480 BELL SYSTEM TECHNICAL JOURNAL 



The balanced voltages in a three-phase power system form a sym- 

 metrical set of vectors equal in magnitude and 120 degrees apart in 

 phase or may be readily analyzed into two such symmetrical sets of 

 vectors. In either case, of course, the vector sum is equal to zero. In 

 spite of this symmetry of voltages the induction to another conductor 

 from the three balanced voltages is not necessarily zero since the 

 coupling between each power wire and any other wire such, for example, 

 as a wire of a telephone circuit, depends largely on its position with 

 respect to such other wire. Since the spacings of the power conductors 

 must be sufficient to provide adequate insulation, the distances from 

 the various power conductors to the telephone conductor will usually 

 be different and the inductions from these conductors will, therefore, 

 be different and will not total zero. If the positions of the power 

 conductors are rotated 120 electrical degrees periodically, however, the 

 induction from the balanced components tends to be neutralized in 

 each three successive equal lengths since the telephone line is thus 

 exposed equally to all of the power wires. Such an arrangement of 

 three successive equal lengths with two transpositions between them is 

 called a transposition "barrel." The action of a barrel in neutralizing 

 induction into adjacent circuits due to balanced voltages is illustrated 

 in Fig. 5. It can be seen from this figure that the phase of the induc- 



SECTION I SECTION 2 SECTION 3 



TELEPHONE LINE 



TO AMPLIFIER 



AND 

 LOUDSPEAKER 



A - X\ {?-- 



RESULTANT INDUCTION / 



=£^0 SECTION I INDUCTION INDUCTION 



SECTION 2 SECTION 3 



Fig. 5 — Effect of power transpositions on induction due to balanced voltages. 



tion into an adjacent circuit is rotated 120 degrees by each transposition 

 so that in three sections the vector sum of the inductions would become 

 zero if the inductions from the sections were identical in magnitude 



