EE203-SUNYBuffalo-06-Chapter09-04

EE203-SUNYBuffalo-06-Chapter09-04 - 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 Kirchhoff’s Voltage Law (KVL) in the Frequency Domain EE 203 Circuit Analysis 2 Lecture 06 Chapter 9.5 KVL & KCL in the Freq Domain KVL in the time domain 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 06 | Chapter 09 | 4/7 | 1/15 KVL in the frequency domain EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 2/15 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 Kirchhoff’s Current Law (KCL) in the Frequency Domain EE 203 Circuit Analysis 2 Lecture 06 Chapter 9.6 Series, Parallel, Delta-to-Wye KCL in the time domain KCL in the frequency domain EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 3/15 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 06 | Chapter 09 | 4/7 | 4/15 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 Current and Voltage Division Combining Impedances in Series and Parallel Series Parallel EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 5/15 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 6/15 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 9.6 Combining Impedance in Series Example 9.7 Combining Impedance in Series and in Parallel The phasor transform of vs is Z R1 = 10 Ω, Z R 2 = 6 Ω Vs = 750∠30° V Z L = jωL = j ( 200,000)( 40 × 10 −6 ) = j8 Ω Z R = R = 90 Ω 1 1 = = − j5 Ω jωC j ( 200,000)(1 × 10 −6 ) 1 1 1 1 1 1 1 =, = = , = Z1 10 Z 2 Z R + Z L 6 + j8 Z 3 − j5 ZC = Z L = jωL = j (5000)(32 × 10−3 ) = j160 Ω 1 1 =−j = − j 40 Ω jωC (5000)(5 × 10−6 ) Z ab = Z R + Z L + Z C = 90 + j160 − j 40 ZC = 1 1 1 1 1 1 1 = + + = + + Z eq Z1 Z 2 Z 3 10 6 + j8 − j5 6 − j8 j5 + (6 + j8)(6 − j8) ( − j5)( j5) 1 6 − j8 j 5 = + + = 0.1 + 0.06 − j 0.08 + j 0.2 10 100 25 = 0.16 + j 0.12 = 0.2∠36.87° S = 0.1 + = 90 + j120 = 150∠53.13°Ω 750∠30° V V = Z 150∠53.13° Ω 750 = ∠(30° − 53.13°) A = 5∠ - 23.13°A 150 ∴ i = 5 cos(5000t − 23.13°)A I= EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo ∴ Z eq = Lecture 06 | Chapter 09 | 4/7 | 7/15 1 1 = = 5∠ − 36.87° Ω 0.16 + j 0.12 0.2∠36.87° S EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 8/15 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 9.7 Combining Impedance in Series and in Parallel Δ-to-Y (π-to-T) Transformations (Recall Chapter 3.7) V = Z eq I = (5∠ − 36.87° Ω)(8∠0°A ) = 40∠ − 36.87° V ∴ I1 = V 40∠ − 36.87° = Z1 10 = 4∠ − 36.87° = 3.2-j 2.4 A ∴ I2 = V 40∠ − 36.87° 40∠ − 36.87° = = Z2 6 + j8 10∠53.13° = 4∠ − 90° = − j 4 A ∴ I3 = V 40∠ − 36.87° 40∠ − 36.87° = = Z3 − j5 5∠ − 90° Rab = Rc ( Rb + Ra ), Rbc = Ra ( Rb + Rc ), Rca = Rb ( Rc + Ra ) = 8∠53.13° = 4.8 + j 6.4 A EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 9/15 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 10/15 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 3.7 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Δ-to-Y (π-to-T) Transformations Lecture 06 | Chapter 09 | 4/7 | 11/15 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 12/15 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 9.8 Zad = Zan + Z nd = {( Zab + Z bn ) ( Zac + Zcn )} + Z nd = {( − j 4 + 12 + j 4) (63.2 + j 2.4 − j 2.4 − 3.2)} + (8 − j 2.4) = {12 60} + (8 − j 2.4) = Z1 Zc Zb Z2 Za I0 = V 120∠0° 120(18 + j 24) = = = 2.4 + j 3.2A Zad 18 − j 24 (18 − j 24)(18 + j 24) V nd = Z nd I 0 = ( 8 − j 24 )( 2 . 4 + j 3 . 2 ) = 96 − j 32 V Z3 ∴ V an = V − V nd = 120 − ( 96 − j 32 ) = 24 + j 32 V Za=-j 20 I 1 = I abn = Zc=10 Za+ Zb+Zc=30+j 40 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 13/15 SMALL for Big Things University at Buffalo Nanobio Sensors & MicroActuators Learning Lab The State University of New York V 1 = V − V ab = V − I 1 ( − j 4 ) 8 328 = 120 − ( 2 + j )( − j 4 ) = + j8 V 3 3 V 2 = V − V ac = V − I 2 ( 63 . 2 + j 2 . 4 ) 4 8 104 +j )( 63 . 2 + j 2 . 4 ) = 96 − j V 10 15 3 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 15/15 V an 24 + j 32 8 = =2+ j A Z abn 12 3 I 2 = I acn = Zb=20+j 60 = 120 − ( (12)(60) + (8 − j 2.4) = 18 − j 2.4 12 + 60 V an 24 + j 32 4 8 = = +j A Z acn 60 10 15 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 06 | Chapter 09 | 4/7 | 14/15 ...
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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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