RADIATION CHARACTERISTICS OF AN ANTENNA. 



231 



_ C-"" cos^ (j>d<l) _ T'^/^ cos^ (f) 

 Jo 1 — sin^ 6 cos^ </) Jo 1 — sin^ ^ 



d4> 

 6 cos^ ^ 



by reasoning similar to the above. Expanding the denominator by 

 (93a), we have 



W 



rw2 c 



= 4 I dcf) cos^ (j) \ 1 -\- sin^ 6 cos^ <^ + sin^ cos^ (j) + 



1 



= 2.-i^+2^-^«+^^si„<.H- 



i- 



(90) 



(If we need it, this integral can be obtained by direct integration in 

 the form 



W = 2w 



J I 



I cos 0(1 + cos 0) 



but the expanded form is more useful for our purpose). 

 Now substituting (95) and (96) in (89) we obtain 



P 



_2P r'^/2 



C Jo 



dd sin 6 sin {A cos 6) \ cos B cos (A cos 6) 



— sin B cos 6 sin (A cos 6) — cos G 



1 



- {B - sin B) sin 



1-3 / 5^ 

 + ^(^£-3, -sin5)sin^0 



+ ^r^n^ 5 - - + - - sin B sm^ 



2-4-6 



3! ' 5! 



+ 



(97) 



To evaluate this expression we must obtain the following integrals: 



'-£ 



sin (2A cos 6) 



Ii= j dd sin" d 



'o 2i 



f 



Oo 



■/2. 



dB sin"^ Q cos B sin^ (^ cos ff), 



(98) 

 (99) 



