tailieunhanh - Electric Circuits, 9th Edition P37

Electric Circuits, 9th Edition P37. 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. | 336 Sinusoidal Steady-State Analysis To the internal source voltage Vs the impedance appears as Vj Ij or vs _ _ ZhZ22 á-M- _ a -M T - zint 7 - Z11 7 1 z22 z22 The impedance at the terminals of the source is Zint Z5 so n . T w2M2 Zab - 11 H O LX _L -7 X 9-64 z22 R2 j l2 ZL Note that the impedance Zab is independent of the magnetic polarity of the transformer. The reason is that the mutual inductance appears in Eq. as a squared quantity. This impedance is of particular interest because it shows how the transformer affects the impedance of the load as seen from the source. Without the transformer the load would be connected directly to the source and the source would see a load impedance of ZL with the transformer the load is connected to the source through the transformer and the source sees a load impedance that is a modified version of ZL as seen in the third term of Eq. . Reflected Impedance The third term in Eq. is called the reflected impedance Zr because it is the equivalent impedance of the secondary coil and load impedance transmitted or reflected to the primary side of the transformer. Note that the reflected impedance is due solely to the existence of mutual inductance that is if the two coils are decoupled M becomes zero Zr becomes zero and Zab reduces to the self-impedance of the primary coil. To consider reflected impedance in more detail we first express the load impedance in rectangular form ZL Rl JVL where the load reactance XL carries its own algebraic sign. In other words XL is a positive number if the load is inductive and a negative number if the load is capacitive. We now use Eq. to write the reflected impedance in rectangular form z _ 2M2 R2 RL j o L2 AjJ _ a 2M2 R2 L - 2 l R2 Rl 2 uL2 XL 2 2 j 2 7 l 2 l - 7 2 lZ22l The derivation of Eq. takes advantage of the fact that when ZL is written in rectangular form the self-impedance of the mesh containing the secondary winding is Z22 R2 L . .

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