EE203-SUNYBuffalo-37-Chapter15-01

EE203-SUNYBuffalo-37-Chapter15-01 - 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 EE 203 Circuit Analysis 2 Lecture 37 Chapter 15.1 First-Order Low-Pass and High-Pass Filters 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 37 | Chapter 15 | 1/2 | 1/12 Passive Filters vs. Active Filters Passive Filters Up to this point, we have considered only passive filter circuits, that is, filter circuits consisting of resistors, inductors, and capacitors. Active Filters There are areas of application, however, where active circuits, those that employ op amps, have certain advantages over passive filters. For instance, active circuits can produce bandpass and bandreject filters without using inductors. This is desirable because inductors are usually large, heavy, and costly, and they may introduce electromagnetic field effects that compromise the desired frequency response characteristics. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 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 If General OP Amp Circuit / Low-Pass Filter Is + I f = In Is Vi − Vn Vo − Vn + = In Zi Zf Zf Vi − 0 Vo − 0 + = 0 ∴Vo = − Vi Zi Zf Zi In Active Active Low-Pass Filter H (s) = R2 sC Vn Vp= zero where K = 1 R2 , ωc = R1 R2C if 1 < K then 1 < H ( jω ) Passive Low-Pass Filter Filt R2 1 s ωc R RC R1 R2 =− = − 1 2 = −K 1 s 1 s + ωc R1 ( R2 + ) s+ sC R1 R2 R2C R2 sC H (s) = Vo ( s ) ωc = Vi ( s ) s + ωc where ωc = R2 1 , ωc = R1 R2C EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Vo ( s ) − Z f ωc = = −K Vi ( s ) Zi s + ωc 0 < H ( jω ) 1 1 R2 || ( ) R2 + Vo ( s ) − Z f sC = − sC H (s) = = =− Vi ( s ) Zi R1 R1 where where K = Gain K 1 RC 0 < H ( jω ) < 1 Lecture 37 | Chapter 15 | 1/2 | 3/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 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 Active High-Pass Filter Frequency Response Plots: Bode Plots Vo ( s ) − Z f R2 = =− 1 Vi ( s ) Zi R1 + sC s R2 s R2 s R1 R1 =− ⋅ =− = −K 1s 1 s + ωc R1 + s+ sC R1 C R1C 0 < H ( jω ) R 1 ⇒ where K = 2 , ωc = R1 R1C if if 1 < K then 1 < H ( jω ) then Bode Plots H (s) = Named in recognition of the pioneering work done by H. W. Bode Decibels (dB) versus the log of frequency Made on semilog graph paper for greater accuracy in representing the wide range of frequency values A dB = 20 log10 H ( jω ) A dB = 0 ⇒ H ( jω ) = 1 Passive High-Pass Filter A dB < 0 ⇒ 0 < H ( jω ) < 1 H ( s) = A dB > 0 ⇒ 1 < H ( jω ) A dB = −3 dB ⇒ H ( jω c ) = 1 where ωc = 2 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Vo ( s ) s = Vi ( s ) s + ωc Lecture 37 | Chapter 15 | 1/2 | 5/12 1 RC 0 < H ( jω ) < 1 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 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 Example 15.2 (1) Example 15.2 (2) Gain Figure Figure 15.5 shows the Bode magnitude plot of a highpass filter. Using the active high-pass filter circuit in Fig.15.4, calculate values of R1 and R2 that produce the desired magnitude response. Use a 0.1 μF capacitor. If a If 10 kΩ load resistor is added to this filter, how will the magnitude response change? EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo 20 dB dB 20 = 20 log10 H ( j∞) ∴ H ( j∞) = 10 ⇒ K = 10 = R2 R1 3 dB point 500 rad/s ωc = 500 rad/s = 1 R1C 500 ∴ R1 = 1 ωc C = 20 kΩ, R2 = 200 kΩ Because we have made the assumption that th th the op amp in this high-pass filter circuit is ideal, the addition of any load resistor, regardless of its resistance, has no effect on has the behavior of the op amp. Thus, the magnitude response of a high-pass filter with a lload resistor is the same as that of a high-pass oad filter with no load resistor. Lecture 37 | Chapter 15 | 1/2 | 7/12 EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 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 OP Amp Bandpass Filters: Bode Plot EE 203 Circuit Analysis 2 Lecture 37 Chapter 15.3 OP OP Amp Bandpass and Bandreject Filters We We can see from the plot that the bandpass filter consists of three separate components: 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 37 | Chapter 15 | 1/2 | 9/12 1. A unity-gain low-pass filter whose cutoff frequency is ωc2, the larger of the two cutoff frequencies; 2. A unity-gain high-pass filter whose cutoff frequency is ωc1, the smaller of the two cutoff frequencies; and 3. A gain component to provide the desired level of gain in the passband. EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 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 Cascaded OP Amp Bandpass Filter Cascaded OP Amp Bandpass Filter These three components are cascaded in series Transfer Transfer Function The resulting filter is called a broadband bandpass filter, because the band of frequencies passed is wide. The formal definition of a broadband filter requires to satisf the equation fy Unity-Gain Low-Pass Filter it Filt Unity-Gain Hi h-Pass Filter it Filt High ωc 2 ≥2 ωc1 Gain Component V⎛ ωc 2 ⎞⎛ s ⎞⎛ R f ⎞ H ( s) = o = ⎜ − ⎟ ⎟⎜ ⎟⎜ ⎜ s + ω ⎟⎜ − s + ω ⎟⎜ − R ⎟ Vi ⎝ c 2 ⎠⎝ c1 ⎠⎝ i⎠ ωc 2 s ωc 2 s = −K = −K 2 ( s + ωc 2 )( s + ωc1 ) s + (ωc1 + ωc 2 ) s + ωc1ωc 2 If ωc 2 >> ωc1 then (ωc1 + ωc 2 ) ≈ ωc 2 H ( s) = − K ωc 2 s s 2 + ωc 2 s + ωc1ωc 2 Two Cutoff Frequencies ωc 2 = Gain 1 1 , ωc1 = RL C L RH C H ω c 2 ( jω o ) H ( jω o ) = − K ( jωo ) 2 + ωc 2 ( jωo ) + ωc1ωc 2 =K= EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo Lecture 37 | Chapter 15 | 1/2 | 11/12 Rf Ri H(s) for Unity-Gain Low-Pass Filter H(s) for Unity-Gain High-Pass Filt Filter H(s) for Gain Component SMALL for Big Things nanobioSensors & MicroActuators Learning Lab University at Buffalo The State University of New York Two RLC Bandpass Filters 2 ωc1 = − R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 2 ωc 2 = ωo = R 1 ⎛R⎞ + ⎜ ⎟+ 2L ⎝ 2 L ⎠ CL 1 LC R β= L Q= H (s) = βs 2 s 2 + β s + ωo 2 ωc1 = − 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC ⎝ 2 RC ⎠ CL 2 L CR 2 ωc 2 = 1 1 ⎛1⎞ +⎜ ⎟+ 2 RC ⎝ 2 RC ⎠ CL 1 LC 1 β= RC ωo = Q= R 2C L Lecture EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo| Spring 2007 | Prof. Kwang W.LOh | EE@SUNY-BuffaloChapter 15 | 15| |Chapter |1412/89/8 ecture 37 | 38 | Chapter 1/2 2/2 | 5/5 | | 12/12 EE 203 Circuit Analysis 2 Lecture 32 ...
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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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