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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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## Influence of boundary effects on characteristics of wideband antenna array

Published: 01/01/2007

Based on the obtained formulas (where Г = 0) the dependency of the direction diagram of radiating strip with length l = 0,14, width = 0,03 on the magnitodielectric layer with thickness t = 0,032 permittivity = 10, = 2 (= j1060.49, , ) on its position in the array containing 1681 radiators located in the nodes of the square grid with period T = 0,14 (array has size 6 x6) was calculated. The radiators are matched in the direction of normal to antenna array () provided the array is infinite. The model corresponds to the finite array in the infinite screen coated with a layer of magnitodielectric with permittivity , and thickness t. On the fig.2 there are directional diagrams of radiators in the H-plane when = 0 and = 0 (curve 1, — number of radiators in the OX axis, — in the OY axis), = 4 (curve 2), = 12 (curve 3). Since radiators are positioned symmetrically on the OY axis, this symmetry is retained in the diagrams. In the same plane but for other positions of the radiators the fig.3 displays directional diagram of the radiating strip for = 0 и = 4 (curve 1), = 12 (curve 2). The curve 3 displays the directional diagram of the radiator in the infinite array. Directional diagrams of radiating strips in the E−plane are illustrated by fig.4 and 5. All diagrams of radiators of the finite antenna array are normalized to the directional diagram of the radiator with number = = 0. It follows that:

— the directional diagram is most distorted in the H−plane since interdependence between radiating strips is less than in the E−plane;

— in the E−plane the directional diagram stops being distorted starting approximately from the fifth radiator from the edge of the array, in H−plane — from the thirteenth.

Fig. 6 Behavior of the module of the reflection coefficient of the radiating strip of the finite array in the infinite screen in E−plane depending on its position in the OX axis (1 — , 2 — , the dotted line corresponds to radiating strip in the infinite antenna array when ).

Fig. 7 Behavior of the module of the reflection coefficient of the radiating strip of the finite array in the infinite screen in E−plane depending on its position in the OY axis (1 — , 2 — , the dotted line corresponds to radiating strip in the infinite antenna array when ).

Fig. 8 Behavior of the module of the reflection coefficient of the radiating strip of the finite array in the infinite screen in H−plane depending on its position in the OX axis (1 — , 2 — , the dotted line corresponds to radiating strip in the infinite antenna array when ).

Fig. 9 Behavior of the module of the reflection coefficient of the radiating strip of the finite array in the infinite screen in E−plane depending on phasing angles (1 — = 0, 2 — = 4, 3 — = 12, 4 — = 20; = 0; the curve 5 corresponds to radiating strip in the infinite antenna array).

Let’s consider the characteristics of the given antenna array when exciting the entire array uniformly with linear phase incursion. The radiators like in the previous case are matched in the infinite array. The fig.6 presents curves which display the dependency of the reflection coefficient module on the number of radiator (along the radiating strip axis) when = 0 in E−plane for array phasing angles (curve 1) and (curve 2). The same dependencies on the number of radiator (across the radiating strip axis) when = 0 are displayed at fig.7.

Change of the reflection coefficient module for H-plane depending on the radiating strip number when phasing the array in the direction is illustrated by fig.8. The dotted line displays the reflection coefficient of the radiator in the infinite array for angle (for , ). In all cases, the module of the reflection coefficient is greater for boundary radiators and have oscillating character caused by the interference of non−excited currents and total boundary wave [4].

Analysis of the curves given on the fig.6…8 confirms the results received when analyzing the directional diagrams (fig.2…5). Behavior of the reflection coefficient of the antenna array in sector of angles is displayed at fig.9, where curve 1 corresponds to the radiator = 0, curve 2 — radiator = 4, curve 3 — = 12, curve 4 — = 20 and = 0, the dotted line corresponds to the infinite array. The charts show that in the finite array, decreasing of sector of angles where takes place. For the infinite array this sector is equal to ±60°, for radiators of the finite array with numbers = 0, 4 — ±55°, for radiator = 12 — −50°…+60°, and for boundary radiator (= 20) the sector of angles doesn’t exist .

Fig. 10 Envelopes of the maximums of directional diagrams of the fully excited array when phasing in E−plane (curve 1) and in H−plane (curve 2).

As the fig.10 shows when exciting the entire finite array, strong interdependence causes the maximums of directional diagrams to form a smooth curve in the sector of angles to ±60° preserving the average width of the diagram corresponding to the width of the directional diagram of the radiator in the infinite array.

Conclusion

— for multiunit radiators of finite antenna arrays, formulas received in [2] have been generalized. For calculating amplitudes of the total boundary wave, an equation of second kind is constructed, norm of the operator of which is always less than one;

— after experimental research of the diagram of the radiator of antenna array with strong connection the methods of measuring related to exciting of one element of the array and let the other elements loaded on matched loads cannot be used. For such an array, measures of maximum of diagrams must of fully excited antenna array with different phasing angles are required;

— the strongest distortions of reflection coefficient in a finite antenna array are for radiators located in the scanning plane. In this case, deviation of the reflection coefficient from the reflection coefficient of the radiator of the infinite array does not exceed 25% for radiators of the central part of the antenna array approximately starting from the distance of (1…1.15) from the edge of the array (the radiator is matched in the infinite array).

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References

1. Chulkov V. I. About widebandedness of flat antenna arrays of microstrip radiators. // Second All−Union Science−Technical conference “Devices and methods of applied electrodynamics”, 9…13 September, 1991 (Odessa). Report theses.— M.: MAI, 1991, p. 148.
2. Filippov V. S. Generalized method of subsequent reflections in the theory of finite antenna arrays. // Proceedings of institutes. Radioelectronics, 1991, v. 34, №2, p. 26…32.
3. Chaplin A. F. Analysis and synthesis of antenna arrays.— Lvov: LSU, 1987.— 179p.
4. Filippov V. S. Boundary waves in finite antenna arrays. // Proceedings of institutes. Radioelectronics.— 1985, v. 28, № 2, p. 61…67.
5. Corn G., Corn T. Mathematics reference book for scientists and engineers; Edited by I.G. Aramanovich.— M.: Nauka, 1968.— 720p.
6. Hutson V., Pym J. Applications of functional analysis and operator theory.— M.: Mir, 1983.— 431p.
7. Polozhy G. N., Pakhareva N. A., Stepanenko I. Z. et al. Mathematical practicum /Edited by G. N. Polozhy.— M.: GIFML, 1960.— 232p.

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