SELF-TIMING REGENERATIVE REPEATERS 901 



III ILLUSTRATIVE REGENERATION CHARACTERISTICS 



3.0 General 



In this section the general equations given in the preceding sections 

 are applied to a particular case, in order to obtain specific expressions 

 for the regeneration characteristics and illustrative curves, as an aid 

 to further analysis. The particular case selected for illustration approxi- 

 mates the conditions in experimental Wrathall repeaters, and may be 

 regarded as an idealized model of such a repeater, in which certain effects 

 to be discussed later are ignored. 



3.1 Pulse Shape 



It will be assumed that the pulses are transmitted at intervals T 

 and that the shape of the received pulses after equalization is given by : 



TT t 



Pit) - I 



1 + cos 



(3.1) 



This is the familiar "raised cosine" type of pulse. With rj = I the pulse 

 width is the maximum that can be tolerated without intersymbol inter- 

 ference. With 7? = f , the amplitude of a pulse train at a point midway 

 between two success pulses is equal to half the peak amplitude of a 

 pulse. The latter assumption will be made here, for reasons discussed 

 later. 



3.2 Retiming Wave 



The retiming wave is assumed to be given by 



R{t) = --cosiA 



cos 



(3.2) 



This type of retiming wave can be obtained if a sinusoidal wave of the 

 pulse repetition freciuency / = 1/ T is applied to a resonant circuit to 

 reduce distortion of the timing wave by noise. The resonant circuit 

 would have a nominal resonant frequency/ = l/T", but because of mis- 

 tuning it would actually be /o . The output of the resonant circuit after 

 appropriate adjustment of amplitude would be of the form [Appendix I, 

 equation (2)]: 



i?o(0 = ^ cos ,A cos {2r ^ - ^), (3-3) 



where \p is the phase shift of the resonant circuit at the frecjuency /, 



