90 BELL SYSTEM TECHNICAL JOURNAL 



?'i = 2lViV + 2Wn'% ^^' ~ ^^ ' <3(2^^^, 0) 



+ WX72'^' t, N - K){N - K)-Q(2TrKA, 2irKA). (26) 



This, like equation (13), corresponds to the practical case of 

 transmission from an antenna curtain and reflector each made up 

 of N vertical columns of N elements, all driven in the same phase. 



(2) If we assume that no stacking is involved, then N = 1 and we 

 have for the test ratio for N couplets 



T2 = 27v+ W^Sl^^ ~ -^)-'3(27rX^, 0) 



_ 1 _L ^ V/y V) r sin27ri^^ 



- 2"7V + 2N^h ^^^ ^^ [ 2tKA (2^^ 



, cos lirKA sin 2tKA 



' (27rKA)^ {2TrKAf 



This equation was used in the calculation of the data given in 

 Figs. 6, 7, and 8. 



(3) If we wish to apply equation (25) to the case of a single array 

 of N linear oscillators driven in phase we have n = N = 1 and B = 0, 

 so 



Ts =^ + 1, e'(A^ - K)-Q(2tKA, 0), (28) 



which differs from equation (27) by a factor of two. This indicates 

 that an array of N equiphased linear couplets gives twice the field in 

 the preferred direction as received from JV equiphased linear elem.ents 

 radiating the same power. 



(4) Applying equation (25) to the extremely simple case of one 

 couplet, n = 2, a = J, b = — j and N = N = I and 



T, = h (29) 



(5) We may calculate the test ratio for a single stack of linear 

 couplets (earth effects not considered) by placing iV = 1, » = 2, a = j 

 b = — J, and 5 = and get 



^^ = 2lV + A^ %[ (N-K)- (2(0, 2.KA) 



1 3 ^=1 



COS (2TrKA) sin {2TrKA] 



2N N^K^i 'I {2TrKAf {2TrKA)' 



(30) 



