Antenna

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$% and (c) the a!ue of the required series capacitance. capacitance. GIVEN: & ' 2H  '15pf f ' 5"#H$

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 eect eectie ie 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

3/

REQ’D: SOL’N: 3/ ' /o4 3/ ' (2""2")(5) ERP = 900#

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 eectie isotropic radiated power for an antenna with directiity ' ++ d7% e9ciency ' :2% and input power ' 1"".

GIVEN: D ' ++ d7 < ' :2  /in ' 1"" 

REQ’D: 30/

SOL’N:

d7 REQ’D: /D SOL’N:

 PtGt  /D '

4 πr

2

' (6" )(".@5)(+=.:1)6B(+""""m2) PD = %05.599 )#*+ 2 @. Determine the directiity in d7 of an antenna that produces power density of 2 um 2 at a point when the reference antenna produces ".5 um 2 at the same point. GIVEN: /D ' 2 um2 /ref  ' ".5 um2 REQ’D: D(d7) SOL’N: D(d7) '

 PD  Pref 

 ' 1"!o-(2 um2  ".5 um 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 fronttobac? ratio for an antenna with forward -ain of @ d7 and a reerse -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 preious 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

4241 '

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  cyces (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 endIre 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

4'

2

( πD ) 3

 λ

' (15)(1")("."5)(".1B)2  (+N1":ms  5""N1">) ' +.62 G,"&- = 5.'5 "& 52 λ

M'

¿

1 /2

(  )

( πD )  NS  λ

( ) ( 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 ' @"(GD) ' @"(12") 1 = '.5 16. How !ar-e a dish diameter% in wae!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 eectie 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% 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 pointtopoint system operates oer a distance of 2" ?m at a frequency of 2> 4H$. Che antenna is each of diameter =" cm. 3stimate the beam width of the antenna dep!oyed and the power receied if the transmit power is 2" d7 m. GIVEN: r ' 2"?m f o ' 2>4H$ 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