EE203-SUNYBuffalo-20-Chapter13-01

EE203-SUNYBuffalo-20-Chapter13-01 - 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 nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Procedure for Developing an s-Domain Equivalent Circuit EE 203 Circuit Analysis 2 Lecture 20 Chapter 13.1 Circuit Elements in s Domain Kwang W. Oh, Ph.D., Assistant Professor SMALL (nanobioSensors and 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 E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 1/12 First we First, we write the time-domain equation that relates the terminal voltage to the terminal current. Next, we take the Laplace transform of the time-domain equation. This step generates an algebraic relationship between the s-domain current and voltage. s (or Frequency) Domain Time Domain The dimension of a transformed voltage Volt-Seconds The dimension of a transformed current Ampere-Seconds An impedance in the s domain in Ohms Finally, we construct a circuit model that satisfies the relationship between the s-domain current and voltage. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 2/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York A Resistor in the s Domain An Inductor in the s Domain An inductor of L carrying an initial current of I0 amperes Ohm's law The Laplace transform Laplace transform The series equivalent circuit R is a constant. The parallel equivalent circuit If I0 is zero The s-domain equivalent circuit of a resistor is simply a resistance of R ohms that carries a current of I ampere-seconds and has a terminal voltage of V volt-seconds. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 3/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 4/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York A Capacitor in the s Domain A capacitor of C carrying an initial voltage of V0 volts The Laplace transform The series equivalent circuit The paralle equivalent circuit The parallel equivalent circuit EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 5/12 The series equivalent circuit EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo If V0 is zero Lecture 20 | Chapter 13 | 1/8 | 6/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York EE 203 Circuit Analysis 2 Lecture 20 Chapter 13.2 Circuit Analysis in s Domain Kwang W. Oh, Ph.D., Assistant Professor SMALL (nanobioSensors and 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 E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 7/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 8/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Circuit Analysis in the s Domain and also in the Frequency Domain All valid in the s Domain EE 203 Circuit Analysis 2 Lecture 20 Chapter 13.3 Applications All valid in the Frequency domain too! Ohms Law Ohms Law Resistor: Z = R Ohms Oh Inductor: Z = sL Ohms Capacitor: Z = 1/sC Ohms Kwang W. Oh, Ph.D., Assistant Professor SMALL (nanobioSensors and 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 E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.edu Kirchhoff’s Law Node Voltages Mesh Currents Source Transformations Thevenin-Norton equivalents V = j ωL I V= 1 1 I = j (− )I jωC ωC Kirchhoff’s Law, Node Voltages, Mesh Currents Source Currents, Source Transformations, Thevenin-Norton equivalents EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 9/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 10/12 SMALL for Big Things University at Buffalo SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York nanobioSensors & MicroActuators Learning Lab The State University of New York Recall: Chapter 7.2 Natural Response of an RC Circuit Series Parallel EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 11/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 20 | Chapter 13 | 1/8 | 12/12 ...
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