Bulletin . magnetic circuit, it is of interest to considerthe action of such a transformer without iron. The air core type willbe discussed first, since its operation can be expressed by a mathematicalequation, and thus clear insight into the whole problem can readily begiven. As has already been explained, a series transformer is a mutual in-ductance where the effect of the secondary circuit upon the primary cur-rent is so small as to be negligible. Since the secondary circuit is closedupon itself, the differential equation of the circuit becomes, X2 — + r3 i + Xu — = e = 0 (29) d0 cl6 K Wher
Bulletin . magnetic circuit, it is of interest to considerthe action of such a transformer without iron. The air core type willbe discussed first, since its operation can be expressed by a mathematicalequation, and thus clear insight into the whole problem can readily begiven. As has already been explained, a series transformer is a mutual in-ductance where the effect of the secondary circuit upon the primary cur-rent is so small as to be negligible. Since the secondary circuit is closedupon itself, the differential equation of the circuit becomes, X2 — + r3 i + Xu — = e = 0 (29) d0 cl6 K Where r2, X2, and i are the resistance, reactance, and current in thesecondary circuit; XM is the mutual inductive reactance between theprimary and secondary circuit?; and i is the primary current. As stated above i is not affected by x and therefore —— is not a function (19 of i, and the single differential equation is sufficient for the solutionof the problem. Anderson-Woodrow—Series Transformers 25. 20 40 60 80 100 PER CENT FULL LOAD PRIMARY CURRENT Fig. 12. Variation in Phase Angle withStrength of Primary Current If the primary current i contains a transient term, as the startingalternating current in an inductive circuit, A [ sin ( 9 — s ) — sin ( 9X — s ) e^ J (30) Where A = the maximum value of voltage across the primary divided by the primary impedance = — , a = — , s = arc tan —, 6>i is Z x\ a the angular displacement of the voltage from its zero position when the circuit is closed, and 9 is the time in electrical radians counted from the time of closing the circuit, or 9 = ( 6 — 9\). Differentiating equation (30) di — = A(19 cos (9 — s ) + «sin(0 — s) e~at Equation (31) substituted in equation (29) gives diX2 — 4- r2 i =(19 X*A cos ( 9 — s ) + a sin ( 0X — s ) ea6K (31) (32) Equation (32) is easily written in the familiar formJm A di — + hi(19 X7 cos (9 — s ) + a sin ( s ) ea* (33) ri Where the factor — is replaced by b Jl2 26
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Keywords: ., bookcentury1900, bookdecade1900, booksubjectenginee, bookyear1904
