenna is given by E = (sin 8 cos) 0≤0≤ and 0 ≤≤m/2. 3/22 π 0 elsewhere Find the directivity using (a) the exact expression (b) Kraus approximate formula (c) Tai and Pereira's approximate formula U=1E1 Sine cost Umar = 2 (a). Prad = 2. =2 Sine cas de dg=()() Do = 4 Umax = AT (27)=16=5.09-7.0743 (b). Umax= Prad 1 a+8=2=0 In the elevation plane through the maximum =0 and u= sine. The 3-d8 point occurs when U=0.5 Umax = 05()=sin &=Sin (0.5)=30° Therefore id=2(90-30)=120" In the azimuth plane through the maximum 8 = "/2 and u= U=105. The 3-dB point occurs when u= 0.5 Umax = 0.5 (277) = 27c05 - 01 Cos" (0.707)=45", ad2c90-45)=90 Therefore using Kraus formula D. = 41,253 = 3.82-5.82 dB (c) Using Tai and Pereira's formula D72,815 + 120-(90) = 72,815 3.24 = 5.10 dB (120)*+ (90)*
The normalized far-zone field pattern of an antenna is given by E = (sin 8 cos) 0≤0≤ and 0 ≤≤m/2. 3/22 π 0 elsewhere Find the directivity using (a) the exact expression (b) Kraus approximate formula (c) Tai and Pereira's approximate formula U=1E1 Sine cost Umar = 2 (a). Prad = 2. =2 Sine cas de dg=()() Do = 4 Umax = AT (27)=16=5.09-7.0743 (b). Umax= Prad 1 a+8=2=0 In the elevation plane through the maximum =0 and u= sine. The 3-d8 point occurs when U=0.5 Umax = 05()=sin &=Sin (0.5)=30° Therefore id=2(90-30)=120" In the azimuth plane through the maximum 8 = "/2 and u= U=105. The 3-dB point occurs when u= 0.5 Umax = 0.5 (277) = 27c05 - 01 Cos" (0.707)=45", ad2c90-45)=90 Therefore using Kraus formula D. = 41,253 = 3.82-5.82 dB (c) Using Tai and Pereira's formula D72,815 + 120-(90) = 72,815 3.24 = 5.10 dB (120)*+ (90)*
Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter14: Basic Trigonometry And Vectors
Section: Chapter Questions
Problem 1RQ: 1. Which trigonometric function is used to find the angle if the length of the hypotenuse and of the...
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Transcribed Image Text:The normalized far-zone field pattern of an antenna is given by
E =
(sin 8 cos)
0≤0≤ and 0 ≤≤m/2.
3/22 π
0
elsewhere
Find the directivity using
(a) the exact expression
(b) Kraus approximate formula
(c) Tai and Pereira's approximate formula
U=1E1
Sine cost
Umar = 2
(a). Prad = 2.
=2
Sine cas de dg=()()
Do = 4 Umax = AT (27)=16=5.09-7.0743
(b). Umax=
Prad
1 a+8=2=0
In the elevation plane through the maximum =0 and u= sine.
The 3-d8 point occurs when
U=0.5 Umax = 05()=sin &=Sin (0.5)=30°
Therefore id=2(90-30)=120"
In the azimuth plane through the maximum 8 = "/2 and u=
U=105.
The 3-dB point occurs when u= 0.5 Umax = 0.5 (277) = 27c05 - 01
Cos" (0.707)=45", ad2c90-45)=90
Therefore using Kraus formula D. = 41,253 = 3.82-5.82 dB
(c)
Using Tai and Pereira's formula
D72,815
+
120-(90)
=
72,815 3.24 = 5.10 dB
(120)*+ (90)*
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