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Antenna Array


Antenna array

Complex directional antenna consists of separate near-omnidirectional antennas (radiating elements) positioned in the space and driven by high-frequency …

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Viсtor Ivanovich Chulkov, Leading Researcher of Research Institute (Kaluga, Russia).
He is the author and head of the project “EDS–Soft” since 2002.
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Mathematical modeling of multi-layer polarizers on meander lines



Published: 10/29/2003
Original: Radio engineering (Moscow), 1994, №9, p.p.71...75
© V. I. Chulkov, 1994. All rights reserved.
© EDS–Soft, 2003. All rights reserved.


To solve (2) Galerkin’s method can be applied. The conductors cross configuration shown on Fig.2,a and proposed in [1] can be selected as a ML model, considering that and that the period lengths and of ML ( — is the wave length in dielectric in which ML is located), and the transverse currents are neglected. The dependency of longitudinal currents upon the transverse coordinates can be selected in a way to provide for the required singularity on the ridges accordingly to the Meixner conditions [2]. Let’s consider the specific element ML (Fig.2, b), oriented at an angle to ML axis. According to the notes stated above the current within the local coordinate frame , where , and is to be defined by the mode of the basis set chosen along the axis is the actual series development by this basis with unknown factors.

After finding of current on ML it is possible to calculate the scattering matrix elements () of the polarizer. For determinacy reasons let’s think that i,j = 1,3 conform to the flat wave polarized at an angle of to ML axis, and i,j = 2,4 — correspond to the flat wave polarized at an angle of . Moreover, the j indexes equal to 1 and 2, relate to the wave incident in positive direction of the OZ axis, whereas the j indexes equal to 3 and 4, — in the negative one. In this case the element represents for instance the conversion coefficient of the wave polarized at an angle of incident in negative direction into the wave which has passed through the MMP and polarized at an angle of : . The transmission factor of the wave polarized at an angle of is , where , — are the electric field components of the wave which has passed through the MMP in the spherical coordinate frame.

Based on the formulas received a PC calculation program has been made up. Here the full orthogonal system

is used as basis function, where , , , , (please refer to Fig.2,а), and and define the direction where the flat wave come from (3).

Fig.2

The is introduced to eliminate the phase jumps in the points of ML conductors connection

.

To check the algorithm and program efficiency the calculations for one MMP layer from [1] were performed. The results received for the differential phase shift between the factors and are congruent with the results of [1 ] having graphic accuracy.

The calculation results for the four-layer MMP, where the layers are divided by air space =1, 0,1667 wide, having the parameters as follows: =0,0067, =5,4 (i=1… 4); =0,09067; =0,32; ==0,0107; = 0,056; = 0,099 ( — is the wave length at the initial frequency ) within the frequency band at , are given on Fig. 3 (continued and dashed-line curves). This figure also represents the results of experimental investigations on a model where foamed plastic instead of air space was used. The difference does not exceed 8… to 10% and is there due to the lack of fit between the experimental specimen and the mathematical model which is especially noticeable by a large number of MMP layers. This lack of fit lies first of all in the finite size of the real MMP and in use of foamed plastic instead of air space having >1 (=1,05…1,15).

Fig.3

If the space between the ML layers is less than (0,18…0,2) it is necessary to consider the interaction as per higher spatial harmonics. Use of MMP as compared with one-layer ML allows to essentially expand the wave lengths effective range (up to one octave and more).

The author thanks to L. I. Sidorenko for the experimental investigation results provided as well as to V. V. Koryshev for the discussion of received theoretical results and his attention towards this work.


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References

1. Terret G., Levler J.R., Mahdjoubi K. Susceptance Computation of a Meander-Line Polarizer Layer. — lEEETrans., 1984, v.AP-32, no.9. (In Russian).
2. Mittra R., Lee S. Analytical methods of wave guide theory: Translated from English //Under the editorship G.V. Voskresensky.— М.: Mir, 1974. (In Russian).
3. Weinstein L.А. Electromagnetic waves.— М.: Radio and telecommunications, 1988. (In Russian).
4. Amithay N., Galindo V., Wu Ch. Theory and analysis of phased array antennas.— Wiley–Interscience Inc., New York, London, Sydney, Toronto.— 1972.
5. Filippov V.S. Mathematical model and research results of the printed–circuit oscillators responses in the flat PAA //Antenna, issue 32.— М.: Radio and telecommunications, 1985. (In Russian).

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