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BELL SYSTEM TECHNICAL JOURNAL 



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SEPARATION, yd, IN RADIANS 



Fig. 123. — If the planes or tubes considered in Figs. 121 and 122 arc separated bv ap- 

 preciable distance, the modulation coefficients given in those figures must be multiplied 

 by a factor F{y d). In this figure, the multiplying factor is evaluated and plotted vs the 

 separation in radians for two assumptions — that the gap has very blunt edges (Fiiyd)) 

 and that the gap has very sharp edges (Ftiyd)). 



This is zero far to the left and Vix far to the right. This expression is 

 useful only when the wire radius ;- is quite small compared with the separa- 

 tion a. Midway between wires, 



r = V[x/2 + (a l'(/2T)ln 

 V" = (V'lT/la) sech 



2 cosh 



J TT.V 



a 



vx~\ 

 a J 



(b29) 



(b30) 



If we use (b30) for each grid, the values of V" for the two grids will overlap 

 somewhat. However, let us neglect this overlap, apply (b30) at each grid, 

 and using (bl3), integrate for each grid from — j^ to -{- x , giving 



sech" -^ e^"^' dx 



(b31) 



/3o = (l/DO'iTr/Ta) |1 -e^''\\ f 



\ J—o 



-/{sin (yd/2)/iyd/2)\Go{ya) 



f = V[/iV/d) (b32) 



Goiya) = i I [ "e^^^"^-^'" sech'w du = (7a/2)/sinh {ya/2) (b33) 



J— 00 I 



where 



