Filter Design, Active Filters & Review. EGR 220, Chapter 14.7, December 14, 2017

Transcription

1 Filter Design, Active Filters & Review EGR 220, Chapter 14.7, December 14, 2017

2 Overview ² Passive filters (no op amps) ² Design examples ² Active filters (use op amps) ² Course review 2

3 Example: Filter Analysis You are given an electronic device and would like to use it for a filter, hoping for a resonant filter if possible. You assume it is a series circuit and measure a resistance of 100Ω, a capacitive reactance of 5 kω, and an inductive reactance of 300Ω when used at 2MHz. Find: (a) the resonant frequency, and (b) bandwidth of the circuit (including the initial and final frequencies that define the bandwidth). 3

4 Example: Filter Design A simple RC lowpass filter is designed to reduce high frequency noise. If the desired corner frequency is 20 khz and C = 0.5µF, find the value of R. Draw the circuit labeling input, output and all circuit elements. 4

5 Example: Filter Design In an amplifier circuit, a simple RC highpass filter is needed to block the dc component of the input signal while passing the time-varying component. If the desired rolloff frequency is 15 Hz and C = 10 µf find the value of R. Draw the circuit labeling input, output and all circuit elements. 5

6 Example: Filter Behavior Classify the type of filter and describe the Bode plot (magnitude) qualitatively 6

7 Example: Filter Analysis The circuits below are used for a speaker system. One is a lowpass filter connected to a woofer, and the other is a highpass filter connected to a tweeter. Select one circuit below and determine (qualitatively) if it is a lowpass or highpass filter. 8

8 H(s) from a Bode Plot ² Gain at the origin? ² Zeros? ² Poles? ² Write terms and construct H(s) H(s) = # K s 1+ s & % $ ' ( # 1+ s & % $ ' ( # 1+ s & % ( $ ' # s 1+ s & % $ ' ( # 1+ s & % $ ' ( # 1+ s? & % ( $ ' 13

9 Design from a Bode Plot ²Given a Bode plot, determine the transfer function and design a possible circuit from the transfer function. ² Gain at the origin? ² Zeros? ² Poles? ² Write terms & construct H(s) H(s) = # K s 1+ s & % $ ' ( # 1+ s & % $ ' ( # 1+ s & % ( $ ' # s 1+ s & % $ ' ( # 1+ s & % $ ' ( # 1+ s? & % ( $ ' 15

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11 Design from a Bode Plot ² Compare H(s) to the (voltage gain) transfer function of two circuits: series RCL and C + R L H(s) = Ks 2 ( s + 4) ( s +100) = (0.7)s 2 s s

12 Design from a Bode Plot ² Compare H(s) above to the (voltage gain) transfer function of the two circuits ( series RCL and C + R L ) 18

13 Ideal op amps o Golden rules Active Filters Basic feedback amplifier o Z in and Z f rather than R in and R f 19

14 Active Filter: General Transfer function =? o H(s) = Vo / Vi = Zf / Zi 20

15 Active Filter: Low or High Pass? 21

16 Active Filter: Low or High Pass? 22

17 Summary Transfer functions and Bode plots Be able to identify type of filter circuit Filter Design o Determine H(s) from Bode Plot o Iterate to find a circuit for given H(s) Active filters Course concept review 23

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20 Circuit Analysis Identification Identify the type of circuit analysis problem represented by each of the following circuits o Such as: source-free first order circuit, sinusoidal steady state (phasor) analysis, etc Specify, where appropriate, whether you would be finding the natural or step response Specify, where appropriate, mathematical expressions that describe the circuit analysis and behavior 26

21 Circuit Analysis Identification Roughly sketch a reasonable circuit response o Clearly label the axes of your graph. o Clearly identify which signal or waveform you are sketching (e.g., voltage across resistor, R 1 ) o Include important parameters, QUALITATIVELY do NOT calculate any values, such as τ or θ, but do identify where they could be (reasonably) on the graphs 27

22 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 28

23 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 29

24 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 30

25 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 31

26 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 32

27 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 33

28 Input, Sources System Output, Circuit Behavior Identify and discuss a Thevenin Equivalent circuit Analysis Tools? Circuit Laws used? Equations? 34

29 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 35

30 Input, Sources System Output, Circuit Behavior Analysis Tools? Circuit Laws used? Equations? 36

31 Final Exam 1) For this exam you may use one side of one sheet of paper of notes and a calculator. 2) Do not discuss this exam with anyone until after the end of exam period. 3) For the multiple choice problem, some state to: CIRCLE ALL ANSWERS THAT APPLY. 4) For short answers keep them short. 37

32 Final Exam 1) For this exam you may use one side of one sheet of paper of notes and a calculator. 2) Do not discuss this exam with anyone until after the end of exam period. 3) For the multiple choice problem, some state to: CIRCLE ALL ANSWERS THAT APPLY. 4) For short answers keep them short. 5) A number of questions could have more than one answer / solution state assumptions; be sure to put something down. 6) Note the points assigned for each problem, and plan your time and effort accordingly. 7) Circle your final answer. 8) Work neatly and orderly, and be sure to show all your work. Credit might not be given if it is not clear how the answer was obtained. 38