EE203-SUNYBuffalo-08-Chapter09-06

EE203-SUNYBuffalo-08-Chapter09-06 - SMALL for Big Things...

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Unformatted text preview: SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Recall: Ch 4. Mesh-Current Method EE 203 Circuit Analysis 2 Lecture 08 Chapter 9.9 Mesh-Current Method Kwang W. Oh, Ph.D., Assistant Professor SMALL (Nanobio Sensors & MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 1/12 Step Step 1: Assign a current in each mesh in an arbitrary direction Step 2: Show polarities according to the assigned direction of current in each each mesh Step 3: Apply KVL around each Step closed mesh M1 : − v1 + ia R1 + (ia − ib ) R3 = 0 M1 : v2 + (ib − ia ) R3 + ib R2 = 0 Step 4: Solve the resulting equations for the mesh currents EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 2/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.12 EE 203 Circuit Analysis 2 Lecture 08 Chapter 9.10 Transformer Mesh 1: KVL Mesh 2: KVL Kwang W. Oh, Ph.D., Assistant Professor SMALL (Nanobio Sensors & MicroActuators Learning Lab) Department of Electrical Engineering University at Buffalo, The State University of New York 215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920 Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656 kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 3/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 4/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Transformer Linear Transformer Transformer: A device that is based on magnetic coupling Linear Transformer found primarily in communication circuits in communication to match impedances and eliminate DC signals from portions of the system Ideal Transformer used to model the ferromagnetic transformer found in power circuits in power circuits to establish ac voltage levels that facilitate the transmission, distribution, and consumption of electrical power When When analyzing circuits containing mutual inductance use the mesh- or loop-current method for writing circuit equations. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo VS = the internal voltage of the sinusoidal source ZS = the internal impedance of the source ZL = the load connected to the secondary winding of the transformer I1 = the primary phasor current I2 = the secondary phasor current Lecture 08 | Chapter 09 | 6/7 | 5/12 M = k L1 L2 , k : coefficient of coupling li EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 6/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Linear Transformer Linear Transformer Vs/I1( Mesh-current equations Zint) Let Self-impedance of the mesh containing the primary winding Self-impedance of the mesh containing the secondary winding the impedance seen looking into the primary terminals of the transformer Zab= Zint- Zs Then, EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Impedance at the terminals (ab) of the source Lecture 08 | Chapter 09 | 6/7 | 7/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 8/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.13 (1) Reflected Impedance Reflected Impedance Zr M = k L1 L2 the impedance of the primary winding Reflected Impedance (Zr) The equivalent impedance of the secondary coil and load impedance transmitted, or reflected, to the primary side of the transformer Due solely to the existence of mutual inductance (if M 0, then Zr 0) j ωM c R2 R1 L1 Z11 The linear transformer reflects the conjugate of the self-impedance of the secondary secondary circuits (Z22*) into the primary winding by (ωM/|Z22|)2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 9/12 L2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Z22 d Lecture 08 | Chapter 09 | 6/7 | 10/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York Nanobio Sensors & MicroActuators Learning Lab The State University of New York Example 9.13 (2) Example 9.13 (2) b) the self-impedance of the primary circuits is f) f) the impedance seen looking into the primary terminals of the transformer = the impedance of the primary winding + the reflected impedance = (R1 + jωL1) + (Zr) c) the self-impedance of the secondary circuits is g) The Thévenin voltage will equal the open circuit value of Vcd. The open circuit value of Vcd will equal j1200 times the open circuit value of I1. The open circuit cd value of I1 is d) the impedance reflected into the primary winding is The Thévenin impedance will be Equal to the impedance of the secondary winding plus the impedance reflected from the primary when the voltage source is replaced by a short-circuit. Thus e) the scaling factor for the reflected impedance The scaling factor by which Z*22 is reflected is 8/9 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 11/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 08 | Chapter 09 | 6/7 | 12/12 ...
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