304 



BELL SYSTEM TECHNICAL JOURNAL 



2 ■••,are such that [Zi^*) - Zi2(*>][Z2(*> - Zia^*^]-^ is a constant, may 

 be completely specified by its three transducer parameters {with transducer 

 terminal pairs each made up of adjacent terminals on opposite ladder 

 sides'^), the driving-point impedance between short-circuited transducer 



A . Network Diagram 



(K) 2^n-0 



B. Network Equivalents 

 (V + a)Z|2:34- 



o3 



VZ|2:i2+aZ|2:34 VZ34:34+aZ|2;34 

 Z-v(l-v)(Z|2:i2 + Z34:34-2Z|2;34) . 



Ci-v)z,p.|p-az 



I2;|2-^^I2:34 



.Ci-v-a)Z|2:34 



(l-V)Z34:34-aZ|2:34 



A 4 



aZ + v2(Z|2:i2-Z|2:34) 



(l-a)Z + V^(Z34:34-Z|2:34) 



0CZ + (1-V)2(Z|2..|2-Z|2:34) 



(l-a)Z + Cl-V) (Z34;34-Z|2:34) 



Notation 

 p = Pk = [Z/*) - Z,2f«][Z,(*) + Zs^*) - 2Zi2('=)]-i 



»S'l2:i2 = (Zl2:i2Z34:34 — Z^12:34)/Z34:S4 





■534:34 = (Zi2:i2Z34:34 — Z'i2:34)/Zi2; 12 

 •5'l2:34 = (Zi2:i2Z34:34 — Z-12:34)/Zi2:34 



Zi(*) + Z2(*' - 2Z,2<*) 



a = Arbitrary Constant 



Fig. 1 — A sample ladder network illustrating notation; and some network equivalents. 



^ The theorem also holds when the terminals of each pair are non-adjacent, that is, 

 for terminal pairs 1, 4 and 3, 2 of Fig. \A ; this result is of no importance in the railway 

 applications. 



