DISTORTION CORRECTION 509 



Bridged-T Type: 



and 



cosh r = 1 + , ,^/°?i , — (112) 



Za{Za + 42c) + 4ZbZc 

 ^=\ 4(2„ + 2.) • ^^1^) 



As an aid in obtaining the propagation constant, V = A -\- iB, from 

 any of the three hyperboHc cosine formulae it will be found convenient 

 to use the following formulae. 



Computation Formula; for the Complex Anti-IIyperholic Cosine 

 It is known that many formulae have already been derived for such 



evaluations but those below appear to give accurate results more 



readily. 



Let it be desired to obtain A and B from the formula 



cosh {A + iB) = X + iy, (114) 



wherein x and y are known. A transformation of the x and y variables 

 is first made so as to use the form of substitution and formulae given in 

 B. S. T. J., October, 1924, pages 577 and 578. A further substitution 

 and the application of hyperbolic formulae give the following results 

 where 



U = hix- 1), 



P = 4(C7+ f/'+ V), (115) 



and 



(2 = 1 sinh-i ^ 



When P is Positive: 



A = sinh-i (VPcosh(2) 

 and (116) 



B = ± sin-i (VFsinh Q). 



When P is Negative: 



A = sinh-i (V- P sinh Q) 

 and (117) 



B = zk sin-i (V- P cosh Q). 

 When P is Zero, a Special Case: 



^ = sinh-iV2|F| = icosh-i(l +4lFl) 

 and (118) 



B = ± sin-i ^^2\V\ = ±h cos-^ (1 - 4| V\). 



