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how to generate barcode in ssrs report MUTUAL INDUCTANCE AND TRANSFORMERS in Software
MUTUAL INDUCTANCE AND TRANSFORMERS Recognize QR Code ISO/IEC18004 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Making QR Code In None Using Barcode maker for Software Control to generate, create Denso QR Bar Code image in Software applications. [CHAP. 14
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(see Section 10.7). But V1 E1 aE2 aV2
and so, a being real, V1 I2 a V2 I1 The input impedance is readily obtained from relations (15): Zin V1 aV2 V a2 2 a2 Z L I1 I2 =a I2 16 15 Fig. 1413 CHAP. 14] MUTUAL INDUCTANCE AND TRANSFORMERS
EXAMPLE 14.6 The ideal transformer may be considered as the limiting case of the linear transformer of Section 14.7. Thus, in (14a) set R1 R2 X11 X22 0 (no losses) and then let XM ! 1 (in nite core permeability), to obtain jXM =a ZL Zin lim a2 a2 ZL XM !1 jXM =a ZL in agreement with (16) AmpereTurn Dot Rule Since a N1 =N2 in (15), N1 I1 N2 I2 that is, the ampere turns of the primary equal the ampere turns of the secondary. A rule can be formulated which extends this result to transformers having more than two windings. A positive sign is applied to an ampereturn product if the current enters the winding by the dotted terminal; a negative sign is applied if the current leaves by the dotted terminal. The ampereturn dot rule then states that the algebraic sum of the ampereturns for a transformer is zero. EXAMPLE 14.7 The threewinding transformer shown in Fig. 1414 has turns N1 20, N2 N3 10. given that I2 10:0 53:138 A, I3 10:0 458 A. With the dots and current directions as shown on the diagram, Find I1 Fig. 1414 N1 I1 N2 I2 N3 I3 0 from which 20I1 10 10:0 53:138 10 10:0 458 I1 6:54 j7:54 9:98 49:068 A AUTOTRANSFORMER
An autotransformer is an electrically continuous winding, with one or more taps, on a magnetic core. One circuit is connected to the end terminals, while the other is connected to one end terminal and to a tap, part way along the winding. Referring to Fig. 1415(a), the transformation ratio is V1 N1 N2 a 1 V2 N2 which exceeds by unity the transformation ratio of an ideal twowinding transformer having the same turns ratio. Current I1 through the upper or series part of the winding, of N1 turns, produces the ux 1 . By Lenz s law the natural current in the lower part of the winding produces an opposing ux MUTUAL INDUCTANCE AND TRANSFORMERS
[CHAP. 14
Fig. 1415 2 . Therefore, current In leaves the lower winding by the tap. The dots on the winding are as shown in Fig. 1415(b). In an ideal autotransformer, as in an ideal transformer, the input and output complex powers must be equal. 1 2 V1 I1
1 V1 I 1 V2 I L ab 2 2 IL a 1 Iab
whence
That is, the currents also are in the transformation ratio. Since IL Iab Icb , the output complex power consists of two parts: 1 2 V2 IL
1 V2 I 1 V2 I 1 V2 I a 1 V2 I ab cb ab ab 2 2 2 2
The rst term on the right is attributed to conduction; the second to induction. Thus, there exist both conductive and magnetic coupling between source and load in an autotransformer. REFLECTED IMPEDANCE
A load Z2 connected to the secondary port of a transformer, as shown in Fig. 1416, contributes to its input impedance. This contribution is called re ected impedance. Using the terminal characteristics of the coupled coils and applying KVL around the secondary loop, we nd V1 L1 sI1 MsI2 0 MsI1 L2 sI2 Z2 I2 By eliminating I2 , we get Fig. 1416 CHAP. 14]

