TAILIEUCHUNG - Electric Circuits, 9th Edition P77

Electric Circuits, 9th Edition P77. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 736 More on Magnetically Coupled Coils and Ideal Transformers continuously the use of a capacitor to simulate negative inductance is practically worthless. You can circumvent the problem of dealing with negative inductances by introducing an ideal transformer into the equivalent circuit. This doesn t completely solve the modeling problem because ideal transformers can only be approximated. However in some situations the approximation is good enough to warrant a discussion of using an ideal transformer in the T- and r-equivalent circuits of magnetically coupled coils. An ideal transformer can be used in two different ways in either the T-equivalent or the -equivalent circuit. Figure C. 12 shows the two arrangements for each type of equivalent circuit. Verifying any of the equivalent circuits in Fig. requires showing only that for any circuit the equations relating vx and v2 to di-Jdt and di2 dt are identical to Eqs. and . Here we validate the circuit shown in Fig. a we leave it to you to verify the circuits in Figs. b c and d .To aid the discussion we redrew the circuit shown in Fig. a as Fig. adding the variables and v . From this circuit M dix M d z. - I L I Tt 01 io y a dt a dt and L2 m ditt Md I---------- i ---------7 vo Z1 - y a2 a J dt a dt d a LxL2 - M2 J2 a LxL2-M2 a2L - Ma p Figure The four ways of using an ideal transformer in the T- and 77-equivalent circuit for magnetically coupled coils. a Figure The circuit of Fig. a with z and v defined. The Need for Ideal Transformers in the Equivalent Circuits 737 The ideal transformer imposes constraints on v and i v2 z0 ai2. Substituting Eqs. and into Eqs. and gives Vj di M d x 2 dt a dt and 2 a L2 d . M di -y ai2 -L. a2 dt a dt From Eqs. and dii di- L 1 M- dt dt and V2 di di2 M- L2-A dt dt Equations and are identical to Eqs. and thus insofar as terminal behavior is concerned .

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