EE203-SUNYBuffalo-32-Chapter14-05

EE203-SUNYBuffalo-32-Chapter14-05 - 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 EE 203 Circuit Analysis 2 Lecture 32 Chapter 14.5 Band Band-Reject Filters (continue…) Series RLC Circuits – Quantitative Analysis (4) 2 ωc1 = − ωc 2 = 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 32 | Chapter 14 | 5/5 | 1/5 β ⎛β ⎞ 2 + ⎜ ⎟ + ωo ⎝2⎠ 2 2 β ⎛β ⎞ 2 + ⎜ ⎟ + ωo 2 ⎝2⎠ 2 ⎡ 1 + ωc1 = ωo ⎢− ⎢ 2Q ⎣ ⎡ 1 + ⎢ 2Q ⎣ ωc 2 = ωo ⎢ 2 ⎤ ⎛1⎞ ⎟ + 1⎥ ⎜ ⎟ ⎜ ⎥ ⎝ 2Q ⎠ ⎦ ωc1 = − 2 ωc 2 = R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 1 LC ωo = β= R L L CR 2 Q= 2 ⎤ ⎛1⎞ ⎜ ⎟ + 1⎥ ⎜ 2Q ⎟ ⎥ ⎝ ⎠ ⎦ EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL Lecture 32 | Chapter 14 | 5/5 | 2/5 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 RLC Bandreject Filters Example 14.8 Designing a Bandreject Filter Q: Q: Using the series RLC circuit in Fig. 14.28(a), compute the component values that 14 compute yield a bandreject filter with a bandwidth of 250 Hz and a center frequency of 750 Hz. Use a 100 nF capacitor. Compute values for R, L, ωc1, ωc2, and Q. Solution f c 2 − f c1 = 250 Hz, f o = 750 Hz ⇒ β = 2π (250) rad/s, ωo = 2π (750) rad/s β 2π (250) ⎛β ⎞ ⎛ 2π (250) ⎞ 2 2 + ⎜ ⎟ + ωo = − +⎜ ⎟ + (2π ⋅ 750) = 3992.0 rad/s ⇒ f c1 = 3992.0 / 2π = 635.3 Hz 2 2 2 ⎝2⎠ ⎝ ⎠ ωc1 = − ωc 2 = ωo = Q= β 2 2π (250) ⎛ 2π (250) ⎞ ⎛β ⎞ 2 2 +⎜ + ⎜ ⎟ + ωo = ⎟ + (2π ⋅ 750) = 5562.8 rad/s ⇒ f c 2 = 5562.8 / 2π = 885.3 Hz 2 2 2 ⎠ ⎝ ⎝2⎠ 2 2 R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 2 ωc 2 = ωo = ω 2π (750) Q= o = =3 β 2π (250) 2 2 ωc1 = − β= 1 R ⎛R⎞ + ⎜ ⎟+ 2L 2 L ⎠ CL ⎝ 1 LC R L L Q= CR 2 Q= Lecture 32 | Chapter 14 | 5/5 | 3/5 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC 2 RC ⎠ CL ⎝ 2 ωc 2 = β= L L 0.45 ⇒R= = = 707 Ω CR 2 CQ 2 (100 ×10 −9 )(3) 2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo 2 ωc1 = − ωo = 1 1 1 ⇒L= 2 = = 450 mH LC ωo C (2π ⋅ 750) 2 (100 ×10 −9 ) s 2 + ωo 2 s 2 + β s + ωo 2 H (s) = 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC ⎝ 2 RC ⎠ CL 1 LC 1 RC R 2C L Lecture 32 | Chapter 14 | 5/5 | 4/5 SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York Two RLC Bandpass Filters 2 ωc1 = − R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 2 ωc 2 = ωo = β= 1 R ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 1 LC R L L Q= CR 2 H (s) = 2 ωc1 = − 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC ⎝ 2 RC ⎠ CL 2 ωc 2 = ωo = β= Q= EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo βs 2 s + β s + ωo 2 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC 2 RC ⎠ CL ⎝ 1 LC 1 RC R 2C L Lecture 32 | Chapter 14 | 5/5 | 5/5 ...
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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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