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BELL SVSTE.Vf TECHNICAL JOVRNAL 



The equations (e22) and (e23) may look as if drastic measures would now 

 be needed, but a parametric solution is sur{)risingly easy; one need only 

 solve (e22) for G h , and substitute back into the power expression (e20). 

 The results are 



Gh = 



(: 



^ §' e sin e (iJo + "V i-x-'Jo - XA\ 





(e25) 



Pl = -/oT'o ?sin 6 llJ, - AVo + ~ 



+ 



Gl = ^Ge — Gr = 



X' 



/l 



+i 



y7l + (-fX' + 



\X')J^ 



(e26) 



^0 ,p2 ^ • air 1 V 7 I cot 



— ^ - sm d\Ji - ^X/o + 



[(•-?)^-(-f-|>»] 



+ -[1XV, + (-3%X^ + 



AX^)/o ) 



One further convolution is necessary, because the equations (e25) and 

 (e26) are still subject to the optimum phase angle condition (e23). Since 



we are here carrying only terms as far as — , approximations are in order. 

 I'Vom (e24) we get the hint that 6 cot 6 is of the order of unity, so that 

 terms in are of the same order as those in — . Accordingly an ap- 

 proximate solution is obtainable by adding (e22) and (e2v^) and neglecting 

 these small terms. The result is 



'\ herefore the optimum phase angle is given by 

 . . FiX) 



sin = - 1 + 



e,, = (« + f)27r 



\t\X)\' 



2dl 



(e28) 



(e29) 

 fe30) 



