TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1339 



lust evaluate 20 logio ( 1 + a). The quantity loge (1 + a) can be ex- 

 )anded in a series to give 



loge (1 + a) =a — -a-\--a+ • • • . 



A.S long as a <3C 1, we can approximate it by taking only the first term of 

 the above expression. Converting to the base ten and converting Ad 

 Prom radians as it appears in (6) to degrees, we find that 



k. 



0.152 



Ad (in degrees) 

 A input level (in db) 



(7) 



Now let us consider the case in which the signal of Fig. 41 is put 

 through an amplifier having AM-to-PM conversion. Fig. 43 shows the 

 vector picture of the resulting signal after the level of the signal at /i 

 has been brought back to amplitude A. In this case the original PM 

 sidebands and the compressed AM sidebands are the same as in Fig. 42, 

 but there is now an additional set of PM sidebands as a result of the AM- 

 to-PM conversion. Since the peak deviation of output phase due to this 

 latter set of sidebands comes when the instantaneous amplitude is either 

 a maximum or a minimum, they are 90 degrees out of phase with the 

 other two sets of sidebands. From Fig. 43 it is seen that we can write 





PM VECTORS 



GENERATED BY 



AMPLIFIER 



AM 

 VECTORS 



PM 

 VECTORS 



(a) 



o j » o ) » 



ys. 





Fig. 43 



(a) After passing through an amplifier having both compression and amplitude 

 to phase conversion, the AM vectors are reduced in magnitude and a new set of 

 PM vectors have appeared. 



(b) The locus of the resultant signal of the vectors shown above is elliptical but 

 the axis is tilted with respect to vector A. 



