The aperture is defined as the area, oriented perpendicular to the direction of an incoming radio wave, which would intercept the same amount of power from that wave as is produced by the antenna receiving it. A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are widely used as antennas at UHF and microwave frequencies, above 300 MHz.
2. OUTLINE
1)Aperture Antenna
a) Huygen’s Principle
b) Radiation Pattern
c) Directivity
d) Rectangular Apertures
e) Circular Apertures
2)Horn Antenna
a) E Plane Sectoral Horn
b) H Plane Sectoral Horn
c) Pyramidal Horn
d) Conical Horn
e) Other types of Horn Antenna
3) Application
3. APERTURE ANTENNA
•Most common at microwave frequencies (300MHz-
300GHz)
•They may take the form of a waveguide or a horn
whose aperture may be square, rectangular, circular,
elliptical, or any other configuration.
•We will analyze radiation characteristics at far field
• Rectangular Aperture
• Circular Aperture
4. FIELD EQUIVALENCE PRINCIPLE:
HUYGEN’S PRINCIPLE
• Introduced in1936 by A. Schelkunoff, which is a more
rigorous formulation of Huygen’s Principle which states that
“Every point on a wave-front may be considered a source of
secondary spherical wavelets which spread out in the
forward direction at the speed of light. The new wave-front
is the tangential surface to all of these secondary wavelets.”
• A principle by which actual sources, such as antenna and
transmitter, are replaced by equivalent source.
6. FIELD EQUIVALENCE PRINCIPLE:
HUYGEN’S PRINCIPLE
• The Huygen’s principle is based on the uniqueness theorem
which states that “a field in a lossy region is uniquely
specified by the sources within the region plus the
tangential components of the electric field over the
boundary, or the tangential components of the magnetic
field over the boundary, or the former over part of the
boundary and the latter over the rest of the boundary.”
7. FAR FIELD IS THE F OF THE NEAR FIELD
• Fourier Transform for 1-D
• For two-dimensions, x and y;
dxexwkW xjk
x
x
)()( x
xjk
x dkekWxw x
)(
2
1
)(
f
t
U kx, ky u(x, y)e
jkxx jky y
dx dy
yx
yjkxjk
yx dkdkekkUyxu yx
),(
4
1
),( 2
10. Now, we define,
And we obtain,
Which has a solution of
Then we take the inverse transform
2222
yxoz kkkk
0),,(
),,( 2
2
2
zkkk
z
zkk
yxz
yx
E
E
zjk
yxyx
z
ekkzkk
),(),,( fE
yx
j
yx dkdkekkzyx rk
fE ),(
4
1
),,( 2
11. If z=0, then, we are at the aperture
Which looks like:
Which is the inverse of F…
yx
yjkxjk
yxa dkdkekkyxyx yx
),(
4
1
)0,,(),( 2tan fEE
yx
yjkxjk
yx dkdkekkUyxu yx
),(
4
1
),( 2
12. This is the Fourier transform for 2 dimensions, so:
dxdyeyxEkk
yjkxjk
a
S
yxt
yx
a
),(),(f
sinsin,coscos
2
cos
)( bkake
r
jk
r oot
rjko o
fE
U kx, ky u(x, y)e
jkxx jky y
dx dy
Therefore, if we know the field at the aperture, we can
used these equations to find E(r).
=>First, we’ll look at the case when the illumination at
the rectangular aperture it’s uniform.
It can be shown that,
13. UNIFORMLY ILLUMINATED
RECTANGULAR APERTURE
elsewhere0
for),(
b|y|a|x|Eyx oa xE
dxdyeE
yjkxjk
a
a
b
b
ot
yx
xf
v
v
u
u
abE
bk
bk
ak
ak
abE
bk
bk
ak
ak
abE
o
o
o
o
o
o
y
y
x
x
o
sinsin
4
sinsin
sinsinsin
cossin
cossinsin
4
sinsin
4
x
x
x
coscosˆsinˆsinsin
2
4
)( φθE
v
v
u
u
e
r
abEjk
r rjkoo o
14. HOW DOES THIS PATTERN LOOKS…
sinsin
cossin
bkv
aku
o
o
15. In this report we considered TE10 and TE11
mode for illuminated rectangular aperture.
17. RECTANGULAR APERTURE:
DIRECTIVITY
• For TE10 illuminated Rectangular Aperture the aperture
efficiency is around 81%.
• For the uniform illumination, is 100% but in practice
difficult to implement uniform illumination.
2
4
abD apo
19. CIRCULAR APERTURE W/ UNIFORM
ILLUMINATION
• For TE11 illuminated Circular Aperture the aperture
efficiency is around 84%.
• For the uniform illumination, is 100% but in practice
difficult to implement uniformity
2
C
D apo
20. flared waveguides that produce a nearly uniform
phase front larger than the waveguide itself
constructed in a variety of shapes such as
sectoral E-plane, sectoral H-plane, pyramidal,
conical, etc.
HORN ANTENNA
22. APPLICATION AREAS
used as a feed element for large radio astronomy,
satellite tracking and communication dishes
A common element of phased arrays
used in the calibration, other high-gain antennas
used for making electromagnetic interference
measurements
23. E-PLANE SECTORAL HORN
Fields expressions OVER THE horn are similar to the
fields of a TE10 mode for a rectangular waveguide with
the aperture dimensions of a and b1.
difference is in the complex exponential term,
parabolic phase error,.
)2/(
1
1
2
cos),( ykj
y ex
a
EyxE
)2/(
1
1
2
sin),(
ykj
z ex
aka
jEyxH
)2/(1 1
2
cos),(
ykj
x ex
a
E
yxH
24. • this is the plane containing the magnetic field vector
(sometimes called the H aperture) and the direction of
maximum radiation
H-PLANE SECTORAL HORN
31. DIRECTIVITY:
• Directivity of an E-plane sectored horn is:
𝐷 𝐸 =
4𝜋𝑈𝑚𝑎𝑥
𝑃 𝑟𝑎𝑑
=
64𝑎𝜌1
𝜋𝜆𝑏1
𝑐2 𝑏1
2𝜆𝜌1
+𝑠2 𝑏1
2𝜆𝜌1
• Directivity of an H-plane sectored horn is:
𝐷 𝐻 =
4𝜋𝑏𝜌2
𝑎1 𝜆
𝑐 𝑢 − 𝑐 𝑣 2 + 𝑠 𝑢 − 𝑠 𝑣 2
where 𝜌1 = 𝜌e cos 𝜑 𝑒
c(u),c(v),s(u) & s(v) are Fresnel integrals
a & b are dimensions of wave guide
32. DIRECTIVITY:
• Directivity of a pyramidal horn antenna is:
𝐷 𝐻 =
𝜋𝜆2
32𝑎𝑏
𝐷 𝐸 ∗ 𝐷𝐻
where D 𝐻 = Directivity of an H−plane sectored horn
DE= Directivity of an E-plane sectored horn
a & b are dimensions of wave guide
33. OTHER HORN ANTENNA TYPES
Multimode Horns
Corrugated Horns
Hog Horns
Biconical Horns
Dielectric Loaded Horns
etc.