CC BY
5
Y^K 621.396
Equivalent Microwave Circuit Technique for Waveguide Iris Polarizers Development
Bulashenko A. V., Piltyay S. I.
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" E-mail: an_ bulashcnko(<H.ua. crosspol-ar&ukr.ncl.
The increase of information volumes, which are transmitted in modern satellite telecommunication systems, requires the development of new signal processing technologies, microwave devices, antenna systems and methods of their analysis. In particular, polarization-adaptive antennas are widely used for this purpose. Such antennas provide the possibility to transmit and receive radio signals with polarization of any type. Polarization processing devices of antenna systems must provide low levels of voltage standing wave ratio of waves with horizontal and vertical linear polarizations and high crosspolar discrimination simultaneously. Therefore, there is the need to improve designs and methods of analysis of modern polarization processing devices. Polarizers based on a square waveguides with irises are widely used due to the simplicity of their design and manufacturing by milling technology. The article considers a new mathematical model of waveguide polarizers with reactive irises. For the example of model application we have simulated and optimized a polarizer based on a square waveguide with four irises. A mathematical model of this waveguide polarizer was developed based on the description of microwave devices and their elements by wave scattering and transmission matrices. The general scattering matrix of the polarizer has been obtained analytically. The main electromagnetic characteristics of the polarizer were determined based on the elements of this matrix. As a result, we have analyzed main characteristics of the model, including differential phase shift, voltage standing wave ratio for vertical and horizontal polarizations, axial ratio and crosspolar discrimination. The optimization of the characteristics of a polarizer has been performed using the developed mathematical model and a software based on the finite integration technique. The optimal characteristics and geometrical sizes of the structure are in good agreement, which proves the correctness of the developed mathematical model of square waveguide iris polarizers.
Key words: polarizer: waveguide polarizer: iris polarizer: circular polarization: scattering matrix: transmission matrix: differential phase shift: voltage standing wave ratio: axial ratio: crosspolar discrimination
DOI: 10.20535/RADAP. 2020.83.17-28
Introduction
Nowadays a progressive area of modern telecommunication technologies is adaptive antenna systems with signal polarization processing. Application of polarization processing increases the efficiency of telecommunication and radar systems for various purposes. The key elements of such systems are devices for transformation of polarization type and separation of signals with orthogonal polarizations to different channels.
A large number of scientific papers are dedicated to numerical simulation and analysis of microwave devices of signal polarization processing fl 7]. For development of new waveguide polarizers and optimization of their characteristics it is necessary to calculate them with high accuracy. Therefore, it is important engineering problem to create new analytical techniques and mathematical models for simulation of waveguide polarizers and improvement of their
performance. In this research we develop a simple mathematical method for the analysis of polarizers based on reactive elements in a waveguide. The obtained model is effectively applied for the optimization of new waveguide iris polarizer for C-band 3.4 4.2 GHz.
1 Analysis of modern researches on waveguide polarizers
Modern microwave devices for signal polarization processing are created based on the waveguides with posts, ridged structures, corrugations and irises. The application of ridges in the design allows to create nltrawideband waveguide polarizers [8, 9]. Modern investigations of ridged structures and structures with irises are carried out using various mathematical methods. Among such methods there are mode matching technique [10], transverse field-matching technique fll 14], magnetic field integral equation technique
[15.16]. arid integral equations technique [17 20] with the account of singularity of the fieldsat the conducting edges, which excludes the relativity of the convergence of series in the transverse field matching technique [21].
One of the main disadvantages of all known numerical techniques based on rigorous mathematical models of polarizers is their great complexity. Therefore, in our research the main emphasis of the investigation is on the use of simpler methods of creating mathematical models based on matrix methods. Such approaches require the application of scattering and transmission wave matrices to describe the characteristics of the waveguide iris polarizer.
The best wideband characteristics are reached in polarizers based on waveguides with irises [1. 22]. A significant number of researches on matrix methods is used to calculate phase shifters based on reactive elements in the waveguide [22 24] and various microwave filters. In [25] the procedure of designing microwave filters is given, which is based on the representation of the filter in the form of a model of a circuit with distributed parameters. This method takes into account multimode interaction and does not use the numerical optimization process. The article [26] is devoted to the general approach to mathematical methods of filter calculation using the method of analytical gradient optimization. Nevertheless, a large number of scientific publications on waveguide polarizers contain only the results of simulations, the process of which takes a large amount of time [27 45].
The article [28] presents a rigorous theoretical and experimental comparison of two kinds of rectangular-waveguide polarisers for use in Ka-band gyro-travelling wave amplifier. It is shown by the author how overall field distribution inside of waveguide polariser structures having different kinds of corrugation affects the resulting performances.
In [29] the authors developed and manufactured a new compact septum polarizer operating in the frequency range from 18.5 GHz to 21.5 GHz. The polarizer has an integrated transition from a square to a narrower circular waveguide. The simulated and measured parameters provide an axial ratio less than 0.6 dB. The polarization discrimination is less than 25 dB in the frequency range 18.5 21.5 GHz.
The article [32] introduces parallel-plate ridge gap waveguide consisting of a metal ridge in a metamaterial surface, which is covered by a metallic plate at a small height above it. The metamaterial surface is designed to provide a frequency band where normal global parallel-plate modes are cutoff, thereby allowing a confined gap wave to propagate along the ridge.
In article [33.34] the authors developed and optimized a new broadband coaxial polarizer for the operating frequency band from 3.4 GHz to 4.8 GHz. In the whole operating frequency band the polarizer [33] provides a differential phase shift of 90° ± 2.5° and the reflection coefficient less than — 33 dB. The application of
a coaxial waveguide in the structure of a polarizer-allows to use it in dual-band antenna feed systems with orthogonal circular polarizations. The antenna feed system includes an iris polarizer for reflector antennas of terrestrial stations with double circular polarizations operating in the extended C-band 3.4 4.8 GHz [34]. The VSWR of the polarizer is 1.14. its crosspolar isolation exceeds 30 dB. The polarizer of the system provides a differential phase shift of 90° ± 2.8°.
In [35] the authors developed a broadband compact three-dimensional printed polarizer for the operating frequency band 28 34 GHz. The design consists of a pair of radially opposite grooves inside a circular-waveguide and excited using a coaxial probe. This makes the developed design simple and highly compact as compared to the other conventional circular polarizers. The polarizer provides an axial ratio less than 3.0 dB.
The article [36] investigates septum polarizers performance for various fractional bandwidths. In [36] the authors developed and optimized Q- and K-band waveguide polarizers with longitudinal septums of constant thicknesses. The optimal designs and their electromagnetic performance were analyzed for fractional bandwidths from 5% to 20% using finite elements method in the frequency domain.
The authors of [37] developed a broadband septum polarizer with relative bandwidth of 37.8%. This wide operating frequency band is provided by the application of an equilateral triangular waveguide. This waveguide ensures the maximum possible frequency-range between the fundamental and first higher modes. Developed polarizer provides an axial ratio less than 1.0 dB.
In the article [38] a new cylindrical horn antenna with left circular polarization for the W-band from 79.5 GHz to 88 GHz was suggested. The developed antenna's feature is the application of an inbuilt polarizer structure and a single side-fed linear polarized input to offer symmetric LHCP radiation pattern. The
antenna provides axial ratio less than 1.2 dB and the
—
The wideband coaxial OMT for the extended operating C-band 3.4 5.4 GHz has been developed in [30.39]. It provides the coherent reception of orthogonal linearly polarized electromagnetic waves in the whole
operation frequency band. The reflection coefficient of —
In [40. 41] the authors suggested a new waveguide polarizer for operating Ivu-band 10.7 12.8 GHz. The electromagnetic characteristics of the developed waveguide polarizer were simulated and optimized using finite integration technique. The polarizer-provides VSWR less than 1.24. The axial ratio is less than 0.53 dB. The XPD of the polarizer is higher than 30.3 dB.
The study [42] presented a horn antenna based on a circular waveguide with circular polarization in the
range from 54 GHz to 60 GHz. An integral part of the antenna is a polarizer with mono-grooves, which are located at an angle of 45° relative to both input ports. This design creates right and left hand circular polarizations. The system provides an axial ratio of less than 2.2 dB. Polarization isolation is higher than 25 dB. The isolation between the ports is 15 dB
The papers [43. 44] present the results of development of a X-band compact stepped-thickness septum polarizer in the operating frequency band 7.70 8.50 GHz for a quasi-monopulse feed of a dual-polarized ground station antenna system. VSWR of the designed polarizer is less than 1.4. XPD of the polarizer is higher than 30 dB. The measured differential phase shift varies from 83° to 100°.
The new method to design a compact tunable polarization plane rotator in a circular waveguide for X-band was demonstrated by numerical simulations and an experiment in [45]. Being relatively narrowband, the polarizer operates on the eigenosci-llations excited inside a pair of conjugated planarchiral irises, which provide different polarization planes on both sides of the unit. Longitudinal dimensions of such a rotator can be less than A0/30. In [ ] it was demonstrated that in a two-layer symmetric waveguide the operating frequency band of the polarizer can be expanded.
In [47] the authors proposed a new waveguide polarizer for operating Ivu-band 10.7 12.8 GHz. The electromagnetic characteristics of the waveguide polarizer were simulated and optimized using finite integration technique. The polarizer provides VSWR less than 1.13. The axial ratio is less than 0.4dB. XPD of the developed polarizer is higher than 33 dB. The differential phase shift varies from 87.4° to 92.6°.
Research [48] presents a compact notched-septum polarizer in the form of an integral substrate. The slots close to the notches are used to increase the polarization frequency. Axial ratio is less than 3dB in 4.5/
In paper [49] the authors suggested a new waveguide iris polarizer for operating X-band 7.4 8.5 GHz. The electromagnetic characteristics of the waveguide polarizer were simulated and optimized using finite integration technique. The polarizer provides VSWR less than 2.8. The axial ratio is less than 1.6 dB. the XPD is higher than 21.7 dB. The differential phase shift
82° 98°
In [50] the mathematical model of a waveguide polarizer with irises was created, taking into account the thickness of the irises. A new analytical model of a polarizer has been developed using the equivalent substitution circuits. The main electromagnetic characteristics of the model were determined through the elements of the scattering matrix of a polarizer. The characteristics of a waveguide iris polarizer were optimized in the Ivu-band
The authors of an article [51] proposed a compact waveguide polarization rotator capable to rotate the polarization plane by an arbitrary angle. Its operational principle is based on a strong electromagnetic coupling between two conjugated quadruple-slot planar-chiral irises in a square waveguide by the below cutoff modes.
A compact integrated silicon and graphene polarizers are proposed in [52.53]. The developed polarizer [52] has low insertion loss for TM mode of 0.7 dB and high attenuation for TE mode of 41.25 dB. The configurable waveguide polarizer [53] has highest exting extinction ratio for TM mode of 46 dB and highest extinction ratio for TE mode of 34.9 dB. The variation in the polarization extinction ratio is less than 3.0 dB.
2 Formulation of the research problems
The purpose of current research is to develop a new simple analytical technique for the calculation of all electromagnetic characteristics of square waveguide iris polarizers. The results obtained by the analytical technique must be in good agreement with the ones obtained by other numerical techniques. Another problem, which is solved in the article, is the optimization of the characteristics of a square waveguide polarizer with 4 irises for the operation in C-band 3.4 4.2 GHz.
A waveguide polarizer in the receiving antenna system generates signals with orthogonal linear polarizations at the output. To simplify the analysis in this article we will consider the characteristics of the polarizer in the transmitting antenna. In this case the signals with orthogonal circular polarizations are generated at the output of the polarizer. The development and optimization of the waveguide polarizer is carried out in order to ensure effective polarization and matching
characteristics. In particular, the differential phase shift 90° ± 4°
polarizations must be less than 1.4. The axial ratio is required to be less than 0.6 dB. The XPD higher than 30 dB is required in the developed polarizer.
3 Theoretical analysis of a square waveguide polarizer with four
lriSGS
To eliminate the additional phase distortions of the signals with vertical and horizontal polarizations in the waveguide outside the irises region we choose a waveguide with square cross-section.
The developed model uses thin irises in contrast to the model [50]. which uses thick irises. In addition. various analytical calculation methods are used to
determine the reactive conductivities of the irises and various equivalent substitution circuits.
The inner structure of the polarizer based on a square waveguide with four irises and the designation of the dimensions of the structure is shown in Fig. 1. In Fig. 1 we see that the two outer irises have the same height hi and the two middle irises also have the same height h2, and the height h2 is greater than the height hi to better matching of the structure. The distance between the inner irises is l2, and the distance between the outer and inner irises is l\.
Fig. 2. Equivalent circuit of a waveguide with four irises
Each two-port circuit is described by a wave matrix of transmission [55]
[Ti] = [Tr] = [Ts] = [T5] = P2] = [Ts] =
[n] =
Tii Ti2
T2i T22_
T' ii T 'i2
T' 2i T' 22_
-eje1 0 ■
0 e-je1
0 -
0 e-j62
(1)
e =
2w ■ I
77
The wavelength in the waveguide is described by the expression
A„
An
^77
(3)
where Ao = c/f is the wavelength in free space expressed in millimeters, Xc = 2a is cutoff wavelength expressed in millimeters for the TEi0 mode in the waveguide, a is the length of the wall of a square waveguide expressed in millimeters.
As a result, the transmission matrix is determined
fe ]
Pi] ■ [T2] ■ [T3] ■ [T4] ■ [T5] ■ [Ts] ■ [Tr]
T
E ii TE 12
LTE 2i
T
22
(4)
Fig. 1. Inner structure of a waveguide polarizer with four irises
As a result, a mathematical model was developed for the considered waveguide polarizer with four irises by analyzing microwave circuits based on wave matrices of scattering and transmission [54], which contains inductive and capacitive reactive elements.
In Fig. 2 shows a general view of the circuit of a waveguide with four reactive elements based on a single-wave approximation.
The relationship between transmission and scattering matrices is as follows
fe ] =
E ii ^E12
L^E 2i
22
1
T
T
2i
1
\T |
-T
i2
ii
of a matrix [T^]
(5)
from
where |T | is determinant expression (2).
As a result, we have elements of the scattering matrix
1
E21
T
T
E"
E"
E21
T
E"
(6)
To compensate the total reflection from all discontinuities it is necessary to nse reactive elements with the same conductivities (irises with equal windows) pairwise. Besides, the distance between the irises must be approximately equal to quarter-wavelength in the waveguide at the central frequency of the operating band.
For a waveform model with inductive (Fig. 3) and capacitive (Fig. 4) irises, the elements of the scattering matrix will be as follows
where 02 are electric lengths of the transmission
line expressed in radians.
The electrical length is determined
SiiL =
Siic =
jbL 2 - jbL' —jbc 2+ jbc'
S2iL =
S2iC =
2
2 — jbL 2
2 + ]h¡ ■
(7)
(2)
where I is the length between irises expressed in millimeters; Xg is the guide wavelength expressed in millimeters.
Fig. 3. Equivalent circuit of a waveguide with four inductive irises
2
Fig. 4. Equivalent circuit of a waveguide with four capacitive irises
We use the formulas of reactive conductivities of irises in a rectangular waveguide [56]. taking into account the influence of higher types of waves
bL = -
2-K
a ■ ß
ctg
( tt ■ d \
1 +
a ■ 7i — 3tÏ
4-K
( -k ■ d \
sin I—)
be =
4ßb
ln cos ec
+
2t\
a ■ 72
/ tt ■ d \
- l) ■ (cos (£))"
where
7i =
= -k2
a !
0 ;
/(W
fi = Vk0 —
72 = \/( fj — ß2-
ko = = 2tT/ A° c '
d = a — 2 • h.
The differential phase shift at the output of the polarizer is determined as follows
A(p = -^c = arg(S'E21 l) - arg(S'^21c). (11)
VSWR of the polarizer is determined by the following formula
VSWR-
1+ |SE ii I
E11I
(12)
The axial ratio can be calculated using the modules of expressions (6) [57]:
r (dB) =
A2 + B2 + v^4 + B4 + 2A2B2 cos(2A<^)
10 lg
; (8)
A2 + B2 — \JA4 + B4 + 2A2B2 cos(2A<^) '
(13)
where A = |^2iB = |^2ic|-
XPD of the polarizer is expressed in dB using the following formula [58]
XPD (dB) = 20 lg
(9)
/10°'°5r + 1 \ Vio°'05r — 1 )
(14)
where a mid b are the lengths of the wide and narrow walls of the rectangular waveguide expressed
expressed in millimeters; k0 is wave number in vacuum; P is the propagation constant of the fundamental mode
H10 in a rectangular waveguide. In the case of a square
=
The size of the irises window (Fig. 5) is determined by the value of the iris height h
Note that the alteration of the amplitudes of the waves at the output of the polarizer is influenced by VSWR of both polarizations. The axial ratio and corresponding XPD are determined simultaneously by the amplitudes of the waves at the polarizer's output and by the differential phase shift.
Depending on the ratio of the amplitudes at the output and the differential phase shift of the polarizer. it is possible to obtain a wave with any polarization type. In the case of a perfect polarizer the VSWR is equal to 1 for both polarizations, and the differential phase shift is 90°. Then the polarizer in the receiving antenna will transform input waves with orthogonal circular polarizations into output waves with orthogonal linear polarizations and vice versa in the transmitting antenna system.
(io) 4 Results of analysis
the theoretical
Fig. 5. Inductive and capacitive irises in a rectangular waveguide
Differential phase shift, axial ratio, crosspolar discrimination (XPD). voltage standing wave ratio (VSWR) are the main electromagnetic characteristics of the polarizer.
Consider the results of the calculation of the mathematical model of the polarizer in the case of thin irises in the C-band 3.4 4.2 GHz. In this frequency range the wall length of the single-mode square waveguide will vary approximately from 44 mm to 71 mm. The value of the wavelength in the waveguide at the center frequency of the band 3.8 GHz is Ao =78.9 mm. According to the method suggested in [59] we choose the size of the wall of the square waveguide of the polarizer and the distance between the irises, which is determined by the ratio I = 0.25 A0. Next, to provide the required differential phase shift we change
h1 h2
2
2
■K
the structure is obtained by alteration of the distances between the irises.
We plot the enrve frequency dependences of electromagnetic characteristics of the investigated polarizer on the basis of a square waveguide with four reactive irises.
In Fig. 6. Fig. 7, Fig. 8. Fig. 9 shows the dependences of the differential phase shift. VSWR, axial ratio. XPD on the frequency, respectively.
Fig. 6 shows that the differential phase shift takes 90° at 3.5 GHz and 4.15 GHz. The maximum deviation of the differential phase shift from 90° is 2.8° at 3.8 GHz.
0.6 0 5 0.4 0.3 0 2 0.1 0 0
3.4 3.5 3,6 3.7 3.8 3.9 4.0 4.1 4.2 Frequency, GHz
Fig. 8. Dependence of the axial ratio on frequency
Fig. 6. Dependence of differential phase shift on frequency-
Fig. 7 shows that the maximum valne of VSWR for horizontal polarization is 1.38 and for vertical polarization is 1.42 at the minimum and maximum frequencies, respectively.
Fig. 7. VSWR vs. frequency for the optimized polarizer solid line horizontal polarization: dotted line vertical polarization
Fig. 8 and Fig. 9 show that the maximum value of the axial ratio is 0.51 dB, the maximum valne of the XPD is -30.8 dB at a frequency of 3.8 GHz.
Fig. 9. Dependence of the XPD on frequency
Therefore, in the operating range of 3.4 4.2 GHz. the calculated polarizer based on a square waveguide with four irises provides VSWR for both polarizations less than 1.42. Its differential phase shift lies within the angles of 90° ±2.8°. The axial ratio is less than 0.50dB, and XPD is higher than 30.8 dB.
5 Results of simulation by numerical method
The section contains the results of optimization of the design of a polarizer based on a square waveguide with four irises by finite integration technique in the C-band 3.4 4.2 GHz. The created mathematical model was verified by simulation of electromagnetic characteristics of a polarizer using CST Microwave Studio software. The 3-D model of a waveguide iris polarizer, which was developed and simulated in the software, is demonstrated in Fig. 10.
Fig. 10. Dependence of differential phase shift on frequency
In Fig. 11 presents the dependence of the differential phase shift on the frequency for the optimized polarizer.
t
О
У-У 93 92
J1 90 RQ
ОУ RR
oo 87 86
3.4 3.5
3.6
3.7 3.8 3.9 Frequency, GHz
4.0
4.1 4.2
Fig. 12. VSWR vs. frequency for the optimized polarizer solid line horizontal polarization: dotted line vertical polarization
In Fig. 12 it is seen that the maximum value of VSWR for both polarizations is 1.3C. It is observed at the frequency band edges 3.4 and 4.2 GHz. The minimum value of VSWR of horizontal polarization is 1.0 ctt 3. frequency of 3.73 GHz. and for vertical polarization it is 1.11 clt 3. frequency of 3.4 GHz. As one can see in Fig. 12. the increase of frequency results in the decrease of VSWR of the horizontal polarization and the increase of VSWR of the vertical polarization. Using the theory of microwave circuits, this feature can be explained as follows. For the wave with horizontal polarization the irises are inductive and for the wave with vertical polarization they are capacitive. In the first case, the equivalent circuit contains inductances that are connected in parallel. They short the line at low frequencies. In the second case the equivalent circuit contains parallel capacities that short the line at high frequencies.
Fig. 13 contains the dependence of the axial ratio on the frequency for the optimized polarizer.
Fig. 11. Dependence of differential phase shift on frequency
In Fig. 11 we see that the maximum deviation of the differential phase shift from 90° is 3.4° at 3.75 GHz and takes the value of 90° at frequencies 3.45 GHz and 4.0C GHz. respectively.
In Fig. 12 shows the frequency dependence of VSWR for the optimized polarizer.
Fig. 13. Axial ratio vs. frequency for the polarizer
Fig. 13 demonstrates that the coefficient of axial ratio in the frequency range from 3.4 GHz to 4.2 GHz does not exceed 0.53 dB. The maximum value of the axial ratio is reached at frequencies of 3.75 GHz and 4.2 GHz. and the minimum value corresponding to the value of 0.085 dB is reached at frequencies of 3.41 GHz and 4.052 GHz.
Fig. 14 contains the dependence of XPD on the frequency for the optimized polarizer.
Frequency,
Fig. 14. XPD vs. frequency for the polarizer
Table 1 Sizes of C-barid waveguide iris polarizer
Size name Development method CST Microwave Studio
1 Size of square waveguide walls, mm a = 64,2 a = 64,2
2 Height of the lowest irises, mm hl = 7,0 h1 = 6,9
3 Height of the medium irises, mm h2 = 11,0 h2 = 11,45
4 Gap between the outer irises, mm L1 = 22,4 L1 = 22,3
5 Gap between the inner irises, mm L2 = 24,0 L2 = 24,2
6 Thickness of all irises, mm w = 1,0 w = 1,0
Table 2 Characteristics of the optimal C-barid waveguide polarizer with irises
Characteristic Development method CST Microwave Studio
1 Differential phase shift 90° ± 2, 8° 90° ± 3,4°
2 VSWR 1,42 1,36
3 Axial ratio 0,50 dB 0,53 dB
4 XPD 30,8 dB 30,0 dB
In Fig. 14 we see that the XPD in the frequency range from 3.4 GHz to 4.2 GHz does not exceed 30 dB, which corresponds to the maximum value at frequencies of 3.75 GHz and 4.2 GHz. The minimum valne corresponding to the valne of 53 dB is reached at frequencies of 3.41 GHz and 4.052 GHz. respectively.
Therefore, in the operating range of 3.4 4.2 GHz. the optimized polarizer based on a square waveguide with four irises provides VSWR for both polarizations less than 1.3C. Its differential phase shift lies within the angles of 90° ±3.4°. The axial ratio is less than 0.53 dB, and XPD is higher than 30 dB.
The optimized polarizer sizes are summarized in Table 1 using equivalent circuit model and the numerical method in the C-band 3.4 4.2 GHz.
Table 2 compares the characteristics of the polarizer for the equivalent circuit model and the numerical method.
The results shown in the tables and obtained by-two methods are in good agreement. Nevertheless, one can observe in the presented tables that there are small differences in the sizes and characteristics of the polarizer. They are caused by the fact that the developed mathematical model does not take into account the thickness of the irises and the higher-order modes in the structure of a polarizer.
Conclusions
In this research we have developed a rigorous mathematical model of a square waveguide iris polarizer, which allows to calculate its electromagnetic characteristics for the given geometrical sizes of the design. The model allows to vary the heights of the irises and the distances between them in order to provide optimal performance of the polarizer. The irises are simulated as reactive discontinuities, which are indncti-vities or capacitances depending on the polarization
type. Developed model allows to carry out the analysis of influence of the design parameters on the differential phase shift, VSWR for horizontal and vertical polarizations, axial ratio and XPD. Using the mathematical
model we have simultaneously provided the required
90°
of the polarizer in the operating C-band 3.4 4.2 GHz.
For the first time a simple mathematical model of waveguide polarizers with reactive irises based on a general wave scattering matrix was created. Developed model allows to calculate the electromagnetic characteristics much faster than the finite differences and finite elements methods. The novelty of the created model is the combination of matrix methods for the calculation of microwave circuits performance with accurate variational or mode matching techniques, which allow to obtain equivalent capacitances and inductances of discontinuities in waveguides.
The created mathematical model was verified by-comparison with the results of simulation in specialized software based on the finite integration technique. On the whole, very good matching of the results is observed. The deviations of obtained by the mathematical model characteristics from the ones obtained by numerical simulations are caused by the influence of higher order modes and of the thickness of real irises. Therefore, developed mathematical model can be suggested for the analysis and development of waveguide polarizers with different numbers of irises.
The developed in research square waveguide polarizer with 4 irises has a compact design and excellent polarization and matching characteristics. In the operating C-band 3.4 4.2 GHz it provides a differential phase shift 90° ±2.8°. The maximal level of VSWR 1.42 for both polarizations. XPD is higher than 30.8 dB. The corresponding axial ratio is less than 0.50 dB.
Future researches will be dedicated to the improvement of developed equivalent microwave circuit model in order to provide higher accuracy
of electromagnetic characteristics calculation. Besides. the analysis and comparison of the designs and performance of waveguide polarizers with larger number of irises are actual problems for the development of modern satellite telecommunication systems.
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Метод екв!валентних мкрохвильових кш для розробки хвилеводних поляри-затор!в 13 д!афрагмами
Булашеико А. В., Шльтяй С. I.
Збглынеппя обсяпв ¡пформацп, що передаються в сучаспих супутшжових телекомушкациших системах, вимагае розробки пових техпологш обробки сигпатв. мшрохвильових пристрош. аптешшх систем та метод!в i'x апал1зу. Зокрема, для ц!е! мети широко використо-вуються иоляризаццшо-адаитивш аптепи. Так! аптепи забезпечують можлшмсть передач! та прпйому радюси-гпал!в з поляризац1ею будь-якого типу. Прилади для обробки поляризацп в аптешшх системах повипш за-безпечувати пизький р!вепь коефкцепта стшпих хвиль за папругою для хвиль горизонтально! та вертикально! лшшпих поляризацш та високий р!вепь кросполяриза-цшпо! розв'язки одпочаспо. Тому випикае пеобх!дшсть вдоскопалеппя копструкцш та метод!в апал!зу сучаспих пристро!в поляризацишо! обробки. Поляризатори па основ! квадраташх хвилевод!в з д!афрагмами широко використовуються завдяки простои !х копструкцп та виготовлеппя за допомогою фрезерпо! технолог!!. У статт! розглядаеться нова математичпа модель хвиле-вод1шх поляризатор1в з реактивпими д!афрагмами. Для прикладу застосуваш1я модел! ми моделювали та опти-м!зували поляризатор па основ! квадратного хвилеводу
з чотирма д!афрагмами. Математична модель цього хвилеводпого поляризатора була розроблепа па оспо-в! опису мшрохвильових пристро!в та !х елемептав за допомогою матриць розсповаппя та передач!. Загальпа матриця розсповаппя поляризатора отримапа апал!ти-чпо. Осповш електромагштш характеристики поляризатора визпачалися па основ! елемептв ц!е! матриц!. У результат! ми проапал1зували осповш характеристики модель включаючи диферепцпший фазовий зсув. кое-фццепт стшпо! хвил! за папругою для вертикально! та горизонтально! поляризацп, коефщ!епт елштичпост та кросполярнзацпшу розв'язку. Оптим1зац1я характеристик поляризатора проведена за допомогою розроблепо! математпчпо! модел! та програмпого забезпечеппя па основ! методу скшчепих елемептав. Оптимальш характеристики та геометричш розм!ри структури добре узго-джуються, що шдтверджуе правильшсть розроблепо! математичпо! модел! поляризатор!в па основ! квадратного хвилеводу 1з д!афрагмами.
Ключоег слова: поляризатор: хвилев1дпий поляризатор: поляризатор з д!афрагмами: матриця розсповаппя: матриця передач!: диферепцпший фазовий зсув: коефь ц!епт стайно! хвил! за папругою: коефкцепт елштичпост: кросполяризацшпа розв'язка
Метод эквивалентных микроволновых схем для разработки волноводных поляризаторов с диафрагмами
Булашеико А. В., Пильтяй С. И.
Увеличение объемов информации, передаваемых в современных спутниковых телекоммуникационных системах. требует разработки новых технологий обработки сигналов, микроволновых устройств, аптеппых систем и методов их анализа. В частности, для этой цели широко используются поляризациошю-адаптивпые аптеппы. Такие аптеппы обеспечивают возможность передачи и приема радиосигналов с поляризацией любого типа. Приборы для обработки поляризации в аптеппых системах должны обеспечивать низкий уровень коэффициента стоячих волн по напряжению для волн горизонтальной и вертикальной линейных поляризаций и высокий уровень кроссполяризациошгой развязки одновременно. Поэтому возникает необходимость совершенствования конструкций и методов анализа современных устройств поляризационной обработки.
Поляризаторы па основе квадратных волноводов с диафрагмами широко используются благодаря простоте их конструкции и изготовления с помощью фрезерной технологии. В статье рассматривается новая математическая модель волповодпых поляризаторов с реактивными диафрагмами. В качестве примера применения модели мы моделировали и оптимизировали поляризатор па основе квадратного волновода с четырьмя диафрагмами. Математическая модель этого волповодпого поляризатора была разработана па основе описания микроволновых устройств и их элементов с помощью матриц рассеяния и передачи. Общая матрица рассеяния поляризатора получена аналитически. Основные электромагнитные характеристики поляризатора определялись па основе элементов этой матрицы.
В результате мы проанализировали основные характеристики модели, включая дифференциальный фазовый сдвиг, коэффициент стоячей волны по напряжению для вертикальной и горизонтальной поляризации, коэффициент эллиптичности и кроссполяризационную развязку. Оптимизация характеристик поляризатора проведена с помощью разработанной математической модели и программного обеспечения на основе метода конечных элементов. Оптимальные характеристики и геометрические размеры структуры хорошо согласуются, что
подтверждает правильность разработанной математической модели поляризаторов на основе квадратного волновода с диафрагмами.
Ключевые слова: поляризатор; волноводный поляризатор; поляризатор с диафрагмами; матрица рассеивания; матрица передачи; коэффициент стоячей волны по напряжению; дифференциальный фазовый сдвиг; коэффициент эллиптичности; кроссполяризационная развязка
