TRANSIENT RESPONSE OF AN FM RECEIVER 



727 



On Fig. 5 is given a plot of this function for a value a/ A = 1 of the rela- 

 tive damping. Calculations for other values of a/A show that the output os- 

 cillates only weakly for a/ A = h and is nearly dead-beat for a/A = 2 



0.9 

 2 0.8 



. ro.7 



0.6 



0; 0.4 



0.3 



-0.1 



20 40 60 80 too 120 140 160 180 200 220 240 260 280 300 320 340 360 



At IN DEGREES 



Fig. 5 — Transient response of a balanced frequency detector for a step in the carrier 



phase. 



Example 2: Signal Reception 



If the carrier is frequency-modulated by a signal 



s{t) = S cos qt (39) 



and the frequency modulation factor of the transmitter is /x, the phase of the 

 carrier wave is made to vary in accordance with the relation 



s(t) dt = — sin qt = X sin qt 



00 



(40) 



/x5 is then the radian frequency deviation of the transmitter and fiS/q, 

 which is the ratio of this frequency deviation to the frequency of the signal, 

 is commonly referred to as the '^frequency deviation ratio." This factor, 

 which is denoted by x in the above equation, enters as a fundamental 

 parameter in all FM theory. 



To find the envelope function of the voltage wave produced across the 

 impedance (26), when the frequency-modulated carrier is received at the 

 frequency detector, we put (40) in (28). To effect the integration, the 

 expansion 



e'"'°"= Z Mx)e""" 



(41) 



