15 - MEEN260 IntroductiontoEngineering Experimentation...

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1 MEEN 260 Introduction to Engineering Experimentation Analog Filters Reza Langari* Department of Mechanical Engineering Texas A&M University [email protected] *Incorporates a number of slides from Brian Rasmussen, TAMU MEEN, Copyright 2008. Analog vs. Digital Filters Analog Filters Made of physical components (RC circuit, bike shock absorber, etc.) Operate continuously in time (at every instant in time) Advantage: cheap (RLC circuits are pennies) Disadvantage: semi permanent design Digital filters Mathematical algorithm implemented using a microprocessor or computer Operates at fixed instances in time (e.g. every 0.1 seconds) Advantage: flexible design, modular, easy to implement Disadvantage: $$$ (DSP ~ $20) Passive vs. Active Filters Passive Filters Do not add energy to the signal Examples RLC circuits Active Filters Add energy to the signal Examples Circuits with Op Amps
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2 Impedance We define the impedance as: For a resistor For a capacitor For an inductor current voltage Impedance = () j ω I j ω V j ω Z = R j ω Z R = R t i t v = ω Cj j ω Z C 1 = [] t i t v dt d C = Lj j ω Z L = t i dt d L t v = Example #1 ( ) 1 1 1 1 Cj out C in R C Cj Vj ω Z ω ZZ R j τω == = = ++ + ()() ( ) 2 2 2 2 2 2 2 2 2 1 1 1 0 1 Im Re Im Re + = + + = + + = j ω V j ω V in out 1 1 1 1 tan 1 tan 1 0 tan Re Im tan = = = j ω V j ω V in out Example #1 cont’d 10 0 10 1 10 2 10 3 10 4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Magnitude 10 0 10 1 10 2 10 3 10 4 -40 -35 -30 -25 -20 -15 -10 -5 0 5 Magnitude (dB) Bode Diagram Frequency (rad/sec) Log( ω ) Log( ω ) dB 1 0 0 dB Low Frequencies Pass Through -3 dB Bandwidth Identify the filter type What is the magnitude at low frequencies What is the magnitude at high frequencies 1 0 1 1 2 0 = + = = τ j V j V in out 0 = 0 1 1 2 0 = + = >> j V j V in out 0 >>
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3 Example #1 cont’d Determine the bandwidth of the filter Recall that the bandwidth of a filter is the frequency range for which the magnitude is greater than 3 dB Define the cutoff frequency (in this case) as: What happens at () dB 3 2 1 1 1 1 1 1 2 2 = = + = + = j ω V j ω V c in out ω RC ω c 1 1 = = τ ω ω c = = 2 1 log 20 dB 3 707 . 0
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This note was uploaded on 12/26/2010 for the course MEEN 260 taught by Professor Langari during the Fall '08 term at Texas A&M.

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15 - MEEN260 IntroductiontoEngineering Experimentation...

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