If no direction is compensated for, the directivity function is 
SUB hy GM 9 Ns 
2 2 2 
ee ) y DBs i ,exp.se [(471/2)d, cosa 
Sik Sis il 
Op eh =z 2 = 3 
Ua Coot ay 
+(7+ +(At a a 
(241/2)ds cosst(h+1/2)ds3 cosy Psie, (COs, | an 1)] 
By taking account of the symmetry, and letting D>», and 
assuming f, Lh are constant 
we,  \, jo 
i 2 oye!) ) Y Lexp j(t-1/2)dy cosa] - 
Cmte mlanml 
[exp jz(2-1/2)d2cos8] - [expjx(h-1/2)d3cosy ] 
Since each summation variable is independent of the other: 
pes iB n ne) exp jk(i-1/2)d, cosa ] [2) exp jA(2-1/2)dz cos8] 
[ 2) exp ji(h-1/2)dz cosy | 
Using the identity in the previous section, the directivity 
function becomes 
R=E. sin(h §) : sin(W2 1) t sin(Wa( ) 
i, 4,hsin(e) sin(») sin(c ) 
