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Use of Quadratic Form to Study Phase Direction Finder Implementing Frequency Substitution Circuit for Multi-Target Situations


I. D. Zolotarev, V. A. Berezovsky

The article is devoted to research of the phase direction-finder realizing the circuit with substitution of frequency, functioning on a stream of signals from the sources of radiation spased in space. Thus the case of identical construction of phase channels of the direction-finder providing equality of vectors of signals amplitudes, accepted by spared in space antennas is considered. For the description of work of a direction-finder in this case we use transition from the bilinear form of record of signals on the output of phase channels to a square-law form. To simplify the research of work of a direction-finder in a multi-purpose situation we give resulting matrixes in a triangular form. The mathematical apparatus allowing to investigate generalized direction-finding characteristic in defining bearing of long-distance sources of radiation is stated. In this case the big distances up to the purposes will lead to close values of phases differences for all sources that will determine two special cases when all radiation sources symmetrize concerning a line of sight or on a line of sight. Decomposition of phase matrixes of signals to Hermitian matrix and to skew-Hermitian matrix in the output of phase channels of the direction-finder defined as arguments of elements of square-law matrixes is considered. In private conditions Hermitian matrix passes into symmetric, and skew-Hermitian matrix reduces to a null matrix that results in reduction of an bearing error for imposed signals from long-distance radiation sources.

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