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BP.I.L SYSTEM TECHNICAL JOURNAL 



instant, for example, the directly transmitted field may be repre- 

 sented by ai in this figure, x^ssuming a difference in length of path, 

 we may compute on the basis of the integral equation (13), the rela- 

 tive phase position of the vector representing the indirectly trans- 

 mitted field bi. The relative amplitude of this vector may also be 

 determined by substituting A0 in equation (Ic). 



After establishing a sufficient number of vectors to represent the 

 cyclic variation we may combine the respective components to obtain 

 the resultant representative of the successive instants. These are 



♦.H9lV 



K-mh' 



A 



♦.•213 V 



♦. Z36V 



Fig. 47 — Synthetic wave forms showing distortion due to frequency modulation 



shown as Ri, Ri, Rz, etc., a broken line being drawn through their 

 extremities to identify their positions. Now, if we plot these re- 

 sultants as vertical ordinates in their successive time relation as 

 shown on the lower right of Fig. 46, we have the envelope of the 

 resultant wave at the receiver. 



When the mean position of the two vectors (a) and (b) in Fig. 27 is 

 180 degrees separation, the signal is experiencing a fading minimum. 

 When they are on the average in phase the amplitude is at a maximum. 

 We can, therefore, trace a relation between quality distortion and 

 fading by such an analysis, assuming a constant percentage modula- 

 tion. Fig. 47 shows a series of high-frequency wave envelopes ob- 

 tained by this method of graphic analysis. The mean vector rela- 

 tion is represented by 4>o, and for <^o = 180 degrees the fading may be 

 considered at a minimum. The waves shown in Fig. 47 being en- 

 velopes of the^high frequency will undergo certain changes in the 

 process of detection. These, however, would only slightly modify 

 the wave. 



