Antennas Short notes | Electromagnetics - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


An tennas in Electromagnetics F orm ula Sheet for
GA TE
Basic An tenna P arameters
• Radiation In tensit y : P o w er radiated p er unit solid angle.
U(?,?) =
r
2
2?
|E|
2
(Units: Wsr
-1
)
wherer is distance,? is in trinsic imp edance (37673 ? in free space),E is electric field.
• Directivit y : Ratio of radiation in tensit y in a direction to the a v erage radiation in-
tensit y .
D(?,?) =
4pU(?,?)
P
rad
, D
max
=
4pU
max
P
rad
where P
rad
is total radiated p o w er.
• Gain : Includes an tenna e?iciency .
G =?
e
D, ?
e
=
R
r
R
r
+R
L
where ?
e
is e?iciency , R
r
is radiation resistance, R
L
is loss resistance.
• Radiated P o w er :
P
rad
=
?
2p
0
?
p
0
U(?,?)sin?d?d?
An tenna Characteristics
• Effectiv e Ap erture : Relates receiv ed p o w er to inciden t p o w er densit y .
A
e
=
?
2
4p
G
where ? is w a v elength, G is gain.
• F riis T ransmission Equation : P o w er receiv ed b y an an tenna.
P
r
=P
t
G
t
G
r
(
?
4pr
)
2
where P
t
is transmitted p o w er, G
t
and G
r
are transmitter and receiv er gains, r is
distance.
• Radar Range Equation : Receiv ed p o w er for radar systems.
P
r
=
P
t
G
t
A
r
s
(4p)
2
r
4
where s is radar cross-section, A
r
is receiv er effectiv e ap erture.
• Beam width : Angular width of the main lob e (e.g., Half-P o w er Beam width, HPBW).
HPBW˜
?
L
(for linear an tennas, in radians)
where L is an tenna length.
1
Page 2


An tennas in Electromagnetics F orm ula Sheet for
GA TE
Basic An tenna P arameters
• Radiation In tensit y : P o w er radiated p er unit solid angle.
U(?,?) =
r
2
2?
|E|
2
(Units: Wsr
-1
)
wherer is distance,? is in trinsic imp edance (37673 ? in free space),E is electric field.
• Directivit y : Ratio of radiation in tensit y in a direction to the a v erage radiation in-
tensit y .
D(?,?) =
4pU(?,?)
P
rad
, D
max
=
4pU
max
P
rad
where P
rad
is total radiated p o w er.
• Gain : Includes an tenna e?iciency .
G =?
e
D, ?
e
=
R
r
R
r
+R
L
where ?
e
is e?iciency , R
r
is radiation resistance, R
L
is loss resistance.
• Radiated P o w er :
P
rad
=
?
2p
0
?
p
0
U(?,?)sin?d?d?
An tenna Characteristics
• Effectiv e Ap erture : Relates receiv ed p o w er to inciden t p o w er densit y .
A
e
=
?
2
4p
G
where ? is w a v elength, G is gain.
• F riis T ransmission Equation : P o w er receiv ed b y an an tenna.
P
r
=P
t
G
t
G
r
(
?
4pr
)
2
where P
t
is transmitted p o w er, G
t
and G
r
are transmitter and receiv er gains, r is
distance.
• Radar Range Equation : Receiv ed p o w er for radar systems.
P
r
=
P
t
G
t
A
r
s
(4p)
2
r
4
where s is radar cross-section, A
r
is receiv er effectiv e ap erture.
• Beam width : Angular width of the main lob e (e.g., Half-P o w er Beam width, HPBW).
HPBW˜
?
L
(for linear an tennas, in radians)
where L is an tenna length.
1
Common An tenna T yp es
• Infinitesimal Dip ole : Electric field in far-field.
E
?
=j
I
0
le
-jkr
4pr
sin?
(
?
c
)
where I
0
is curren t, l is dip ole length, k =
2p
?
, c is sp eed of ligh t.
• Half-W a v e Dip ole :
D
max
˜ 1.643, R
r
˜ 73?
• Isotropic Radiator : Hyp othetical p oin t source with uniform radiation.
D = 1, U =
P
rad
4p
• Y agi-Uda An tenna : Directiv e an tenna with driv en elemen t, reflector, and directors.
Gain˜ 7 –12dB (dep ends on n um b er of elemen ts)
An tenna Arra ys
• Arra y F actor : Radiation pattern due to arra y geometry .
AF =
N-1
?
n=0
I
n
e
j(nkdcos?+ßn)
where I
n
is curren t amplitude, d is elemen t spacing, ß
n
is phase shift.
• Uniform Linear Arra y (Broadside) : Maxim um radiation p erp endicular to arra y
axis.
AF =
sin
(
N?
2
)
sin
(
?
2
), ? =kdcos?+ß
• Directivit y of Uniform Arra y :
D˜ 2N
d
?
Practical Considerations
• F ree-Space P ath Loss :
FSPL =
(
4pr
?
)
2
(in linear scale)
• P olarization : Linear, circular, or elliptical; mismatc h reduces p o w er transfer.
• Imp edance Matc hing : Maximize p o w er transfer usingZ
in
=Z
0
(e.g., 50? or 75? ).
• F requency and W a v elength : ? =
c
f
, where c = 3×10
8
ms
-1
, f is frequency .
2
Page 3


An tennas in Electromagnetics F orm ula Sheet for
GA TE
Basic An tenna P arameters
• Radiation In tensit y : P o w er radiated p er unit solid angle.
U(?,?) =
r
2
2?
|E|
2
(Units: Wsr
-1
)
wherer is distance,? is in trinsic imp edance (37673 ? in free space),E is electric field.
• Directivit y : Ratio of radiation in tensit y in a direction to the a v erage radiation in-
tensit y .
D(?,?) =
4pU(?,?)
P
rad
, D
max
=
4pU
max
P
rad
where P
rad
is total radiated p o w er.
• Gain : Includes an tenna e?iciency .
G =?
e
D, ?
e
=
R
r
R
r
+R
L
where ?
e
is e?iciency , R
r
is radiation resistance, R
L
is loss resistance.
• Radiated P o w er :
P
rad
=
?
2p
0
?
p
0
U(?,?)sin?d?d?
An tenna Characteristics
• Effectiv e Ap erture : Relates receiv ed p o w er to inciden t p o w er densit y .
A
e
=
?
2
4p
G
where ? is w a v elength, G is gain.
• F riis T ransmission Equation : P o w er receiv ed b y an an tenna.
P
r
=P
t
G
t
G
r
(
?
4pr
)
2
where P
t
is transmitted p o w er, G
t
and G
r
are transmitter and receiv er gains, r is
distance.
• Radar Range Equation : Receiv ed p o w er for radar systems.
P
r
=
P
t
G
t
A
r
s
(4p)
2
r
4
where s is radar cross-section, A
r
is receiv er effectiv e ap erture.
• Beam width : Angular width of the main lob e (e.g., Half-P o w er Beam width, HPBW).
HPBW˜
?
L
(for linear an tennas, in radians)
where L is an tenna length.
1
Common An tenna T yp es
• Infinitesimal Dip ole : Electric field in far-field.
E
?
=j
I
0
le
-jkr
4pr
sin?
(
?
c
)
where I
0
is curren t, l is dip ole length, k =
2p
?
, c is sp eed of ligh t.
• Half-W a v e Dip ole :
D
max
˜ 1.643, R
r
˜ 73?
• Isotropic Radiator : Hyp othetical p oin t source with uniform radiation.
D = 1, U =
P
rad
4p
• Y agi-Uda An tenna : Directiv e an tenna with driv en elemen t, reflector, and directors.
Gain˜ 7 –12dB (dep ends on n um b er of elemen ts)
An tenna Arra ys
• Arra y F actor : Radiation pattern due to arra y geometry .
AF =
N-1
?
n=0
I
n
e
j(nkdcos?+ßn)
where I
n
is curren t amplitude, d is elemen t spacing, ß
n
is phase shift.
• Uniform Linear Arra y (Broadside) : Maxim um radiation p erp endicular to arra y
axis.
AF =
sin
(
N?
2
)
sin
(
?
2
), ? =kdcos?+ß
• Directivit y of Uniform Arra y :
D˜ 2N
d
?
Practical Considerations
• F ree-Space P ath Loss :
FSPL =
(
4pr
?
)
2
(in linear scale)
• P olarization : Linear, circular, or elliptical; mismatc h reduces p o w er transfer.
• Imp edance Matc hing : Maximize p o w er transfer usingZ
in
=Z
0
(e.g., 50? or 75? ).
• F requency and W a v elength : ? =
c
f
, where c = 3×10
8
ms
-1
, f is frequency .
2
Key Notes
• Standard v alues: ? ˜ 376.73? , c = 3×10
8
ms
-1
.
• Use dB for gain: G
dB
= 10log
10
(G) .
• F or GA TE, fo cus on half-w a v e dip ole, F riis equation, and arra y factor calculations.
• An tenna e?iciency ?
e
< 1 due to losses (ohmic, dielectric).
3