EE203-SUNYBuffalo-38-Chapter15-02

EE203-SUNYBuffalo-38-Chapter15-02 - 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 EE 203 Circuit Analysis 2 Lecture 38 Chapter 15.3 OP Amp Bandpass and Bandreject Filters (continue..) 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 38 | Chapter 15 | 2/2 | 1/5 Example 15.5 Design a bandpass filter for a graphic equalizer to provide an amplification of 2 within the band of frequencies between between 100 and 10,000 Hz. Use 0.2 Use μF capacitors. Low-pass stage Gain stage we see there are two unknowns, so one of the resistors can be selected arbitrarily Let arbitrarily. Let's select a 1 kΩ resistor for Ri. High-pass stage EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 38 | Chapter 15 | 2/2 | 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 OP Amp Bandreject Filters: Bode Plot Parallel OP Amp Bandreject Filter We We can see from the plot that the bandreject filter consists of three separate components: These These three components are connected in parallel Two cutoff frequencies are wo cutoff frequencies are widely separated, so that the resulting design is a broadband bandreject bandreject filter 1. A unity-gain low-pass filter whose cutoff frequency is ωc1, the smaller of the two cutoff frequencies; 2. A unity-gain high-pass filter whose cutoff frequency is ωc2, the larger of the two cutoff frequencies; and 3. A gain component to provide the desired level of gain in the passband passband. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Unity-Gain Low-Pass Filter + Unity-Gain High-Pass Filter Gain Component ωc 2 >> ωc1 Transfer Function H(s) H ( s) = Vo Vi ⎡⎛ ωc1 ⎞ ⎛ s ⎞⎤⎛ R f = ⎢⎜ − ⎟⎜ ⎟⎜ ⎜ s + ω ⎟ + ⎜ − s + ω ⎟⎥⎜ − R c1 ⎠ ⎝ c 2 ⎠⎦⎝ i ⎣⎝ Lecture 38 | Chapter 15 | 2/2 | 3/5 ⎞ ⎟ ⎟ ⎠ EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 38 | Chapter 15 | 2/2 | 4/5 SMALL for Big Things University at Buffalo nanobioSensors & MicroActuators Learning Lab The State University of New York Parallel OP Amp Bandreject Filter Transfer Function H ( s) = =K Vo ⎡⎛ ωc1 ⎞ ⎛ s ⎞⎤⎛ R f = ⎢⎜ − ⎟⎜ ⎟⎜ ⎜ s + ω ⎟ + ⎜ − s + ω ⎟⎥⎜ − R Vi ⎣⎝ c1 ⎠ ⎝ c 2 ⎠⎦⎝ i ⎞ ⎟ ⎟ ⎠ s 2 + 2ωc1s + ωc1ωc 2 ωc ` ( s + ωc 2 ) + s ( s + ωc1 ) =K ( s + ωc1 )( s + ωc 2 ) ( s + ωc1 )( s + ωc 2 ) where, K = Rf Ri Two Cutoff Frequencies ωc1 = Gain Unity-Gain Low-Pass Filter it Filt + Unity-Gain High-Pass Filter Gain Component 1 1 , ωc 2 = RL C L RH C H H ( jω o ) = K if if ωc 2 >> ωc1 ( jωo ) 2 + 2ωc1 ( jωo ) + ωc1ωc 2 2ωc1 2ω =K ≈ K c1 ( jωo + ωc1 )( jωo + ωc 2 ) ωc1 + ωc 2 ωc 2 2R f the magnitude at the center frequency is th then H ( jωo ) << Ri much smaller than the passband magnitude EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 38 | Chapter 15 | 2/2 | 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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