To obtain first principle the usual variants of waveguilding, vibrator, resonant microstrip and other frequency–dependent radiators are not matched up, because required Г behavior in the sector of broad band frequency (octave and more) and wide angle sector (about ±60⁰), is not provided.

Let us examine a WMAA, described in the work [4]. It represents grid composed of narrow strip band, length , lying on axe OX on the magneto dielectric layer, there thickness is and penetrations are . Here T_x, T_y — АA periods lengthwise ОХ и OY axes. In the etch angle sector and the closest to it invisible angle sector input resistance of such radiator can be written as follows [4]:

where W=120π, and reflectance looks like:

where , . Angles , determined direction, in which WMAA radiators are adjusted.

The second principle achievement leads to task solution of physically feasible GPD synthesis on conditions that directivity level of both subarrays is the highest [5].

As an example lets examine the follows gain distributions in BF outcomes [6]:

Table 1 Distribution n AE SLL, dB 0 1.000 -13.3 2 0.660 -31.5 1.7 0.930 -20.8 2.4 0.808 -32.1 3.2 0.650 -47.5

P₂ takes on a minimal value in case of equal-amplitude distribution:

Table 2 n = 0 n = 2 -600 -39.16 -82.42 -450 -41.40 -89.94 -300 -42.47 -100.73 -150 -43.83 -95.99 00 -45.22 -98.60 150 -45.10 -78.01 300 -47.51 -71.42 450 -47.18 -54.30 600 -61.76 -38.69

In the table 2 estimated on the basis of IBM by formulas (5) and (6) decoupling levels between emitting and secondary subarrays, size of each is 5λx5&lambda (АA periods T_x=T_y=0.14λ) are an example in the case of emitting subarray phase angle =–60⁰ situated in the E–plane (φ=0⁰) for line radiators based on the magneto dielectric layer. Radiators are matched in the direction , . Based on the computation, character of gain distribution in H–plane (φ=90⁰) doesn’t have an influence on coupling magnitude in the E–plane. That’s why equal–amplitude distribution in both subarrays is admitted to H–plane everywhere.

Table 3 n = 0 n = 2 -600 -45.67 -116.81 -450 -47.68 -136.99 -300 -48.36 -129.87 -150 -49.46 -119.67 00 -48.80 -128.29 150 -48.76 -110.03 300 -47.35 -119.94 450 -46.29 -102.52 600 -46.24 -66.33

Table 4 n = 0 n = 2 -600 -58.32 -143.84 -450 -56.69 -151.57 -300 -54.50 -157.75 -150 -53.67 -161.07 00 -52.18 -153.89 150 -51.00 -143.92 300 -49.68 -145.81 450 -48.16 -133.62 600 -46.67 -117.86

There are subarrays (size 10λx10λ) computation results of decoupling levels in the table 3 and the same computation results for subarrays (size 20λx20λ) in the table 4.

As it’s necessary to numerically calculate sums for gain distributions (6), that concerned with plenty of computer time spending, the Euler–MacLaurin summation formula has been used in this paper [7]. At that term of N₀ series quantity in the expression for probability integral of complex argument [8], which is computed with the Euler-MacLaurin summation formula, doesn`t depend on radiators quantity in subarrays. Beside it’s substantially smaller than amount, computed with formula (6), especially in the case with great number of radiators.

Table 5 n = 1.7 n = 2 n = 3.2 -600 -57.53 -59.03 -68.96 -450 -55.85 -65.56 -78.82 -300 -57.59 -69.44 -92.46 -150 -54.31 -65.43 -84.38 00 -58.32 -72.47 -91.08 150 -56.18 -66.87 -83.58 300 -50.78 -55.36 -77.13 450 -38.67 -48.22 -52.62 600 -37.02 -56.48 -45.97

Table 6 n = 1.7 n = 2 n = 3.2 -600 -75.51 -82.33 -92.73 -450 -68.75 -80.16 -100.62 -300 -67.18 -80.62 -99.35 -150 -65.75 -77.87 -100.34 00 -66.20 -76.76 -93.09 150 -65.86 -77.60 -99.23 300 -67.47 -78.16 -94.68 450 -53.38 -58.03 -76.72 600 -40.86 -54.36 -68.34

Table 7 n = 1.7 n = 2 n = 3.2 -600 -94.83 -103.26 -131.86 -450 -73.47 -87.84 -110.29 -300 -62.29 -87.31 -109.99 -150 -72.96 -86.29 -108.66 00 -72.10 -86.34 -108.95 150 -73.64 -86.61 -109.05 300 -75.46 -87.73 -109.75 450 -77.72 -85.78 -96.26 600 -46.96 -59.29 -85.42

There are GPD of type decoupling levels for close located emitting and secondary subarrays of different sizes in tables 5…7 (for subarrays with size 5λx5λ, 10λx10λ, 20λx20λ accordingly, for emitting subarray phase angles =–60⁰). In this connection N₀ series quantity in all cases is less than 15, and mean time of decoupling level computation using IBM РС-АТ-80286/287 for 93x93 points of numerical integration of , amounts 15 minutes.

Based on the results obtained in this paper we can conclude:

— the WMAA decoupling level with gain distributions (AE=0.66, SLL=–31.5dB) are greater than with gain distributions (AE=0.808, SLL=–32.1dB). It relates to directivity decrease in second case due to slower NL decline moving off main lobe;

— in both cases decoupling level decreases than , because of radiators interaction in invisible angle sector of differential phase shifts. Interaction increases as far as visible ray of diagram approximates verge of etch and invisible sectors;

— for gain distributions using WMAA decoupling level no less than 100dB in ±60⁰ angle sector lying in E–plane, is gain on conditions that and subarray sizes no less than 10λx10λ. At that each subarray AE is no more than 0.66.