Suppose, that all subarrays are belong to infinite two–dimensional AA and all feeder line have equal wave resistance. Failing loss in BF they can be circumscribed with unitary scattering matrix with the zero–order terms on principal diagonal. Let BF generates in outcomes GPD, which in general case can be described with complex–valued functions , *i*=1,2. Indices *i*=1,2 conform with BF_{1} and BF_{2}.

For emitting subarray under unit amplitude of principle wave in input, in BF_{1} outcomes we`ll get follows amplitudes of same wave:

(2) |

At that wave amplitudes in secondary subarrays radiator will equal to:

(3) |

where *C*_{pt} — mutual coupling coefficient between infinite AA radiators and wave amplitude in BF_{2} input is:

(4) |

Then formula (1) taking into account (2), (3), (4) can be written as:

where *P*_{1} is connected with infinite AA radiators interaction, *P*_{2} is determined from gain distribution on BF outcomes and doesn’t depend on phase distribution, radiator`s type and their position in array.

Taking into account linkage between coefficient *C*_{st} and reflectance , depending on equal–amplitude feed of infinite AA with linear phase progression, expression can be written as follows:

(5) |

where * — complex conjugation symbol

(6) |

, — differential phase shift lengthwise *OX* and *OY*. *f*_{1} and *f*_{2} functions represent subarray multiplier and possess only the finite data modulo for realizable gain–phase distribution.

On the basis of expression analysis (5) it’s possible to develop the follows relation approach of AA and BF for wideband bypassing increase, concerned with radiators interaction (in case then subarrays workspaces are in etch angle sector):

— in etch angle sector and given frequency band of infinite AA radiator reflectance *Г* should take on a lower–range value modulo (in the limit — zero value for all ):

— BF_{1} and BF_{2} have to generate in outcomes GPD, then "basis ray" of *f*_{1}, *f*_{2} functions should be narrow at most and "side lobes" should have lower–range value modulo (in the limit — zero value for all ) in the invisible angle sector (where |*Г*| = 1 in case of diffraction lobe of higher order lack):

then