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“High performance horn antenna
design”
Dr. Carlos del Río Bocio
Antenna Group
Public University of Navarra
Objective
• To explain the fundamentals of the high performance
feed horn antennas designed by us (HISPASAT,
ASTRA, PLANCK, AMAZONAS, etc) and by others,
offering an overview of the applications where the feed
horn antennas are involved, especially in relation with
reflector antenna systems: Radio-links, satellite
reception and transmission, sensing, communications,
etc.
Contents
• Fundamental Theory
– Aperture radiation
– Main features and parameters
• Canonical Primary Feed-horn antennas
• Lens/Reflector systems
– Definition and classification
• High performance Feed-horn antennas
–
–
–
–
Conical rectangular and circular horn antennas
Scalar horn antennas
Gaussian shaped horn antennas
Other designs
James Clerk Maxwell
• James C. Maxwell (1831-1879)
• Born in Edinburgh was
contemporary of:
–
–
–
–
–
–
–
–
Hans Christian Oersted (1777-1851)
André-Marie Ampère (1775-1836)
Michael Faraday (1791-1867)
Samuel F.B. Morse (1791-1872)
Alexander Graham Bell (1847-1922)
Herman von Helmholtz (1821-1894)
Nikola Tesla (1856-1943)
Heinrich Rudolf Hertz (1857-1894)
James Clerk Maxwell
• Previous works:
– 1820, Oersted and Ampère
established the relation between the
electric currents and the generation of
a magnetic field.
– Ampère define the fundamental theory
of the electrodinamics, relation
between current and forces created by
the magnetic fields.
– 1831, Faraday shows the
autoinduction phenomena, obtaining a
electrical current from a magnetic field
created by another electrical current.
James Clerk Maxwell
• James C. Maxwell, after different
studies following the research lines of
Ampère and Faraday,
– "On Faraday's Lines of Force“ (1856)
– “On Physical Lines of Force" (1861)
– "On a dynamical Theory of the
Electromagnetic Field" (1865)
compile the previous studies about
electricity, magnetism and optics in a
single and concise theory (1873):
– A Treatise on Electricity and Magnetism
James Clerk Maxwell
• The famous Maxwell equations were
originally thirteen and they were
reorganized by Heaviside in the final
and very well known version of the
four equations:


Ampère equation:   H  J 

D
t 
B


Faraday equation:   E   M 
t

D  
Gauss:

B 
Maxwell equations
• Being:

–
–
–
–

E and H , the electric and magnetic field intensity

D and B , the electric and magnetic flux density

J and M , the electric and magnetic current intensity
 and , the electric and magnetic charges


Ampère equation:   H  J 

D
t 
B


Faraday equation:   E   M 
t

D  
Gauss:

B 


D   E

B   H
Maxwell equations
• Starting from the Maxwell equations, considering
only the electric charges and currents,


 D 
H  J 

t 



B
E  

t



D  



B  0
Contour
Conditions

A

Sources:

J

Intermediate
functions
(Potentials)

E

H
Potential functions

B  0
• From the Gauss equation,
knowing that the divergence of a curl
 is zero, we
could define the vector potential A as:


B  A
   A
Ay
z
  A  x 

z
 y

  Az A y

  A 


x  y
z


   Ax Az    A y Ax
  y


  z 

x 
y
 z

 x




   Ax Az    A y Ax


 y  z  x   z  x  y





0


Potential functions
• From the Faraday equation, substituting B by the
previous expression,

E  

B
t


  E   

  A 
0
E 



t



A
t
A vector field with zero Curl becomes from the
gradient of a scalar function, , the scalar potential.

E

A
t
  
Potential functions
• Substituting the previous definitions in the Ampère
equation,

H 

B



B  A


H  J 

D
t


  B   J  

E
t


D  E

E    



 
A 
    A   J  
   

t 
t 

A
t
Potential functions



 
A 
    A   J  
   

t 
t 



2
 
    A   A   A

 A




2
  A   A   J   
 
2
t
t

2


 A
 
 
2
 A  
   J     A  
2

t

t


 
2
Potential functions

 A  

 A

 
 
   J     A  
2

t

t







 

A
E 
D  

   

 


t





2
   
A
 t
2
2
 
 
2
   
2
t
2
  
 
 
 A  

 t 
 t 

Potential functions

 A  
2

 A
2
t
2
 
2
   
2
t
2

 
 
   J     A  


t


  
 
 
 A  

 t 
 t 

Fortunately, the divergence of the vector potential have
been not defined yet, so imposing the Lorentz condition:


 A  
0
t
Potential functions

 A  
2

 A
2
t
2
 

  J
2
   
2
t
2



De-coupled
Potential Wave
Equations
• We need to solve these equations to obtain the
potential functions and, substituting them in the
previous formulae, the final expressions for the
electrical and magnetic fields could be determined.
Coordinate System
Punctual source radiation
From the scalar potential wave equation:
 
2
   
2
t

2
q0

supposing a sinusoidal temporal variation,


jwt
 ( r ' , t )   (r ' )e
k  w 
The final equation would be:
 k  
2
2
q0

Punctual source radiation
• Let suppose a punctual source, q(t), placed at the origin
of the coordinate system


jwt
q ( r ' , t )  q 0 ( r ' ) e
 k  
2
2

q 0 ( r ' )

• For this case, since there are no movement of charges
(electrical currents), the vector potential is not needed
to determine the radiated fields.
Punctual source radiation
 k  
2
2

q 0 ( r ' )

• In all points different of the origin where the
charge is placed,
 k  0
2
2
• Since the source is punctual,  does not depends
neither  or q, and it will be a function of the
radial coordinate, r,

jwt
 ( r , t )   ( r )e
Punctual source radiation
• Solving the differential operator,
 k  0
2
2
0
0
1   2  
1
 
 
1
 
2
r

sin
q


k
 0
2
2
2
2




r r 
 r  r sin q  q 
 q  r sin q  
2
1   2  
2
r

k
 0
2


r r 
r 
d 
2
dr
2

2 d
r dr
k  0
2
Punctual source radiation
• The solutions for a second order differential equation
are:
d 
2
dr
2

2 d
r dr
k  0
2
  (r )  C 0
e
 jkr
e
r
• The constant C0 will be determined defining the
function at origin where the charge is placed.
• Additionally, as we stated at the beginning,
 
A(r , t )  0
jwt
Punctual source radiation
• Substituting the scalar and vector potentials in the
electric field expression,

E    

A
t
 jkr
 jkr




e
d
e
jwt
jwt
E    C 0
e   C 0e

r
dr


 r

 rˆ

 jkr

1
e


jwt
E  C 0  jk  
e rˆ
r r

Radiated fields
Induced or “Static”
electrical fields
Arbitrary source radiation
• The general solutions would be obtained by the proper
summation (integral) of each one of the punctual
sources or currents:

 A  
2

 A
2
t
2
 

  J
2
   
2
t
2



 
 
r  r'

J  r ', t 
 
v

A(r , t )  
 
V'
4 r  r '

 (r , t ) 

V'




dV '
 

r  r' 


  r ', t 
v 

dV '
 
4 r  r '
Arbitrary source radiation
• If the time variation is sinusoidal,
 

r r '
jw  t 

v

 
 
 J  r ' e
A(r , t )  
 
V'
4 r  r '
e
 

r r '
jw  t 

v





e





 (r , t ) 
dV '


V'
jwt
j
e
w
v

w  
r r '
v
w
1
00
  r ' e
 

r r '
jw  t 

v





 
4 r  r '
 
 jk r  r '
e
jwt
 w
00  k
e
dV '
Arbitrary source radiation
• So, assuming the sinusoidal variation and neglecting
the ejwt term in all the expressions,
 
A(r ) 
   jkR
 J  r ' e

V'

 (r ) 

V'
4 R
  jkR
  r ' e
4 R
dV '

 
R  R  r  r'
dV '
being R the distance between each differential
charge/current and the observation point.
General Field Expressions
• Once defined the potential functions, substituting in the
equations, the electric fields could be obtained:

E    
 
E ( r )  

V'
 
1
E (r ) 
4
  jkR
  r ' e
4 R

A
t
dV '  jw 
   e  jkR
V '   r '  R


V'
   jkR
 J  r ' e
4 R
   e  jkR

  jw  J  r ' 

 R


dV '

  dV '


General Field Expressions
• Considering that the differential operator  is defined
in the coordinate system of the observer,
 e  jwR
 
 R
 jkR

d e

 dR  R


 jkR
 jkR



R

jk
e

e
ˆ
Rˆ 
R 
2
R

 jkR
1e

   jk  
R R

 
E (r ) 
Rˆ
 jkR
   e  jkR

 ˆ
1e
  r ' R  jw  J  r ' 
 jk  


4 V '  
R R
 R
1

  dV '


General Field Expressions
• For the magnetic fields,


B  A
 
B (r )    
V'



   a      a     a
 

B (r ) 
4
 

B (r ) 
4
   jkR
 J  r ' e
4 R
 e  jkR
V '   R

dV '
  
  J  r ' dV '


 jkR
1  e

V '  jk  R   R

 

 Rˆ  J  r ' dV '


General Field Expressions
• The obtained general and exact field expressions could
be separated in radiated and induced terms, so,
i 
E (r ) 

i r
E E E

i

H H H
r 
E (r ) 
 jkR
 ˆ e
  r '  R 
2

4 V '
R

1
jk
4

i 
1
H (r ) 
4
r
V'
r 
 jk
H (r ) 
4
   e  jkR
 J  r '  
 R


 ˆ
 r 'R 

V'


 dV '


   e  jkR
Rˆ  J  r '  
2
R


V'


 dV '


   e  jkR
Rˆ  J  r '  
 R



 dV '



dV '


Far field approximation
• If we are interested in the fields far from the antenna
location, far radiated fields, some simplifications could
be applied.
 
R  r  r' 
 
r  r ' 2r  r '  r 1  2
2
2
 
r r'
r
2
 

r r'

ˆ
 r 1  2   r  rr '
r 

Rˆ  rˆ
1
R

1
r
e
 jkR

R
e
 jkr
e
r

jk rˆr '
Far field approximation
• Then, the electrical radiated field equation,
r 
E (r ) 
jk e
4
 jkr
r

V'


  r ' rˆ 

 

jk rˆr '
 J  r '  e
dV '
and taking into account the continuity equation,
 
 

1
J 
 0   (r ' )  
 ' J (r ' )
t
jw
the original equation could be rewritten as follows,
r 
E (r ) 
jk e
4
 jkr
r
 
  rˆ
V '  jw  ' J ( r ' ) 

   jk rˆr '
 J  r '  e dV '

Far field approximation
r 
E (r ) 
jk e
4
 jkr
r
 
  rˆ
V '  jw  ' J ( r ' ) 

   jk rˆr '
 J  r '  e dV '

• Let’s study the first integral,
 

jw rˆr '
 ' J (r ' )e
dV '

V'
 


jk rˆr '
a  J (r ' ) ;   e




  a     a     a

 

jk rˆr '
 ' J (r ' )e
dV ' 
V'

V'
 
 


jk rˆr '
jk rˆr '
 ' J (r ' )e
dV '  J ( r ' )  ' e
dV '


V'
Divergence Theorem

V'
 

jk rˆr '
 ' J (r ' )e
dV ' 




S'
e

jk rˆr '
 

J (r ' )ds  0


Far field approximation
r 
E (r ) 
jk e
4
 jkr
r

 rˆ  
jk rˆr '
V '  jw J ( r ' )  ' e 



  jk rˆr ' 
 J  r ' e
 dV '

• And now, let’s focus in the gradient,
rˆ  cos  , cos  , cos 

r '  (x', y', z')

' e

jk rˆr '
   ' e

jk  x ' cos   y ' cos   z ' cos 
 


 
xˆ 
yˆ 
y '
z '
 x '
 jk rˆ  e

jk rˆr '


 jk  x 'cos   y 'cos   z 'cos  
zˆ  e


Far field approximation
r 
E (r ) 
jk e
4
 jkr

r
 
 

jk rˆr '
rˆJ ( r ' ) rˆ  J  r '  e
dV '
 
V'

• Applying the next vector identity, we could conclude,

  
  
 
A B  C  A C  B  A  B C

 



   
  

   
r  r  J ( r ' )  r  J ( r ' )  r  r  r   J ( r ' )

 


 jkr
r 
  jk rˆr '
jw  e
E (r ) 
rˆ  rˆ   J ( r ' )e
dV '
V'
4
r

Far field approximation
• For the case of the magnetic field, taking into account
the same approximations,
r 
 jk
H (r ) 
4

V'
   e  jkR
Rˆ  J  r '  
 R


 ˆ
 R  rˆ ;

1
R

 dV '



1
;
r
 jkr
r 
  jk rˆr '
 jk e
H (r ) 
rˆ   J  r ' e
dV '
V'
4
r
 
R  r- rˆr ' 

Far field approximation
• Summarizing:

 jkr
r 
  jk rˆr '
jw  e
E (r ) 
rˆ  rˆ   J ( r ' )e
dV '
V'
4
r
 jkr
r 
  jk rˆr '
 jk e
H (r ) 
rˆ   J  r ' e
dV '
V'
4
r
 jkr
 
 e
A(r ) 
4
r

V'
  jk rˆr '
J  r ' e
dV '

Far field approximation
• In summary, when the electric charges and currents are
taking into account, the radiated electric and magnetic
fields could be absolutely determined solving the
integral:
 
N (r ) 

V'
  jk rˆr '
J  r ' e
dV '
which is known as the radiation vector, since the
radiating characteristics could be obtained from it.
Far field approximation
• For the general case of having:
 jkr
 
 
 e
A(r ) 
N (r ) ;
4
r
 



A ( r )  A r r  Aq q  A 
taking into account the relation with the radiated
electric and magnetic fields,


 
r  A   A q  Aq 


  
r  r  A   Aq q  A 


r
  
E  j r  r  A


H
r
j


rA
 

the final expressions could be rewritten as follows,
Far field approximation
r


E   j  Aq q  A 


H
being,
r
 j



A q




 Aq   -
E 
Eq 


q 
 jkr
r 


 jw  e
E (r ) 
N qq  N 
4
r
 jkr
r 


jk e
H (r ) 
N q  N q 
4 r





Far field approximation
• The Pointying vector could be calculated by the
formula:
 *


  Re E  H  r



4 r
2
2
N
2
q
 N
2

and, from it, the far field pattern could be obtained,
t q ,   
 q ,  
 max

N
N
q
q
q ,  
q ,  
2
2
 N  q ,  
 N  q ,  
2
2


max
General radiation problem
• With the previous formulae, the radiated fields
generated by the electric charges and currents could be
determined.
General radiation problem
• But it does not include the analysis of apertures,
reflectors and so on, where magnetic currents could be
present.
• We need to solve the dual problem, where the magnetic
charges and currents are considered as sources of the
electromagnetic fields.
Maxwell equations (Dual)
• So, again, starting from the Maxwell equations, but
now considering the magnetic charges and currents,


 D 
H  J 

t 



B
E  

t



D  



B  0
Contour
Conditions

A

Sources:

J

Intermediate
functions
(Potentials)

EJ

HJ
Maxwell equations (Dual)
• So, again, starting from the Maxwell equations, but
now considering the magnetic charges and currents,

D


t


  B 
  E  M 

t



D  0



B 

H 
Contour
Conditions

F

Sources:

M 
Intermediate
functions
(Potentials)

EM

HM
New potential equations
• The new potential wave-equations will be as the ones

shown,
2


 F
 F  
  M
2
t
2
 
2
   
2
t
2



being the Lorentz condition,


 F  
0
t
New potential solutions
• So, assuming the sinusoidal variation and neglecting
the ejwt term in all the expressions,
 
F (r ) 
   jkR
 M  r ' e

V'

 (r ) 

V'
4 R
  jkR
  r ' e
4  R
dV '

 
R  R  r  r'
dV '
being R the distance between each differential
charge/current and the observation point.
New radiation vector
• In this case, we could define a dual radiation vector for
the case of the magnetic charges and currents,
 
L (r ) 
 jkr 
 

 e
F (r ) 
L (r )
4
r

V'
  jk rˆr '
M  r ' e
dV '
and the radiated field expressions,

 jkr
 r 
  jk rˆr '
jw  e
H M (r ) 
rˆ  rˆ   M ( r ' )e
dV '
V
'
4
r
 jkr
 r 
  jk rˆr '
 jk e
E M (r ) 
rˆ   M  r ' e
dV '
V'
4
r

New radiated fields
• The radiated fields in function of the new radiation
vector,
 jkr
 r 


 jk e
E M (r ) 
L  q  Lq 
4
r
 jkr
 r 


 j  e
H M (r ) 
Lq q  L  
4
r




the old ones,
 jkr
 r 


 jw  e
E J (r ) 
N qq  N 
4
r
 jkr
 r 


jk e
H J (r ) 
N q  N q 
4 r




r
 r
 r
E  EJ  EM
r
 r
 r
H  HJ  HM
New radiated fields
• The final expressions for the fields considering both
types of excitations will be,
 jkr
r 


 jk e
 N q  L q   N   Lq 
E (r ) 
4
r
 jkr
r 


 j  e
 N   Lq q   N q  L 
H (r ) 
4
r




New radiated fields
• So, the far field pattern will be,
 *


  Re E  H  r

t q ,   


 q ,  
 max
L
 
 Nq 
2 2
4 r 


2
2
 N 
Lq





2
2

L q ,  
Lq q ,   
 N  q ,   
 N q q ,   





2

L q ,  
Lq q ,  
 N  q ,   
 N q q ,   



2



max
Radiation vectors
• As we had shown, solving the radiation vector integrals
the radiating electromagnetic fields could be properly
defined.
 
N (r ) 

V'
  jk rˆr '
J  r ' e
dV '
 
L (r ) 

V'
  jk rˆr '
M  r ' e
dV '
• These two integrals could be understood
  as a Fourier
transformation from the J , M  to N , L  domain.
defining:





k  kr  k x x  k y y  k z z 



 k cos  x  k cos  y  k cos  z 



 k sin q cos  x  k sin q sin  y  k cos q z
Examples of radiation
• The Fourier Transformation and the antenna size and
dimensions give an idea of how the antenna radiates.
Important Parameters
• Directivity:
D q ,   

 q ,  
 Isotropic

 q ,  
Pr
 q ,  
4 r
S
4 r
2

  q ,  dS

 q ,  
  q ,  r

2
2

d
4 r
4
 eq
2
• It has no units (expressed in dB), and deals with
capabilities of the antenna to drive energy in specific
directions.
Important Parameters
• The Gain is the parameter relating the power delivered
to the antenna and the power density generated at any
direction, considering the losses of the antenna (power
delivered but does not being radiated):
G q ,     D q ,  
• Usually it is referred to a known antenna gain:
– dBi, compared with the Gain of a Isotropic antenna
– dBd, when it is compared with a Half-dipole antenna
Important Parameters
• Effective radiating/receiving area, it is defined in
reception and relates the power delivered to the load
(PL) in relation with the incident power density,
A ef q ,   
PL
 inc q ,  
• For any antenna, the effective area is related with the
directivity by a constant,
Aef q ,  
D q ,  


2
4
Important Parameters
• The far field approximation is not always valid, since
the distances between the different elements of a
antenna system (feeder and reflector, for instance)
could not be long enough.
Radiating regions
• To reconsider the calculation of R, for the case of lineal
current distribution along z axis (r’=z’),
 
R  r  r' 

 
r  r ' 2r  z ' 
2
2
r  r '  2 r  z ' cos q  r 1 
2
2
z'
r
2
2
2
x
2
R  r  z ' cos q 
2
2r
sin q 
2
z'
cos q
r
1 x  1
z'
z'

x
2
8

x
3
...
16
3
2r
cos q sin q  ...
2
2
Radiating regions
R  r  z ' cos q 
z'
2
sin q 
2
2r
z'
3
2r
cos q sin q  ...
2
2
• For r ∞, Fraunhofer region, the two first terms
remain, and the expression corresponds with the Far
Field approx., e  jkR e  jkr jkz 'cos q

e
R
r
• As we get closer the radiation origin, the expression
should be including additional terms,
e
 jkR

R
e
 jkr
e
r
jkz ' cos q
 jk
e
z'
2
2r
 jk
sin q
2
e
z'
3
2r
2
cos q sin q
2
...
Radiating regions
e
 jkR

R
e
 jkr
e
jkz ' cos q
 jk
e
z'
2
 jk
sin q
2
2r
e
z'
3
2r
2
cos q sin q
2
...
r
Fraunhofer Region:
2D

2
r
Fresnel Region: 0 , 6
D

3
r
2D
2

• The border between different Region defined by the
maximum phase error of /8.
• Once the Fresnel Region is reached, the radiated field
vary with the distance, r.
Radiating regions
• In practice, inside the Fresnel Region the fields are
broader as we approach the excitation.
• Many reflectors and lenses will be intercepted inside
this region, we should know in advance that the field
could be broader that the ones obtained by the far field
approximation (Fourier Transformation) in the
Fraunhofer Region.

• Fresnel Zones,
st
  r   R1  R 2   0 , 1 Zone
2
r
R1
R2
   r   R1  R 2  


2
, 2
nd
Zone
Fresnel Zones
f = 500MHz
E (r ) 
E0
r
e
 jkr
Fresnel Zones
f = 500MHz
E (r ) 
E0
r
e
 jkr
Fresnel Zones
f = 500MHz
R = 150 m
R1max= 9.48 m
Fresnel Zone
Radii
R2max= 13.41 m
R3max= 16.42 m
Link calculation
• The power received in a link could be evaluated with a
very simple equation,
PL 
Pr
4 r
2
D Tx Aef Rx
2
2
  
 1 

 D Tx D Rx  
 Aef Tx Aef Rx
Pr
 4 r 
 r
PL
• Constrains:
– Low frequency: D Tx  D Rx  3 2
– High frequency: Aef  A ef  A S
Tx
Rx
Link calculation
• In many practical cases, we need to obtain the higher
directivity possible.
• Having a high directivity is directly related with the
fact of having a big aperture where the fields could be
generated properly.
• The antenna system should provide this aperture with
the fields properly defined in it.
• Antenna technologies:
– Wired antennas (preferable for lower frequencies)
– Waveguide antennas (Horn antennas)
– Reflector/lens antenna system
Wired antennas
• Normally, the wired antennas are preferable for lower
frequencies because is always the lighter option, since
the dimensions could be important.
• Standard Directivities up to 18-19 dB, for frequencies
lower than 1-2GHz.
Waveguide horn antennas
• The radiation aperture is created inside a waveguide.
• There is the possibility of combining waveguide modes
in order to improve some radiating features (side-lobes,
cross-polarization, etc).
Waveguide horn antennas
• The possible directivities could be from 8-9 dB of and
open-ended mono-mode waveguide up to 24-25 dB
combining waveguide modes.
Reflector/lens antennas
• It is the easiest way to get high directivities ( 30 dB).
• It consists of a feeder (low directivity antenna)
illuminating a metallic surface where electric and
magnetic currents are induced, which are responsible
of the radiated fields.
Reflector/lens antennas
• In a parabolic reflector
antenna, the parameter f/D
determines the antenna
appearance as well as some of
its electromagnetic features
• As f/D parameter increases the
parabolic surface is more flat
Reflector/lens antennas
• In this type of configuration, the
feed-horn doesn’t intercept the
reflected wave-front
• Although the radiation pattern
of the feed-horn is symmetric,
the reflector surface
distribution will not be
symmetric. This aspect will
determine some of the
antenna electrical
characteristics
Reflector/lens antennas
• In the Cassegrain configuration, the feed-horn presents
a more directive radiation pattern to illuminate the
parabolic surface through an hyperbolical sub-reflector.
Reflector/lens antennas
• The Gregorian configuration presents a more
directive feed-horn to illuminate the parabolic surface
through an elliptical sub-reflector.
Reflector/lens antennas
• The off-set versions are also possible.
• An adequate selection of a angle improves the aperture
illumination symmetry (Mizugutch condition)
Reflector/lens antennas
• There are another special reflector configurations as
the ones of Compact Antenna Test Ranges (CATR).
• This type of configuration requires the feed-horn
pattern to be quite special since the parameter to
maximize is the Quiet Zone size.
Reflector/lens antennas
• Another special reflector configurations are the radiotelescopes and radiometers
• This type of instruments
require the feed-horn
pattern to be also quite
special since the
parameter to improve
is usually G/T instead
of gain
Reflector/lens antennas
• Lenses operate in transmission mode
• Lenses are usually used at higher
frequency than reflectors because
are less sensitive to mechanical
tolerances, but they have more weight
and volume
• Lenses don’t suffer from blockage
effects but they add dielectric losses
and unwanted reflections in the
discontinuities
Reflector analysis
• The gain of a reflector
antenna is given by:
G  4  
S

2
 t
where S is the reflector
surface and t is the total
illumination efficiency of
the antenna.
Reflector analysis
• The reflector efficiency is a
combination of several loss factors:
–
–
–
–
–
–
Uniformity of the illumination, i
Spillover, s
Phase uniformity, p
Polarization uniformity, x
Blockage efficiency, b
Random error efficiency, r, over the
reflector surface
 t   i  s  p  x  b  r
Reflector analysis
• The reflector efficiency is
mainly derived from
illumination and spillover
efficiencies product.
• It’s maximum lies for 9 to 13
dB illumination taper.
Reflector analysis
• In a parabolic reflector the focus
is farther from the edge of the
reflector than from the center
• Since radiated power diminishes
with the square of the distance,
less energy is arriving at the edge
of the reflector than at the center
• This aspect is commonly known
as space attenuation or space
taper.
Reflector analysis
• In a parabolic reflector, the
position of the feed phase centre
exactly at the focus of the reflector
is very important.
• There are important losses because
of axial defocusing.
• This effect is affected by f/D
parameter of the reflector.
• The best feed-horns must present
the same phase center position for
E and H planes and as stable as
possible in its usable band.
Reflector analysis
• As a summary of reflector analysis we can conclude
that:
– Centered focus configurations are symmetrical than offset
configurations so they present lower cross-polar levels but
suffer from blockage
– The double reflector offset configurations can reduce the
cross-polar levels if they are designed with the Mizugutch
condition
– The double reflector configuration need higher directivity
feeds and present less spillover losses so their noise
temperature is lower.