1234 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



a series of identical sections each containing a single mode-conversion 

 discontinuity at the midpoint. (The actual 500-foot line contains many 

 conversion points, as will be discussed later, and is effectively repeated 

 over and over as the pulse traverses the identical line many times.) A 

 very short signal-pulse of unit amplitude is assumed as an input to the 

 idealized line containing identical conversion points. After the first con- 

 version point the amplitude in the unused mode is k and the amplitude 

 in the signal mode is (1 — t^)^'', where fc is a measure of the size of the 

 conversion irregularity. There is no reconverted wave at this point since 

 there is no input to the first conversion point in the unused mode. After 

 the second conversion point, however, there is a reconverted-wave am- 

 plitude /c^e*-^, where 6^ is defined below. After the n"' conversion point, 

 it may be shown that the amplitude in the signal mode is 



^(„-l)«, (^ _ j^2^nl2 (2) 



the amplitude in the unused mode is 



(«-i) 



A;(l _ /,2^^-,("-l)<'x 

 (n-1) 



-f etc. to + A;(l - k') ^ ,(«-i)»i 

 and the reconverted wave amplitude is 



(n - 1)/^(1 - A:^)^,<'x+(n-2)«x 



+ (n - 2)k\l - A;2)-^V''^+(-«)«i 



(4) 



+ (n - 3)k\l - ^-2)-^,39.+(„-4)fl, 



+ etc.tofc'd - A;^)'-^e^"-i)«x 



in which 



z = distance between adjacent conversion points 



ai and ax are the heat loss coefficients (applying to wave amplitudes) 



for the signal and unused modes respectively. 

 j8i and /3x are the phase constants for the signal and unused modes 



respectively. 

 ^1 = - (ai + j^i)z 



