TRANSIENT RESPONSE OF AN FM RECEIVER 715 



reduced to the circuit shown schematically in Fig. 1, which can be taken to 

 illustrate a generic form of frequency detector. Zi and Z2 are two resonant 

 impedances tuned to different frequencies, one above, the other below, the 

 carrier frequency. ^ For example, the simplest version of Zi and Z2 could be, 

 for each, a parallel combination of i?, L and C. Across each of these 

 impedances is connected a rectifier with load circuit so proportioned that 

 the rectification is substantially linear. The rectifiers are poled so that their 

 low-frequency outputs are opposed, thereby obtaining cancellation of even- 

 order demodulation products. With this arrangement, the low-frequency 

 output voltage Fo, which is apphed to the audio amphfier, is substantially 

 proportional to the difference between the envelopes of the voltage drops 

 across Zi and Z^. 



The resistance elements of the impedances, Zi and Z2, each include a shunt- 

 ing resistance equal to half the load resistance of the associated rectifier, 

 which therefore determines, to some extent, the Q of the tuned circuit. The 

 output diode load, i?o Co, has negHgible impedance at the carrier frequency. 

 Under these conditions, the low-frequency output voltage across the two- 

 rectifier load impedances is 



Vo = V {[Vi] - IV2]) 



where 77 = detection efficiency (nearly unity) 



Fi , F2 = high-frequency voltages across Zi , Z2 , respectively (Fig. 1) 



[F] = envelope of F. 

 All this is in accord with the accepted understanding of the operation of a 

 properly designed linear rectifier working at an efficiency approaching 100 

 per cent. 



The amplitudes of the voltages, Vi and F2 , across the resonant imped- 

 ances, Zi and Z2 , of Fig. 1 are shown in Fig. 2. In the practical engineering 

 analysis of this frequency detector circuit, employing the idea of impedance 

 that varies in step with the instantaneous frequency, the two voltages of 

 Fig. 2 are subtracted (owing to the opposed polarities of the rectifiers) to 

 obtain the over-all voltage-frequency characteristic shown in Fig. 3. Then 

 it is inferred, by physical intuition, that if the instantaneous frequency of 

 the carrier is varied at the input, the output voltage wave will vary as in- 

 dicated by the curve of Fig. 3. Strictly speaking, this is a false assumption, 

 but where the rate of variation of the instantaneous frequency is at an audio 

 signal frequency far below the carrier frequency, the error in the assump- 

 tion is of no importance, whereas the simplification in thinking accomphshed 



2 The term carrier frequency will be used to designate the value of the unmodulated 

 received frequency after all heterodyne conversions. (This frequency is equal to the mid- 

 band frequency of the last intermediate frequency amplifier ahead of the limiter, if tuning 

 is perfect.) 



