TRANSIENT RESPONSE OF AN FM RECEIVER 



717 



The curve of Fig. 3 is not such a transmission curve, because the principle of 

 superposition does not apply and a frequency conversion is involved. 



Owing to the considerations discussed above, the analysis to follow avoids 

 the assumption of variable impedance associated with the varying 

 instantaneous frequency. This does not imply that the assumption, as 

 employed by various writers, is considered seriously erroneous, but, rather, 

 that it seems preferable to develop the theory without invoking the as- 

 sumption, provided that this can be done without faUing into unmanageable 

 comphcations. Briefly, the procedure in the work to follow is to determine 

 directly the envelopes of the voltages Vi and V2 as functions of time, one 

 envelope then being subtracted from the other to obtain the output W5,ve. 



Fig. 4 — Current wave out of limiter. 



General Theory 



When a carrier is being received, the limiter can be regarded as substanti- 

 ally a constant current source having an internal shunt admittance small 

 compared to the admittance of the tuned impedance elements, Zi and Z2 , 

 of the frequency detector. If the hmiting is severe, as it should be for good 

 operation, the current deUvered by the limiter is a rectangular wave as 

 illustrated in Fig, 4. When this current is driven through the impedances, 

 Zi and Z2 , the voltage drops, Vi and V2 , that arise across these elements 

 are substantially sinusoidal in form, owing to the selectivity, which practi- 

 cally extinguishes all harmonics of the carrier frequency. We therefore take 

 the current input to be sinusoidal in the first place, namely 



/(/) = h cos lirfol 



This is the unmodulated current, 7r///4 being the current cutoff point of the 

 Umiter and /o the frequency of the carrier. When the carrier is modulated 

 in frequency, we write 



/(/) = h cos [lirfol + e{l)\ iX) 



where 6{t) is the phase angle varying with time. The instantaneous fre- 

 quency then is 



/(/) =^j^ 12tU + e{i)] = /o + ^ m- 



(2) 



