EE203-SUNYBuffalo-21-Chapter13-02

EE203-SUNYBuffalo-21-Chapter13-02 - 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 Step Response (DC) of a Parallel Circuit (1) EE 203 Circuit Analysis 2 Lecture 21 Chapter 13.3 Applications (continued) 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 21 | Chapter 13 | 2/8 | 1/11 Parallel RLC circuit See Example 8.8: to find the expression for iL after the constant current source is switched across the parallel elements. The initial energy stored in the circuit is zero. Constructing the s-domain equivalent circuit Idc: independent source R: resistor L: inductor C: capacitor EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 2/11 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 Step Response (DC) of a Parallel Circuit (3) Step Response (DC) of a Parallel Circuit (2) Constructing Constructing the s-domain equivalent circuit I dc = IC + I R + I L s (V = IZ ∴ I = V ) Z Idc: independent source sou dc Switching OFF a step change in the current applied to the circuit I 11 + ) = dc R sL s I dc I dc s s C V= = 1 1s s 1 2 s+ sC + + + R sL RC LC V ( sC + C: capacitor Z = 1/sC Ohms R: resistor Z = R Ohms L: inductor Z = sL Ohms If V0 is zero EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo If I0 is zero Lecture 21 | Chapter 13 | 2/8 | 3/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 4/11 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 Transient Response (AC) of a Parallel RLC Circuit (1) Step Response (DC) of a Parallel Circuit (4) AC current source Constructing Constructing the s-domain equivalent circuit × s s =0 × ( s + 32000 − j 24000) s = −32000+ j 24000 Ig: independent source C: capacitor R: resistor L: inductor EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 5/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 6/11 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 Transient Response (AC) of a Parallel RLC Circuit (2) I g V= Transient Response (AC) of a Parallel RLC Circuit (3) s Ig s C = 1 1s 1 s 2 sC + + + s+ R sL RC LC EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 7/11 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 8/11 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 Appendix A: Solution of Linear Simultaneous Equations EE 203 Circuit Analysis 2 Lecture 21 pp Appendix A Matrix 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 a11 x1 + a12 x2 = c1 a21 x1 + a22 x2 = c2 a11 a12 x1 c1 = a21 a22 x2 c2 Δ= EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 9/11 SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York Example: Solution of Linear Simultaneous Equations Matrix 42 + 8.4 s − 42 I1 336 s ⎧(42 + 8.4 s ) I1 − 42 I 2 = 336 s ⇒ = ⎨ 90 + 10 s I 2 0 − 42 ⎩ − 42 I1 + (90 + 10 s ) I 2 = 0 − 42 42 + 8.4 s Δ= = (42 + 8.4 s )(90 + 10 s ) − (−42)(−42) − 42 90 + 10 s = 84( s 2 + 14 s + 24) = 84( s + 2)( s + 12) 336 s − 42 0 90 + 10 s N (336 s )(90 + 10 s ) − ( − 42)(0) 40( s + 9) I1 = 1 = = = 42 + 8.4 s − 42 Δ 84( s + 2)( s + 12) s ( s + 2)( s + 12) − 42 90 + 10 s 42 + 8.4 s 336 s I2 = − 42 0 (42 + 8.4 s )(0) − (336 s )(−42) 168 N2 = = = 42 + 8.4 s − 42 84( s + 2)( s + 12) Δ s ( s + 2)( s + 12) − 42 90 + 10 s EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 21 | Chapter 13 | 2/8 | 11/11 2 x 2 Matrix Matrix Matrix 2 1 x1 0 = 1 1 x2 − 1 a11 a12 21 Characteristic = a11a22 − a12a21 Determinant Δ = = 2 ×1 − 1×1 = 1 a21 a22 11 N1 = c1 c2 N2 = a11 c1 = a11c2 − c1a21 a21 c2 x1 = Two Linear 2 x + 1x = 0 1 2 Simultaneous 1x1 + 1x2 = −1 Equations a12 = c1a22 − a12c2 a22 N1 N , x2 = 2 Δ Δ Numerator Determinant Cramer ’s Method N1 = 01 = 0 × 1 − 1 × (− 1) = 1 −1 1 N2 = 2 1 −1 1 x1 = = 1, 1 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo 0 = 2 × (− 1) − 0 × 1 = −2 x2 = −2 = −2 1 Lecture 21 | Chapter 13 | 2/8 | 10/11 ...
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This note was uploaded on 10/19/2011 for the course EE 203 taught by Professor Staff during the Spring '08 term at SUNY Buffalo.

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