lab6-1 - Boise State University Department of Electrical...

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Boise State University Department of Electrical and Computer Engineering ECE 212L – Circuit Analysis and Design Lab Experiment #6: Transformers, Mutual Inductance, and Coupled Coils 1 Objectives The objectives of this laboratory experiment are: To observe the phenomenon of inductive coupling To perform polarity and turns ratio tests on a transformer To measure the self and mutual inductances of a transformer To measure the inductance of two coupled series-aiding or series-opposing coils 2 Theory Consider the two-winding shown in Figure 1(a) and assume that the primary winding is energized with a current i 1 while the secondary winding is open-circuited. The primary current i 1 creates a magnetic ﬂux ϕ 1 in the iron core with two components: A large portion of this primary ﬂux, the mutual ﬂux ϕ m 1 , is channeled through the magnetic core and links all turns of the secondary winding; A small portion of this primary ﬂux, the leakage ﬂux ϕ l 1 , links all turns of the primary winding but none of the turns of the secondary winding; These two ﬂuxes result in the following ﬂux linkages and inductances in each winding: λ 1 = N 1 ϕ 1 = N 1 ( ϕ l 1 + ϕ m 1 ) = L 1 i 1 (1) λ 2 = N 2 ϕ m 1 = L 21 i 1 (2) Similarly, assume that the secondary winding is energized with a current i 2 while the primary winding is open-circuited as shown in Figure 1(b). The secondary current i 2 creates a magnetic ﬂux ϕ 2 in the iron core with two components: A large portion of this secondary ﬂux, the mutual ﬂux ϕ m 2 , is channeled through the magnetic core and links all turns of the primary winding; A small portion of this secondary ﬂux, the leakage ﬂux ϕ l 2 , links all turns of the secondary winding but none of the turns of the primary winding; These two ﬂuxes result in the following ﬂux linkages and inductances in each winding: λ 1 = N 1 ϕ m 2 = L 12 i 2 (3) λ 2 = N 2 ϕ 2 = N 2 ( ϕ l 2 + ϕ m 2 ) = L 2 i 2 (4) 1

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v 1 N - 1 i * + * l1 m1 φ φ 1 + * φ 2 N 1 N (a) 2 - + v 2 N - * 1 N 2 i 1 i - v 1 - + * 2 v (d) (c) l2 l1 m2 m1 φ φ φ φ 2 N + 2 L * (b) 1 v 2 i 2 v - + l2 φ m2 * * 1 L M 2 i 1 i 2 v 1 v - - + + Figure 1: Tests for Measuring Transformer Self and Mutual Inductances (a)-(c) and Transformer Symbol (d) If both windings are energized simultaneously as in Figure 1(c), the resulting ﬂux linkages of each coil are given by: λ 1 = N 1 ( ϕ l 1 + ϕ m 1 + ϕ m 2 ) = L 1 i 1 + L 12 i 2 (5) λ 2 = N 2 ( ϕ m 1 + ϕ l 2 + ϕ m 2 ) = L 21 i 1 + L 2 i 2 (6)
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