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 AnalysisSlide 22Poles 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!Engineers are very conservative. A “margin” of 3dB is a factor of 2 (power)!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 OverviewTechnique for estimating a complicated transfer function (several poles and zeros) quicklyBreak frequencies :)1()1)(1()1()1)(1()()(22210pmppznzzKjjjjjjjGHii1Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSummary of Individual Factors Simple Pole:Simple Zero:DC Zero:DC Pole:j11j1jj11dB0dB0dB0dB0909090901Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadExampleConsider the following transfer functionBreak frequencies: invert time constants)1)(1()1(10)(3125jjjjjHps100ns10ns100321Grad/s10Mrad/s100Mrad/s10321)1)(1()1(10)(3125jjjjjHDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadBreaking Down the MagnitudeRecall log of products is sum of logsLet’s plot each factor separately and add them graphically)1)(1()1(10log20)(3125dBjjjjjH31251log201log201log2010log20jjjjDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadBreaking Down the PhaseSinceLet’s plot each factor separately and add them graphically)1)(1()1(10)(3125jjjjjHbaba 312511110)(jjjjjHDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: DC Zero80206040-20-60-80-4010410510610710810910101011510j0 dBDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: DC Zero1804513590-45-135-180-9010410510610710810910101011510jDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add First Pole80206040-20-60-80-4010410510610710810910101011dB510jdB71011jMrad/s101Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add First Pole1804513590-45-135-180-9010410510610710810910101011510j71011jDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add 2nd Zero80206040-20-60-80-4010410510610710810910101011dB8101jMrad/s1002Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add 2nd Zero1804513590-45-135-180-90104105106107108109101010118101jDepartment of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadMagnitude Bode Plot: Add 2nd Pole80206040-20-60-80-4010410510610710810910101011dB101011jGrad/s103Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadPhase Bode Plot: Add 2nd Pole1804513590-45-135-180-901041051061071081091010101110101jDepartment 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”?I plotted the transfer characteristics with MathematicaThe 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: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 FunctionThe series resonant circuit is one of the most important elementary circuits: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 AnalysisWith phasor analysis, this circuit is readily analyzed RICjILjIVs1RRCjLjVRIVRCjLjIVss110+Vo−Department of EECS University of California, BerkeleyEECS 105 Fall 2003, Lecture 3 Prof. A. NiknejadSecond Order
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