220 BELL SYSTEM TECHNICAL JOURNAL 



The modulator used employs two vacuum tubes and its circuit is 

 arranged to suppress the carrier frequency together with certain 

 higher order modulation components in the modulator output. 

 These together with other higher order modulation components which 

 are not eliminated in this type of balanced modulator could produce 

 false indications of frequency components in the wave to be analyzed, 

 but it will be shown in the Appendix that these errors may be reduced 

 to any desired extent by keeping the magnitude of the wave to be 

 analyzed as low as is consistent with securing satisfactory meter 

 readings. 



The suppression of the carrier wave is desirable in that it makes it 

 possible to carry the analysis to lower frequencies than could be done 

 if the carrier frequence were present. When analyzing low frequencies, 

 the frequencies of the carrier wave and the lower sideband approach 

 each other and if the relatively large carrier were present in the out- 

 put of the modulator it would tend to obscure the results. 



It will readily be seen that since the resonant frequency of the tuned 

 circuit is 11,000 c.p.s. and since the frequency discrimination at low 

 frequencies depends upon the sharpness of resonance of this circuit, 

 extremely sharp tuning is necessary. The considerations here differ 

 somewhat from the ordinary considerations in tuned circuits where 

 the effect of the resonance depends upon a percentage departure from 

 the resonant frequency. The reactance-resistance ratio, Q, which is 

 in common use in the treatment of electrical circuits, gives a measure of 

 what we may call the percentage sharpness of tuning of a circuit, that is, 

 with a given value of Q, a given percentage departure from the resonant 

 frequency will cause the same loss independent of the resonant fre- 

 quency. While it is possible at frequencies from 10,000 to 20,000 c.p.s. 

 to obtain higher values of Q than at frequencies from 100 to 1,000 c.p.s., 

 it is not feasible to secure the same loss with a given departure in 

 cycles from the resonant frequency at high frequencies as it is at low 

 frequencies. It is evident that in this method of analysis we are not 

 concerned with a percentage departure in frequency from the resonant 

 frequency of the tuned circuit but are concerned with the loss in trans- 

 mission through this circuit per cycle departure from the resonant 

 frequency. Therefore, inasmuch as we would desire to have good dis- 

 crimination between a frequency of 100 c.p.s. and one of 110 c.p.s., the 

 requirements of the 11,000 c.p.s. resonant circuit are extremely rigid. 



Some consideration was first given to the design of an electrical net- 

 work which would give sufficiently sharp tuning. At best, such a net- 

 work required a considerable number of coils and condensers and these 

 coils would require higher values of Q than could be obtained economi- 



