Synthesis of Antenna Arrays and Parasitic Antenna Arrays with Mutual Couplings

Table 1

Weightings applied to the monopole array and resulting antenna impedances.

Monopoles 𝑖	Length (mm)	𝛽𝑖 (=weights for the coupled radiation patterns)	Normalized incident waves (𝑎𝑖) and load impedances (ZLi) that optimize the efficiency (couplings included)
			𝑎𝑖	ZLi
1	10.8	0.286⋅exp^(−𝑗∗48∘)	0.288⋅exp^(−𝑗∗49∘)	29+𝑗∗13
2	9.8	0.293⋅exp^(𝑗∗155∘)	0.30⋅exp^(𝑗∗152∘)	32+𝑗∗10
3	9.3	0.279⋅exp^(−𝑗∗3∘)	0.286⋅exp^(−𝑗∗6∘)	31+𝑗∗9
4	9.3	0.284⋅exp^(−𝑗∗155∘)	0.291⋅exp^(−𝑗∗164∘)	30+𝑗∗1
5	9.3	0.284⋅exp^(𝑗∗47∘)	0.287⋅exp^(𝑗∗35∘)	27−𝑗∗2
6	8.8	0.280⋅exp^(−𝑗∗120∘)	0.283⋅exp^(−𝑗∗124∘)	29+𝑗∗7.5
7	8.8	0.266⋅exp^(𝑗∗82∘)	0.262⋅exp^(𝑗∗79∘)	24+𝑗∗8.5
8	8.8	0.264⋅exp^(−𝑗∗74∘)	0.251⋅exp^(−𝑗∗77∘)	20+𝑗∗8.5
9	8.8	0.254⋅exp^(𝑗∗131∘)	0.227⋅exp^(𝑗∗124∘)	15+𝑗∗3
10	8.8	0.275⋅exp^(−𝑗∗24∘)	0.257⋅exp^(−𝑗∗35∘)	18−𝑗∗1.5
11	8.8	0.319⋅exp^(𝑗∗180∘)	0.323⋅exp^(𝑗∗165∘)	28−𝑗∗7
12	8.3	0.361⋅exp^(𝑗∗0∘)	0.377·exp^(𝑗∗0∘)	48+𝑗∗17