Polarizer parameters improvement for feed horn
G.Balodisi
Abstract - In the paper design for the 32-metre
Cassegrain type antenna polarizer at the Ventspils
International Radio Astronomy Center (VIRAC) is
described. A circularly polarized feed horn antenna
generating a circularly shaped beam is used for
reception from circularly polarized sources in the 6-cm
band. For signal recording equipment it is necessary to
split real time received signal in two orthogonal
polarized components, for example, horizontal and
vertical. The polarizer is realized as rectangular waveguide with two cascade sections. In the first section it is
realized polarization splitter but in the second –
matching network with 50 ohm input impedance. The
performance of the polarizer has been simulated and test
results are presented in the thesis.
Figure 1: The polarizer plate shape.
1 Introduction
A radio astronomy antenna is often required to
receive two orthogonal signals with a symmetrical
beam width. An elliptically polarized beam at input
waveguide of rectangular horn antenna with has been
splitted in two orthogonal plane wave components.
The polarizer contains two cascade sections: a
polarization converter and an impedance transformer.
The polarization converter transforms elliptically
polarized wave into two orthogonal linearly polarized
waves by means of conducting plate. This plate has
specific shape with compensation knobs. The
following section realizes impedance matching with
two ¼ lambda transformers for 50-ohm coaxial inputs.
This paper describes evaluation of this concept, which
enables a polarization converter to split a circularly
polarized beam with low dissipation losses. The
following discussion will show the operational
principle of this polarizer. Simulation results are
shown to be in conformity with the theory.
Equivalent matching circuit (EMC) is presented
in Fig.3.
Winput W1
W2 Woutput=50 ohm
Figure 3: Equivalent matching circuit (EMC).
Two such matching networks are connected in
parallel and must supply matching with first section of
polarization splitter. We can consider input impedance
of polarization splitter the same as for an empty
waveguide. To achieve matching we can adjust the
input impedance to realize matching in the whole
polarizer (Fig. 4).
2 The Polarizer Cascade Components
To efficiently convert a circularly polarized
wave from aperture, the two orthogonal field
components Ex and Ey, must have equal magnitude and
900 degree adjusted phase shift. The first section to
realize polarization splitter it is used plate with
specific shape [1] Fig. 1. Frequency scaling is used to
explore given pate shape. The secondary section as
linear polarization component output is realized as two
impedance transformers coupled in parallel. The input
impedance of coaxial output is a 50 ohms. We have
used two stages of ¼ wavelength transformer [2].
1
EMC1
Polarization
splitter
EMC2
2
3
Figure 4: Equivalent matching circuit for the polarizer.
Input impedance of polarization splitter is not
known exactly but we can use the crossection
dimensions of multimodal horn [3].
For estimation of the matching in polarizer we
have used calculation of scattering matrix combined
calculation [4]. Every element in SHF circuitry can be
represented with equivalent library element of
scattering matrix [5] represented in Appendix 1:
divider, waveguide with definite length and impedance
step. Scattering matrix of polarizer has been calculated
using inner connection matrix [6].
Two multiports with scattering matrixes S1 with
n inputs and S2 with m inputs can be connected using p
inputs. After joining p inputs new matrix SJ will
contain n-p+(m-p)=n+m-2p inputs. Corresponding
circuitry is shown in Fig. 5, where Uinc is incidence
wave and Urefl is reflected wave for inputs M, P and N
correspondingly.
Uinc
UABB
A
A
1
2
3
.
.
.
M-1
M
1
2
3
.
.
.
P-1
P
1
2
3
.
.
.
P-1
P
B
UreflA
UincC
1
2
3
.
.
.
N-1
N
UBAB
SB 
BB
BB
BC
CB
CC
equal. We introduce abbreviation
U
AB
B
AB
B
BA
BA
A
inc
A
BB
B
AB
B
AB
B
BB
B
BA
AC
C
inc
C
refl
CB
B
BA
CC
C
inc
U   S   U   S   U ,
U   S   U   S   U ,
U   S   U   S   U  .
From these equations we must exclude wave voltages
B
B
and UAB . Remaining two equations will
UAB
describe relations on incidence and reflected waves
for remaining M+N inputs and calculate coefficients
for joint scattering matrix SJ. Combining expressions
we can express relations for block matrixes:
S
S
S
S
  S    S   S   S  ,
   S   S 
   S   S 
  S    S   S   S 
where -  S    I   S    S 
J
CC
  S
  S
  S
  S
AA
1
AB
BA
A
BB
BC
1
AB
BC
1
CB
CC
B
BB
BA
1
CB
B
BB
A
BB
1
and [ I ] is a unity matrix. Using these expressions for
scattering matrixes it is evaluated software for
scattering matrix parameters calculation in the chosen
frequency band.
Using MAKETS [5] software there are
calculated matching multiport parameters in 6-cm
frequency band. Combining waveguide parameters we
can optimize the solution. Calculated scattering
matrix coefficients are represented in Fig. 6 and 7.
0.8
0.6
Matrix ||SA|| is quadratic with range M+P, blocks
[SAA] and [SBB] are quadratic with range M and P
correspondingly. Nondiagonal blocks are rectangular
with size MP and PM. For inputs A and C assume
incidence waves coming in multiport A and C and
reflecting waves coming out from these multiports.
For joining inputs B we can’t detect difference
between incidence and reflected waves – they are
B
AB for
A
inc
1
S  S  and
S  S 
S  S  .
S  S 
BA
AA
J
CA
To describe the joining effect for scattering
matrixes at first we need to renumber the inputs of
scattering matrixes. For the first matrix A renumbering
is started from M free inputs, then continue with P
inputs. For C multiport first we renumber P used
joining inputs and then N free inputs. Such
renumbering will give us S1 and S2 matrixes containing
four blocks.
AB
A
refl
J
AC
UreflC
AA
U   S   U   S   U ,
J
AA
C
Figure 5. Joining of two multiports.
A
UBA
SA 
for voltage propagating to multiport B. Using these
abbreviations we can write expressions for matrix A
and B input voltages.
0.4
0.2
0
4600
4800
5000
5200
running
wave voltage propagating to multiport A and
B
UAB
Figure 6. Scattering matrix S11 and S1,2 magnitudes
200
100
0
-100
-200
4600
4800
5000
5200
Figure 7. Scattering matrix S11 and S1,2 phase
To simulate polarizer scattering coeficients we
can join both stages in waveguide with coaxial inputs.
Waveguide size is 3737 mm2, polarizer splitter has
crossection twice less and characteristic impedance
steps are 0.6 and 3 (shown in Fig. 8.)
Figure 10. Polarizer transmission coeficients.
Results for 4.9 GHz 6% bandwidth are
presented in Fig. 9-10.
These patterns reflect that the design has
coincided with its intended objectives:
1. The E- and H-plane transmission coefficients S12
and S13 are closely equal;
2. The reflection coefficients S11, S22 and S33 are
tightly affected by step changes;
3. The given simulation method will allow
reproduce necessary polarizer features in the
other radio astronomy bands.
5 Conclusions
Figure 8. Polarizer simulation design.
Simulated results are shown in Fig. 8 and 9.
Numerical solution for principal mode of polarizer is
calculated by means of simulation software CST
Microwave Studio [6]. CST Microwave Studio is fully
featured software for electromagnetic analysis and
design in the high frequency range. In case of
successful simulation it is possible to evaluate results
of polarizer for other radio astronomy bands used in
Ventspils radio astronomy center.
This technique yields slightly different E- and H-plane
transmission coefficients and low input reflection. The
polarizer simple boundary, free of additional
inhomogenities, provides low standing wave ratio
coefficient, minimum dissipation loss and economical
fabrication. Used software simulation tool will allow
developing the polarizer for other bands useful for
radio astronomy VLBI interferometric measurements
in Ventspils international radio astronomy center.
6 Acknowledgements
The report was supported by the grant N 01.0868 of
the Latvian Council of Science.
7 References
[1] Keller R. Analog Filtering. RF Mitigation
Workshop. Bonn. 02 – 04 April. 2001. Private
communication.
Figure 9. Polarizer input reflection coeficients.
[2] Фелдштейн A. Явич П. Смирнов B. Справочник по элементам волноводной техники М.,
Сов радио, 1967, 652 с.
[3] Polarization Parameters Improvement for Feed
Horn G.Balodis and O. Ceriņš This conference
material
1
2
W0
[4] Gupta K., Garg R., Chadha R. Computer Aided
Design of Microwave Circuits. Artech House,
1981, 430 p.
[6] Устроства СВЧ. Под ред Д М Сазонова М
Высшая школа 1981 256 с

1 
 p3   shl 
p3 
S  A

2


[7] CST Microwave Studio – Getting Started.
http://www.cst.de.
Appendix
where
1
2
W1
W0
l
[5] Balodis G. Sazarotu ķēžu aprēķināšana Rīga
RTU, 1992, 32 lpp.
A.
Scattering matrix for impedance step from impedance
W1 to W2 would be calculated with parameter: step
p1=W1/W2 :
W1
A






1
 p3   shl 
p3 


2
1

1 
2chl    p3  shl 
p3 

C.
Scattering matrix for divider with impedances W1, W2
and W3 and parameters would be calculated with
parameters: step 1 p1=W1/W2 , step2 p2=W1/W3 and
p=0,5(1+p1+p2) :
W2
W2
2
1 W1
S
1  p1  1 2 p1 


1 p1  2 p1 1 p1
B.
Scattering matrix for waveguide for frequency f and
normalization frequency fN with definite characteristic
impedance W1, length l[m] and losses  [dB/m] would
be calculated with length parameter p1=2pfNl/VPH,
losses p2=l, characteristic impedance of waveguide
p3=W1/W0 and propagation coefficient l=p2+jp1f/fN:
W3
1 p
p1
1
S   p1 p1  p
p
 p
p1 p2
 2
i
3
p2 

p1 p2 
p2  p
Department of Radioelectronics, Riga Technical
university, 12 Azenes street, LV-1048, Rīga, LATVIA, Email: balodis@rsf.rtu.lv.