ANALYZER FOR THE VOICE FREQUENCY RANGE 111 



of the modulator. Equation (3) shows the output of one of the tubes, 

 but the output for the other tube in which the voice input is reversed 

 will be 

 /2 = ^o+^i(a-&)+^2(a--2a6 + i2)+^g(^3_3^2j_^3^^2_^3) 



If the circuits of the two tubes are exactly balanced, then since the 

 output of the modulator is so connected that only the algebraic differ- 

 ence of the two plate currents will appear, all of the frequencies arising 

 from the terms of like sign in equations (3) and (4) will be suppressed 

 or, subtracting equation (4) from equation (3), the resultant current 

 will be 



/i_/2= +2^i6+^2( + 4aZ>)+/l3( + 6a26 + 2&'^)+^4( + 8a'^6 + 8a6'^). (5) 



The frequency components arising from the various terms of equation 

 (5) are shown in Table 2. 



TABLE 2 

 Frequency Components Arising from Algebraic Difference of /i — h 



2 AiQ cos (qt - <f>) 



2 AiPQ cos lipt - e) ± (qt -</))] 



3 A sP^Q cos (qt - (t>) 



3/2 A3P-Q cos l{2pt - 26) ± (qt - q!.)] 

 1/2 AiQ^ cos I3qt - 3<^] 

 3/2 AiQ^ cos (qt - 4,) 



AiP^Q cos l(3pt - 36) ± (qt - <^)] 

 3 AiP^Q cos l(pt - 6) ± (qt -</>)] 

 3 AiPQ' cos l(pt - 6) ± (qt - <^)] 

 A4PQ' cos l(pt - 6) ±: (3qt - 30)] 



In the analyzer the only useful order of modulation is the second, 

 that is, the frequencies arising from the A2 term of equation (1). The 

 component of interest here is the term lAnPQ cos [(/>/ ~ 6) — (g/ — <A)]- 

 As can be seen, this frequency component is proportional to both P 

 and Q and for a given value of P is proportional to Q. In other words 

 the input into the tuned circuit is a linear function of the magnitude 

 of the particular frequency component under consideration in the wave 

 to be analyzed. As will be seen from Table 2, there are a number of 

 other frequency components due to the various orders of modulation in 

 the modulator output. A little consideration, however, will show that 

 a number of these components cannot appear in the output of a resonant 

 circuit tuned to approximately 11,000 c.p.s. where the upper frequency 

 limit of the voice input is 5,000 c.p.s. and the range of the carrier 

 oscillator is limited from the resonant frequency of the tuned circuit 

 to 5,000 c.p.s. above. The only components of Table 2 which can be 

 passed by the tuned circuit are: 



