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Journal Antennas №7 for 2015 г.
Article in number:
On the matrix theory of antenna systems with mutual coupling elements
Keywords: antenna array partial pattern continuum directivity gain efficiency matching and coupling (of array element inputs) multi-terminal network dissipative losses lossless scattering matrix unitarity.
Authors:
I. V. Guzeev - Ph.D. (Eng.), Senior Research Scientist
Abstract:
This paper presents enough general and clear matrix-analytical theory of antenna system with mutual coupling antenna elements anda lossless input beamforming network (BFN), which may be non-reciprocal. The network wave theory and scattering matrix expressionof lossless matching and decoupling BFN as function of array scattering matrix [1] have been used.The vector-columns of partial patterns of antenna array, which connected with lossless matching and decoupling BFN have been obtainedfor transmit and receive mode. Number of such systems is continually indefinitely. Ideal matching and decoupling of array inputsdon-t guarantee the orthogonal and normal partial pattern system. This addition is true for lossless antenna array. The equationfor receive mode may be obtained from the equation for transmit mode by a transpose operation of the array scattering matrix. Thisoperation reverses the energy flow direction.The expressions between the array scattering matrix and the matrix of scalar products of pairs of partial patterns as vector functionshave been deduced in case of lossless array and BFN. On basis of this the expressions of relationship between partial pattern systemand pattern system of array with BFN have been also deduced. This allows to express the partial pattern system of array with BNFfrom the one array without BFN and without using the scattering antenna array matrix.The sum of partial directivity of lossless antenna array is invariant for orthogonal and normalized array pattern system continuum andfor linear transformations by any non-singular matrix as well.It has been shown that among the partial pattern systems one can extract the canonical system which has minimally possible normalizedRMS error from the appropriate non-orthogonal initial array partial pattern system. With using of canonical pattern system, theorthogonal partial pattern system expression has been obtained, which have a minimum RMS error to arbitrary assigned nonorthogonalpartial pattern system. This orthogonal partial pattern system allows simplifying the multielement antenna system analysisand synthesis.
Pages: 15-28
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