EE203-SUNYBuffalo-28-Chapter14-01

EE203-SUNYBuffalo-28-Chapter14-01 - 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 The Effect of Varying Source Frequency EE 203 Circuit Analysis 2 Lecture 28 Chapter 14.1 Frequency Selective Circuits 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 28 | Chapter 14 | 1/5 | 1/10 Frequency Frequency Response Up to this point in our analysis of circuits with sinusoidal sources, the source frequency was held constant. In this chapter, we analyze the effect of varying source frequency on circuit voltages and currents. Frequency Selective Circuit: Filter The careful choice of circuit elements, their values, and their connections to other elements enables us to construct circuits that pass to the output only those input signals that reside in a desired range of frequencies. Many devices that communicate via electric signals, such as telephones, radios, televisions, and satellites, employ frequency-selective circuits. Frequency-selective circuits are also called filters because of their ability to filter out certain input signals on the basis of frequency Loss pass Hiigh pass Hh Band pass Band reject EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 2/10 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 Recall 13.7: Transfer Function and Steady-State Sinusoidal Response (3) Transfer Function |H(jω)| Assumption Assumption Note that the approach just outlined assumes that we can vary the frequency of a sinusoidal source without changing its magnitude or phase angle. Therefore, the amplitude and phase of the output th will vary only if those of the transfer function vary as the frequency of the sinusoidal source s changed. Transfer Function: H(s) = Vo(s)/Vi(s) which indicates how to use the transfer function H(s) to find the steadystate sinusoidal response yss(t) of a circuit. The amplitude of the response equals the amplitude of the source, A, times the magnitude of the transfer function, |H(jω)|. th The phase angle of the response, φ + θ(ω), equals the phase angle of the source, φ, plus the phase angle of the transfer function, θ(ω). EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 3/10 Most cases are where both the input and outputs are sinusoidal voltages. The transfer function of interest to us will be the ratio of the Laplace transform of the output voltage to the Laplace transform of the input voltage, or H(s) = Vo(s)/Vi(s). For a particular application, a current may be either the input signal or output signal of interest. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 4/10 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 Ideal Freq Response Plot (1) Ideal Freq Response Plot (2) Passband & Stopband Cutoff Frequency: ωc A low-pass filter passes signals at frequencies lower than the cutoff frequency from ff the input to the output A high-pass filter passes signals at frequencies higher than the cutoff frequency. Thus Thus the terms low and high as used here do not refer to any absolute values of frequency, but rather to relative values with respect to the cutoff frequency. The signals passed from the input to the output fall within a band of frequencies called the passband. Frequency Response Plot Magnitude plot: a graph of |H(jω)| versus frequency ω. Phase angle plot: a graph of θ(jω) versus frequency ω. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 5/10 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 6/10 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 Ideal Freq Response Plot (3) EE 203 Circuit Analysis 2 Lecture 28 Chapter 14.2 Low-Pass Filter A bandpass filter passes a source voltage to the output only when the source frequency is within the band defined by the two cutoff frequencies. A bandreject filter passes a source voltage to the output only when the source frequency is outside the band defined by the two cutoff frequencies. 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 The bandreject filter thus rejects, or stops, the source voltage from reaching the output when its frequency is within the band defined by the cutoff frequencies. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 7/10 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 8/10 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 The Series RL Circuit for Low-Pass Filter Transfer function H(s) R V R RL Vo = Vi ⇒ H ( s ) = o = = sL + R Vi sL + R s + R L RL RL ∴ H ( jω ) = ⇒ H ( jω ) = 2 jω + R L ω + ( R L) 2 The series RL circuit Transfer function Cutoff frequency ω ω ω The series RC circuit Transfer function Cutoff frequency 0 : |H(jω)| 1 ∞ : |H(jω)| 0 ωc : |H(jωc)| 1/√2 Cutoff Frequency (by definition) ⇒ H ( jωc ) = R ∴ωc = L EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 28 | Chapter 14 | 1/5 | 9/10 RL ωc + ( R L) 2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo 2 = 1 1 H max = 1 2 2 H max = H ( jω ) ω =0 = 1 Lecture 28 | Chapter 14 | 1/5 | 10/10 ...
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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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