EE203-SUNYBuffalo-29-Chapter14-02

# EE203-SUNYBuffalo-29-Chapter14-02 - 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 Two circuits that behave as low-pass filters EE 203 Circuit Analysis 2 Lecture 29 Chapter 14.2 Low-Pass Filter 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: [email protected], http://www.SMALL.Buffalo.edu EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 1/12 The series RL circuit Transfer function Cutoff frequency The series RC circuit Transfer function Cutoff frequency EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 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 The Series RL Circuit for Low-Pass Filter The Series RC Circuit for Low-Pass Filter Transfer function H(s) R V R RL Vo = Vi ⇒ H ( s ) = o = = Vi sL + R s + R L sL + R RL RL ∴ H ( jω ) = ⇒ H ( jω ) = 2 jω + R L ω + ( R L) 2 ω ω ω Transfer function H(s) V 1 sC 1 sC 1 RC Vo = Vi ⇒ H ( s ) = o = = 1 sC + R Vi 1 sC + R s + 1 RC 1 RC 1 RC ∴ H ( jω ) = ⇒ H ( jω ) = 2 jω + 1 RC ω + (1 RC ) 2 0 : |H(jω)| 1 ∞ : |H(jω)| 0 ωc : |H(jωc)| 1/√2 Cutoff Frequency (by definition) ω ω ω 1 1 ⇒ H ( jωc ) = = H max = 1 2 2 2 2 ωc + ( R L) R ∴ωc = H max = H ( jω ) ω =0 = 1 L RL EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 3/12 0 : |H(jω)| 1 ∞ : |H(jω)| 0 ωc : |H(jωc)| 1/√2 Cutoff Frequency (by definition) ⇒ H ( jωc ) = 1 ∴ωc = RC 1 RC ωc + (1 RC ) 2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] 2 = 1 1 H max = 1 2 2 H max = H ( jω ) ω =0 = 1 Lecture 29 | Chapter 14 | 2/5 | 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 Two circuits that behave as low-pass filters EE 203 Circuit Analysis 2 Lecture 29 Chapter 14.3 High-Pass Filters Transfer function Cutoff Frequency & Time Time Constant τ= τ= 1 ωc 1 ωc = L 1 = RL R = 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: [email protected], http://www.SMALL.Buffalo.edu 1 = RC 1 RC EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 5/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 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 Two circuits that behave as high-pass filters The Series RC Circuit for High-Pass Filter Transfer function H(s) V R R s Vo = Vi ⇒ H ( s ) = o = = 1 sC + R Vi 1 sC + R s + 1 RC jω ω ⇒ H ( jω ) = ∴ H ( jω ) = 2 jω + 1 RC ω + (1 RC ) 2 The series RC circuit Transfer function Cutoff frequency utoff frequency ω ω ω The series RL circuit Transfer function Cutoff frequency 0 : |H(jω)| 0 ∞ : |H(jω)| 1 ωc : |H(jωc)| 1/√2 Cutoff Frequency (by definition) ⇒ H ( jω c ) = 1 ∴ ωc = RC EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 7/12 ωc ωc + (1 RC ) 2 2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] = 1 1 H max = 1 2 2 H max = H ( jω ) ω =∞ = 1 Lecture 29 | Chapter 14 | 2/5 | 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 The Series RL Circuit for High-Pass Filter Two circuits that behave as high-pass filters Transfer function H(s) V sL sL s = Vi ⇒ H ( s ) = o = Vo = R + sL Vi R + sL s + R L ω jω ∴ H ( jω ) = ⇒ H ( jω ) = 2 jω + R L ω + ( R L) 2 Transfer function Cutoff Frequency & Time Time Constant 0 : |H(jω)| 0 ∞ : |H(jω)| 1 ωc : |H(jωc)| 1/√2 ω ω ω τ= Cutoff Frequency (by definition) ⇒ H ( jω c ) = R ∴ ωc = L ωc ωc + ( R L ) 2 2 = 1 1 H max = 1 2 2 τ= 1 ωc 1 ωc = 1 = RC 1 RC = L 1 = RL R H max = H ( jω ) ω =∞ = 1 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 9/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 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 Example 14.4 –Loaded Filter (1) Vo = sL RL R + sL RL Unloaded Vi H ( s) = sLR ⇒ H (s) = = +R sLR R sL+ RLL + R + RLL R = = ∴ H ( jω c ) = sLR sL R R + RL + R R RL L + R + RLL +R R L Ks s + ωc where K = L + RsRRL + H ( s) = ω ω 2 + ωc 2 R = 15 kHz L ωc ωc + ωc 2 2 = 1 , 2 H ( j∞ ) = 1 Ks 1s 1 ω , H ( jω ) = = s + ωc 2 s + ωc 2 ω2 +ω 2 c R 1 1R = , ωc = = 7.5 kHz R+R 2 2L ωc 1 1 1 ∴ H ( jω c ) = = , H ( j∞ ) = 2 2 ω 2 +ω 2 2 2 c c where K = RL R , ωc = K R + RL L EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] H ( jω ) = Loaded (when RL = R) RL )s R + RL = RL R s+( ) R + RL L ( R R +sRL + RL R + RL where ωc = L L RsRRL + sRL R + RL s , s + ωc sLR L L Vo sL + RL L sL + R L = = sL + RL L sLRL sLR Vi R + sL + RLL R sL + RL + sL + RL L L RsRRL + = Example 14.4 –Loaded Filter (2) Lecture 29 | Chapter 14 | 2/5 | 11/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | [email protected] Lecture 29 | Chapter 14 | 2/5 | 12/12 ...
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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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