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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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Vladimir Sergeevich Filippov, Professor of the Chair of Radio-physics, Antennas and Microwave Devices of MAI (Moscow), Doctor of Science in technics.


Alexey Andreevich Sapozhnikov, Associate Professor of the Chair of Radio-physics, Antennas and Microwave Devices of MAI (Moscow), Candidate of Science in technics.
He is one of the founders and executives of the Autonomous Power Systems.
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Charge method in mathematical modeling of printed radiators



Published: 08/18/2010
Original: Computer-aided design of microwave devices and systems // Interuniversity digest of scientific papers. (Moscow, MIREA), 1982, p.p.138…148
© V. S. Filippov, A. A. Sapozhnikov, 1982. All rights reserved.
© EDS–Soft, 2010. All rights reserved.


The method of researching the electrodynamic characteristics of the PAA radiating curtain described in this work applies to antennas with rectangular printed radiators and also other radiators that can be presented as an array of rectangular items. However, the charge method is applied to researching a printed vibrator radiator (fig.1) being part of an antenna array in this particular example.

As it is known [1], some freedom in choosing the integral representation of electromagnetic fields in diffraction problems makes it possible to get various integral equations. The essence of the proposed method comes down to determining the intermediate characteristic — the charge distribution over the metal plate and then by means of integration — the electric current. The vectors of the electromagnetic field are determined via the vector potential of electric currents using the known equations:

(1)

where .

The radiator is regarded as part of an infinite periodic antenna array, which makes it possible to proceed to the analysis of the field within one period. Due to this, it is reasonable to use a representation in the form of expansion in plane waves for the vector potential [2]:

(2)

where

and is the vector of the electric current volume density, (x,y,z), (x',y',z') are the coordinates of the point of observation and the point of integration respectively.


Fig.1

Presuming that the metal radiators are ideal conductors and they are also infinitely thin, the vector of the electric current volume density can be written down in the following way:

(3)

and it is reasonable to replace the effect of the screen with a mirror view of the radiator:

(4)

where is the vector of the electric charge surface density, is the Dirac delta function.

By integrating expression (2) using the axial coordinate z and taking into account (3) and (4), it is possible to get the values of the vector potential harmonic in two characteristic areas of the structure:

(5)

The wave of the potential is presented in the form of the superposition of waves related to Е- and Н-waves of the spatial waveguide:

(6)

The specified waves are determined by the following expressions:

(7)

where .


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References

1. E.N. Vasiliev Algorithmization of Diffraction Problems Based on Integral Equations. - In Applied Electrodynamics Moscow: Higher School, 1977, #1.
2. G.T. Markov Antennas. – Moscow/Leningrad: Gosenergoizdat, 1960.
3. A.S. Ilyinsky, A.G. Sveshnikov Numerical Methods in Diffraction Theory. Moscow: MGU, 1975.
4. A.N. Tikhonov, V.Ya. Arsenin Solution Methods for Ill-Defined Problems. Moscow: Science, 1979.

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GuidesArray Circular 0.1.4

GuidesArray Circular™ allows to execute electrodynamic modeling of two-dimensional phased antenna arrays for circular waveguides, using the method of moments.


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