ANALYZER FOR THE VOICE FREQUENCY RANGE 225 



A number of other uses of the analyzer in acoustic measurements 

 might be cited; for instance, the output of a transmitter at one partic- 

 ular frequency may be measured in the presence of room noises or other 

 disturbing sounds. In general its high selectivity, convenience of 

 operation and portability make the analyzer an extremely valuable in- 

 strument in a wide variety of acoustic and electrical measurements. 



Appendix 



Inasmuch as the incorrect operation of the modulator could give 

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

 it may be of interest to take up some of the more important aspects of 

 the theory of the vacuum tube plate current modulator as applied to 

 this. analyzer.' In general, the output of a vacuum tube is of the form 



I,=Ao + AiE + A^E^ + AsE' + A^E' + etc., (1) 



where E is the voltage applied between the cathode and grid of the 

 tube and the coefficients Ao, Ai, A^, A3, etc., depend upon the average 

 potential of the grid, the constants of the tube itself and the total 

 impedance of the output circuit to the various frequency components 

 appearing in the output. If we apply two voltages of the form 

 P cos (pt — 6) and Q cos (5/ — <^) simultaneously to the input of a 

 vacuum tube, the above general expression will have the form 



/i = ^0 + AilP cos {pt - e) -\- Q cos {qt - </))] 

 + A^IP cos {pt - e) + Q cos {qt - 4>)J 

 + AzlP cos {pt - e) + Q cos {qt - <i>)J 

 + Ai[_P cos {pt - 6) + Q cos {qt - 0)]^ etc. 



(2) 



For simplicity let o = P cos {pt — 6) and b = Q cos {qt — 0) and 

 then expanding algebraically we obtain 



Ii=Ao-{-Ai{a + b)+A2{a-'+2ab-\-b'')-\-As{a'-\-3a^b-]-3ab^-\-¥) 



-\-Ai{a^-\-4:a'b+6a''b^+4:ab^+b')+ etc. 



Now substituting P cos {pt — 9) and Q cos {qt — 0) for a and b re- 

 spectively and simplifying trigonometrically, the frequencies appearing 

 in the output of the tube are shown in Table 1. 



If we employ a balanced modulator of the type shown in Fig. 7, 

 certain frequency components shown in the table are eliminated. In 

 this modulator the voice input transformer is so connected as to 



' For a more complete discussion of the vacuum tube modulator see Proceedings 

 I. R. E., April 1919; "A Theoretical Study of the Three Element Vacuum Tube," by 

 J. R. Carson. 



