Transient Response of an FM Receiver 



By MANVEL K. ZINN 

 Introduction 



THIS paper develops various formulas for the response of an FM 

 receiver to signal or noise input voltages of arbitrary form. The prin- 

 cipal object in view is to obtain a more complete understanding of how an 

 FM receiver responds to transient voltages, such as those arising from 

 ignition interference, but the more general aspects of the theory have other 

 applications as well. In particular, general formulas are given for the re- 

 sponse of a linear circuit to an applied voltage, or current, of variable fre- 

 quency. The Fourier transforms, or frequency spectra, of the response, and 

 the envelope thereof, are determined. 



Two examples are given: (1) the audio response of an FM receiver to a 

 very large impulse and (2) the response, including harmonic distortion, to 

 a sinusoidal signal wave. 



The element of an FM receiver that demands most discussion is the bal- 

 anced frequency detector. The greater part of the paper accordingly deals 

 with that important element. The general problem can be stated as follows : 

 A limiter and frequency detector are transmitting a steady unmodulated 

 carrier wave to an audio output circuit. At time, / = 0, frequency modula- 

 tion of arbitrary form is applied to the carrier (either by signal modulation or 

 a superposed noise transient) . What is the audio output voltage that re- 

 sults? 



Frequency Detector 



Except for the greater bandwidth, the amplifiers and selective circuits 

 between the antenna and the limiter of an FM receiver are similar to those 

 of an AM receiver in their transmission features. If the selective circuits 

 have a bandwidth ample to accommodate the maximum frequency swing of 

 the FM transmitter, and if the transmission over the band is substantially 

 "flat" and the phase shift nearly linear with frequency, the amplifiers will 

 introduce little distortion. The limiter and frequency detector are therefore 

 regarded as the distinctive elements of an FM receiver meriting theoretical 

 discussion. 



The literature contains descriptions of frequency detectors of several 

 types together with adequate analyses of the action of the circuits based on 

 the variable impedance concept.^ The more generally used circuits can be 



^ See Items 3 to 6 in list of references attached. 



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