ANTENNA 1. Antenn Antenna a has has an inducta inductanc nce e of 2 uH and a capaci capacitan tance ce of 15 pF. pF. Deter Determin mine e (a) (a) the resonant frequency frequency to which the antenna is tuned; (b) the new capacitance a!ue needed to tune the antenna at 5" #H$% and (c) the a!ue of the required series capacitance. capacitance. GIVEN: & ' 2H '15pf f ' 5"#H$
REQ’D: a. f r b. c. *
SOL’N: 1
1
a.
f r '
LC 2 π √ LC
'
2 π √ 2 µH
(
)( 15 pf ) )
1
1
b. f r ' 1
c.
LC 2 π √ LC
=
C
1
+
C '
' 29MHz
; '
2
4 π
1
f r √ L L ' 2
2
(
4 π 50 MHz
) √ 2 µH 2
' 5.07 pf
1 15 pF
; C’ = 7.66 Pf
2. A +"" , antenna is operatin- with 5 A of current. Determine the radiated power. GIVEN: ' +"" , 0 ' 5A
REQ’D: /rad
SOL’N: /rad ' 02 /rad ' (5A)2(+"" ,)
P!" = 7500#
+. Deter Determin mine e the eect eectie ie radia radiated ted power power if the trans transmit mitter ter output output power power is 2"" % transmission !ine !oss is 2" and antenna power -ain is 5. GIVEN: /o ' 2"" &oss ' 2" 4'5
6. Determine the 30/ on an antenna with a power -ain of 6+ d7 and radiated power of 2"". GIVEN: 4(d7) ' 6+d7 /rad ' 2""
REQ’D: 30/
SOL’N: 30/ ' 1"!o- (2"") 8 6+ d7 EIRP = 6$.%6"& 5. Determine the eectie isotropic radiated power for an antenna with directiity ' ++ d7% e9ciency ' :2% and input power ' 1"".
GIVEN: D ' ++ d7 < ' :2 /in ' 1""
REQ’D: 30/
SOL’N:
<'
Prad pin
/rad ' (".:2)(1"" ) ' :2 3.3
D'
10
' 1==5.2> 30/ ' / radD ' (:2 )(1==5.2>) EIRP = %6'.6%% (# >. Determine the power density at a point +" ?m from the antenna that has input power ' 6" % e9ciency ' @5% and directiity ' 1> d7. GIVEN: r ' +" ?m /in ' 6" < ' @5 D ' 1> d7 REQ’D: /D SOL’N:
PtGt /D '
4 πr
2
' (6" )(".@5)(+=.:1)6B(+""""m2) PD = %05.599 )#*+ 2 @. Determine the directiity in d7 of an antenna that produces power density of 2 um 2 at a point when the reference antenna produces ".5 um 2 at the same point. GIVEN: /D ' 2 um2 /ref ' ".5 um2 REQ’D: D(d7) SOL’N: D(d7) '
PD Pref
' 1"!o-(2 um2 ".5 um 2) D,"&-= 6.02 "&
:. hat is the 3/ of a C broadcast station if the output of the transmitter is 1""" % transmission !ine !oss of 5" and antenna power -ain is +E GIVEN: /out ' 1""" &oss ' 5" 4'+ REQ’D: 3/ SOL’N: 3/ ' (/in)(4) ' (1"""5")(+) ERP= 2$50 # =. a!cu!ate the fronttobac? ratio for an antenna with forward -ain of @ d7 and a reerse -ain + d7. GIVEN: /F ' @ d7 /7 ' + d7 REQ’D: AF7 SOL’N: AF7
pF ' 1"!o-( pB ¿
' 1"!o-(1"."2) A& = %0.009"& 1". A he!ica! antenna is operated at twice its ori-ina! frequency. o the new G is the preious G. hat is the chan-e in -ainE GIVEN: 1
Fop '
2
F
G op ' G REQ’D: han-e in 4 SOL’N: 15 NS
4'
2
( πD ) 3
λ
15 NS
4241 '
2
( πD ) 3
λ 2
15 NS
2
( πD )
λ 1
3
' G+.5 G+ G= $00 11. A he!ica! antenna of : turns is to be constructed for a frequency of 1.2 4H$. a!cu!ate the optimum diameter and spacin- for the antenna and Ind the tota! !en-th of the antenna. GIVEN: J ' : turns ' "."5m f o ' 5""#H$
REQ’D: D% K SOL’N:
c = f o
G'
8
m/s cyces (1.2 )( 10 9) ' ".25 D ' sec 3 x 10
λ '
4
λ π '
0.25
π
D=7.96/+
0.25 m
'
4
; ' >.25cm ; K ' J; =0.5+
12. Determine the power -ain and beamwidth for an endIre he!ica! antenna with the fo!!owin- speciIcationsL D ' ".1 m% J ' 1"% ' "."5 m% F ' 5"" #H$. GIVEN: D ' ".1 m J ' 1" ' "."5 m f ' 5"" #H$ REQ’D: 4% M SOL’N: 15 NS
( ) ( 10 )( 0.05 m) ( π ) (0.1 m ) (0.6 m ) 52 0.6 m
(
1 /2
)
1 = %0$.792 1+. hat are the -ain and beamwidth for a dish with D ' 2"GE GIVEN: D ' 2"G REQ’D: 4 M SOL’N: 4 ' >(D G) 2 ' >(2")2 ' 26"" ' ++.: d7
M ' @"(GD) ' @"(12") 1 = '.5 16. How !ar-e a dish diameter% in wae!en-ths and in meters% is needed for a >" d7 -ain at +"" #H$E GIVEN: 4 ' >"d7 f ' +""#H$ REQ’D: D SOL’N:
πD πD 4 ' < ( λ ; ' 1"> ' ".>"( λ ; G '
¿¿
D'
√
2
¿¿
2
c f '
3 ! 10
8
300 ! 10
6
G ' 1m
6
10
2
0.60 π
D = 3%0.93+ 15. For an antenna with input power of 1"" % # current ' 2 A% and eectie resistance ' 2,% determine (a) antenna*s radiation resistance% (b) antenna*s efficiency% and (c) power radiated from the antenna. GIVEN: /0J ' 1"" 0 ' 2Arms r ' 2O REQ’D: rad% <% /rad SOL’N:
P¿ rad '
2
"
100 #
'
2
2
$ rad < ' $ rad + $ r '
; R!" = 25 4 25 25
+2
N 1""; =92.59
/rad '
1>. Determine the efficiency of an antenna with radiation resistance 1:.: ,% effectie resistance ".6 ,% and directiity -ain is 2"". GIVEN: r ' 1:.: , o ' ".6 , D ' 2"" REQ’D: < SOL’N:
$r < ' $r + $o ' 1:.: 1:.: 8 ".6 P1"" = 97.9 1@. Cwo G2 dipo!e are separated by 5" ?m. Chey are a!i-ned for optimum reception. Che transmitter fed its antenna with 1" at 166 #H$. a!cu!ate the power receied. GIVEN: r ' 5" ?m /t ' 1" f ' 166#H$ REQ’D: /r SOL’N:
PtGtGrλ 2 /r ' 16 ( πr )
2
2
'
(10 # )( 1.64 )( 1.64 )( 2.08 ) 16 π ( 50 %m) 2
2
' P = 295.75p#
1:. Che 3/ of a transmittin- station is speciIed as 1@ in a -ien direction. 3Npress this as an 30/ in d7 m. GIVEN: 3/ ' 1@ REQ’D: 30/ in d7 m SOL’N:
1=. Desi-n a !o- periodic antenna to coer the frequency ran-e from 1"" to +"" #H$. Qse R' ".@ and S' +"o. GIVEN: REQ’D: f ' 1""+""#H$ &/A Desi-n R ' ".@ S ' +"o SOL’N: For the !en-th of the 1 st and !ast e!ementL 8
( 3 x 10 )/( 100 MHz )
λ1 K '
2
'
2
=%.5+ d1 ' (".1) "% = 0.'+
K2 ' R K ' (".@)(1.5m) 2 = %.05+
( λ ) 1
' (".1)(+m)
d2 ' R d1 ' (".@)(".+) "2 = 0.2%+
8
λ3 K+ '
2
' '
( 3 x 10 )/(300 MHz ) 2
; ' = 0.5+
2". hat are the -ain% in d7% and beam width of the he!ica! antenna with diameter ' G+% 1" turns at pitch of G6 used at 1"" #H$ (G' + m)E GIVEN: D ' G+ J ' 1" ' G6 f ' 1"" #H$ G' + m
' 52(+) ( π )((1")(".@5))12 1 = '%.3% 21. a!cu!ate the operatin- frequency for a he!ica! antenna that consists of 1" turns with a spacin- of 1" cm and a diameter of 12.@ cm. GIVEN: J ' 1" turns ' 1"cm D ' 12.@ cm REQ’D: f o SOL’N: Che circumference of the turns is about one G% and the spacin- is T G for this type if antenna. First% ca!cu!atin- the wae!en-thL G ' BD ' B(12.@cm) ' +=.:=cm Che spacin- between the coi!s is T G% and four times this a!ue yie!ds 6"cm. Che frequency wi!! be approNimate!yL 8
f o '
3 x 10
m/ s
λ
8
'
m/ s ; 39.38 cm
3 x 10
f = 752MHz 22. An antenna has a beam width of + de-rees. 3stimate its -ain.
GIVEN: REQ’D: o U'+ 4 SOL’N: Assume a sma!! dish operationL f o ' 2: 4H$ G'
c f o '
8
m/ s ' 1".@1mm 28 GHz
3 x 10
λ
U ' @"( D ¿
λ D ' @"( ϴ
¿
10.71 mm
' @"(
&
3
¿
' 25cm
Assume a typica! e9ciency of >"L
πD 4 ' < ( λ ' (".>) (
¿¿
2
π ( 25 cm ) 10.71 mm
¿¿
2
G = '226.65'5.0$"& 2+. a!cu!ate the minimum diameter of a parabo!ic antenna with a beam width of 2 de-rees at a frequency of 12 4H$. GIVEN: 7 ' 2o f ' 124H$ REQ’D: D SOL’N: 8
G'
m/ s ' 2.5cm 12 GHz
3 x 10
λ 2.5 cm o ¿ ) 2 =( 70)( 7 ' @"( D D D = $.75/+ 26. A parabo!ic antenna has a diameter of + m% an e9ciency of >" and operates at a frequency of 6 4H$. a!cu!ate its beam width and -ain in d7. GIVEN: D ' +m < ' >" f o ' 64H$ REQ’D: U% 4(d7) SOL’N:
2
m/ s ' @5mm 4 GHz
3 x 10
G'
75 mm
( Ƞ)(
4'
πD 2
λ
)
¿ ¿
' (".>")(
(¿ 2 ¿) π ( 3 m ) ¿
' 1""5.+1
4(d7) ' 1"!o-4 4(d7) ' +"."2d7 8 2.15d7 G,"&8- = '2.%7"& 25. a!cu!ate the eectie area of a + m dish with an e9ciency of ".@ at + 4H$ and at 12 4H$. GIVEN: D ' +m < ' ".@ f 1 ' +4H$% f 2 ' 124H$ REQ’D: Ae V f 1 and f 2 SOL’N:
πD 2 λ ¿ 4 ' <( λ % Ae ' 4( 4 π 2
¿¿
V f 1L V f 2L G ' ".1m G ' "."25m 4 ' >21@.:5"@@+ +@.=6Db 4 ' ==6:5.>12+> 6=.=:d7 A = 3.93$+2 A = 3.93$+2 2>. A >6 mm diameter parabo!ic reWector fed by a nondirectiona! antenna is used at 16+" #H$. a!cu!ate the beam width between ha!f power points and between nu!!s and the power -ain with respect to a ha!fwae dipo!e% assumin- een i!!umination. GIVEN: D ' >6mm f o ' 16+"#H$
REQ’D: U+d7% UX% 4
SOL’N:
λ U+d7 ' @"( D ¿ ( UX ' 2U+d7% 4 ' >(
D λ 2
¿¿
8
G'
m/ s =¿ 2".=@="cm 1430 MHz
3 x 10
20.9790 cm
U+d7 ' @"( UX ' 2(22=.65o);
64 mm
¿
;
;'"& = 229.35 O
;O = 35$.9 9$.92
64 mm
4 ' >( 20.9790 cm
¿¿
' ".55:6; G = 0.55$3
2
2@. Find the -ain of a pyramida! horn whose dimensions are 12 cm wide and 1" cm hi-h. Che operatin- frequency is assumed to be 1" 4H$. GIVEN:
REQ’D:
d ' 12cm ) 12cm
4
f o ' 1"4H$ SOL’N: 7.5 d * d *
4'
λ
2
8
λ '
m/ s ' +cm 10 GHz
3 x 10
(
)( 10 cm) (3 cm)
7.5 12 cm
4'
2
G = ' 3.77"& 2:. A pointtopoint system operates oer a distance of 2" ?m at a frequency of 2> 4H$. Che antenna is each of diameter =" cm. 3stimate the beam width of the antenna dep!oyed and the power receied if the transmit power is 2" d7 m. GIVEN: r ' 2"?m f o ' 2>4H$ D ' ="cm /rad ' 2"d7m REQ’D: U+d7% / SOL’N:
λ U+d7 ' @"( D ¿ 3 x 10
8
26 GHz
U+d7 ' @"(
90 cm
/ '
Prad G + G $ λ 2
16 π
D 4 ' >( λ
2
¿¿
r
¿
; U+d7 ' ".:=@o
2
2
90 cm
' >( 1.15 cm 2
¿¿
' ++"@+.@26
20 dB m
/rad(d7m) ' 1" !o-
1 m#
' ".1
33073.724
¿ ¿ 1.150 m
/ '
¿ ¿ ¿2 ( 0.1)¿ ¿
PR = 229.02)# '6.3"& + 2=. A transmitter with an output resistance of @2 and an r.m.s. output of 1"" is connected ia a matched !ine to an antenna whose input resistance is @2 . 0ts radiation resistance is a!so @2 . Assumin- that the antenna is 1"" e9cient at the operatinfrequency% how much power wi!! be transmitted into free spaceE GIVEN: o ' @2O o ' 1"" i ' @2O e ' @2O <'1
