616 BELL SYSTEM TECHNICAL JOURNAL 



Introducing the potential differences, for current transmission from 

 terminals a to terminals b 



^'^^bJ^cosh T + /" sinh T, 



\ Wa VWaWt 



and (71) 



V.= Vb-yj^ cosh r+/,Virjri, sinh T. 

 I, = I AE^ cosh T y^^— sinh T, 



Vt = Fa^ ^ cosh T - laVWJV,, sinh T. 



Also, 



Va 

 VWJVb 



and (72) 



II. Recurrent Parametkrs 



1. General Linear Transducer. Here four parameters " of the 

 transducer in Fig. 3 are defined in terms of its properties when it is 

 one section of an infinite recurrent structure which is made up of 

 identical sections, similarly oriented. With such terminal condi- 

 tions for the transducer, its directional propagation constants are 

 defined as follows: raA = log,- {la/h) when transmitting from terminals 

 a to terminals b, and Tt,a=\oge {h/Ia) when transmitting from termi- 

 nals b to terminals a. The characteristic impedance Ka is the im- 

 pedance across terminals a in the direction from a to b, and the char- 

 acteristic impedance Kb is similarly defined for the impedance across 

 terminals b in the opposite direction. 



Terminating the transducer by the general impcxlances Za and Zb 

 and applying an electromotive force £j in series with Za, the current 

 formulae containing the recurrent parameters may be derived in a 

 manner analogous to that used with the image parameters. In this 

 case the total effective electromotive forces acting at the ends a and b 

 of the transducer terminated b>' its characteristic impedances A';, 

 and Ka are, respectively, 



E, + {Kb-Z,)h, 

 and (7.3) 



{Ka-Zb)h- 



" These parameters may also l)e (lesignate<l in tlie general case as those of a 

 generalized artificial line. 



