220 



BELL SYSTEM TECHNICAL JOURNAL 



and only partially successful because a saturation point is soon reached 

 in the gain obtained with more apparatus. 



This difficulty may be overcome by adding networks of the 

 more complicated lattice type shown in Fig. 21."* This may appro- 



L, C, 



Fig. 21 — "Resonant" lattice network 



priately be called the 'resonant' lattice type. Its characteristics are 

 most easily derived from the general lattice network having the 

 impedance Zi/2 in each series branch and the impedance Iz^ in each 

 diagonal shunt branch. Since the characteristic impedance, K, of 

 any section of line is equal to the square root of the product of the 

 open- and closed-circuit impedances and the propagation constant, 

 r, per section, is equal to the anti-hyperbolic tangent of the square 

 root of the quotient of the closed-circuit impedance divided by the 

 open-circuit impedance,''-' we have, for the lattice network, in general, 



cosh r = 1 



2zi 



422 — Zl 



or 



tanh "2 = 2 ^^1/^2, 

 K = VziZo. 



(32) 



{Z3) 



Thus the requirement that the characteristic impedance be a real 

 constant will, in general, be fulfilled provided 



zo = R'/zi, 



(34) 



where i? is a real constant approximately equal to the characteristic 

 impedance of the cable. This gives 



tanh- = 2^. 



'* This suggestion was made by H. Nyquist. 

 ^^ See reference 12. 



(35) 



