SELF-TIMING REGENERATIVE REPEATERS 



929 



Appendix 

 ix resonant circuit response to random binary pulse trains 

 / General 



In the following analysis of the response of a resonant circuit to a 

 binary "on-off" pulse train, the pulses are assumed of sufficiently short 

 duration to be regarded as impulses. This is a legitimate approximation 

 when the duration does not exceed about half the interval between 

 pulses. 



The pulse train is regarded as made up of three components, as indi- 

 cated in Fig. 10. The first is a systematic component consisting of pulses 

 of amplitude \. This component gives rise to a steady state response at 

 the fundamental frequency of the pulse sequence. The second com- 

 ponent consists of pulses of amplitude ±^, with random ± polarity. 

 This component gives rise to a random component in the resonant cir- 



it 



rh iii 



r+i 



[k 



[] [] 



jn 



II 



-T— ♦ 



^ ^ ^ ? 



A=B + C 



B 



FIRST COMPONENT 



C 

 SECOND COMPONENT 



1 



♦— T— ♦! 



THIRD COMPONENT 



F = A+D 



Fig. 10 — Components of random binary on-off pulse train. A. — Transmitted 

 "on-off" pulses. B. — Stead}'- state pulse train of fundamental frequency/ = l/T. 

 C. — Random pulse train with zero mean value. I). — Random pulse train with 

 displacements ±5. F. — "On-off" pulse (rain with displacements ±5 from av- 

 erage pulse interval T . 



