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Berkeley ELENG 105 - Bode Plots

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Lecture 3: Bode PlotsGet to know your logs!Bode Plot OverviewSummary of Individual FactorsExampleBreaking Down the MagnitudeBreaking Down the PhaseMagnitude Bode Plot: DC ZeroPhase Bode Plot: DC ZeroMagnitude Bode Plot: Add First PolePhase Bode Plot: Add First PoleMagnitude Bode Plot: Add 2nd ZeroPhase Bode Plot: Add 2nd ZeroMagnitude Bode Plot: Add 2nd PolePhase Bode Plot: Add 2nd PoleComparison to “Actual” Mag PlotComparison to “Actual” Phase PlotWhy do I say “actual”?Don’t always believe a computer!Second Order Transfer FunctionSeries LCR AnalysisSecond Order Transfer FunctionPoles of 2nd Order Transfer FunctionFinding the poles…Resonance without LossMagnitude ResponseDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 2Lecture 3: Bode PlotsProf. NiknejadDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadGet to know your logs!dB ratio dB ratio-20 0.100 20 10.000-10 0.316 10 3.162-5 0.562 5 1.778-3 0.708 3 1.413-2 0.794 2 1.259-1 0.891 1 1.122z Engineers are very conservative. A “margin” of 3dB is a factor of 2 (power)!z Knowing a few logs by memory can help you calculate logs of different ratios by employing properties of log. For instance, knowing that the ratio of 2 is 3 dB, what’s the ratio of 4?Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadBode Plot Overviewz Technique for estimating a complicated transfer function (several poles and zeros) quicklyz Break frequencies :)1()1)(1()1()1)(1()()(22210pmppznzzKjjjjjjjGHωτωτωτωτωτωτωω++++++=""iiτω1=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSummary of Individual Factors z Simple Pole:z Simple Zero:z DC Zero:z DC Pole:ωτj+11ωτj+1ωτjωτj1τω1=dB0dB0dB0dB090−90+90−90+τω1=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadExamplez Consider the following transfer functionz Break frequencies: invert time constantsps100ns10ns100321===τττ)1)(1()1(10)(3125ωτωτωτωωjjjjjH+++=−Grad/s10Mrad/s100Mrad/s10321===ωωω)1)(1()1(10)(3125ωωωωωωωωjjjjjH+++=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadBreaking Down the Magnitudez Recall log of products is sum of logsz Let’s plot each factor separately and add them graphically)1)(1()1(10log20)(3125dBωωωωωωωωjjjjjH+++=31251log201log201log2010log20ωωωωωωωjjjj+−+−++=Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadBreaking Down the Phasez Sincez Let’s plot each factor separately and add them graphicallybaba∠+∠=⋅∠)1)(1()1(10)(3125ωτωτωτωωjjjjjH+++∠=∠−312511110)(ωωωωωωωωjjjjjH+∠−+∠−+∠+∠=∠Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: DC Zero80206040-20-60-80-4010410510610710810910101011ω510ωj0 dBDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: DC Zero1804513590-45-135-180-9010410510610710810910101011ω510ωj∠Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add First Pole80206040-20-60-80-4010410510610710810910101011ωdB510ωjdB71011ωj+Mrad/s101=ωDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add First Pole1804513590-45-135-180-9010410510610710810910101011ω510ωj∠71011ωj+∠Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add 2ndZero80206040-20-60-80-4010410510610710810910101011ωdB8101ωj+Mrad/s1002=ωDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add 2ndZero1804513590-45-135-180-9010410510610710810910101011ω8101ωj+∠Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add 2ndPole80206040-20-60-80-4010410510610710810910101011ωdB101011ωj+Grad/s103=ωDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add 2ndPole1804513590-45-135-180-9010410510610710810910101011ω10101ωj+∠−Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadComparison to “Actual” Mag PlotDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadComparison to “Actual” Phase PlotDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadWhy do I say “actual”?z I plotted the transfer characteristics with Mathematicaz The range of frequency for the plot is 6 orders of magnitude. The program has to find the “hot spots” in order to plot the function. Near the hot spots, more points are plotted. In between hot spots, the function is interpolated. If you pick the wrong points, you’ll end up with the wrong plot:z mag = LogLinearPlot[20*Log[10, Abs[H[x]]], {x, 10^4, 10^11},PlotPoints -> 10000, Frame -> True,PlotStyle -> Thickness[.005], ImageSize -> 600,GridLines -> Automatic, PlotRange -> {{10^4, 10^11}, {-20, 100}} ]Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadDon’t always believe a computer!Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSecond Order Transfer Functionz The series resonant circuit is one of the most important elementary circuits:z The physics describes not only physical LCR circuits, but also approximates mechanical resonance (mass-spring, pendulum, molecular resonance, microwave cavities, transmission lines, buildings, bridges, …)Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSeries LCR Analysisz With phasor analysis, this circuit is readily analyzed RICjILjIVs++=ωω1RRCjLjVRIVRCjLjIVss++==++=ωωωω110+Vo−Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSecond Order Transfer Functionz So we have:z To find the poles/zeros, let’s put the H in canonical form:z One zero at DC frequency Æ can’t


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Berkeley ELENG 105 - Bode Plots

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