Department of EECS EECS 105 Fall 2003 Lecture 2 Prof Niknejad Lecture 3 Bode Plots University of California Berkeley dB 20 10 5 3 2 1 ratio 10 000 3 162 1 778 1 413 1 259 1 122 Prof A Niknejad University of California Berkeley 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 ratio 0 100 0 316 0 562 0 708 0 794 0 891 Get to know your logs dB 20 10 5 3 2 1 Department of EECS z z EECS 105 Fall 2003 Lecture 3 Bode Plot Overview Prof A Niknejad i Break frequencies K i 1 University of California Berkeley 1 j z1 1 j z 2 1 j zn H G0 j 1 j p 2 1 j p 2 1 j pm Technique for estimating a complicated transfer function several poles and zeros quickly Department of EECS z z EECS 105 Fall 2003 Lecture 3 j 1 DC Pole j DC Zero 1 j 0 dB 0 dB Simple Zero 0 dB 1 1 j Simple Pole 0 dB Department of EECS z z z z 1 1 90 90 90 90 Prof A Niknejad University of California Berkeley Summary of Individual Factors EECS 105 Fall 2003 Lecture 3 Example 1 100 ns 2 10 ns 3 100 ps H j 1 10 Mrad s 1 j 1 j 1 3 j j 1 5 2 10 2 100 Mrad s Prof A Niknejad University of California Berkeley 3 10 Grad s Break frequencies invert time constants 10 5 j 1 j 2 H j 1 j 1 1 j 3 Consider the following transfer function Department of EECS z z EECS 105 Fall 2003 Lecture 3 j 20 log 1 j 2 105 1 j 1 j 1 3 Prof A Niknejad University of California Berkeley Let s plot each factor separately and add them graphically 20 log 1 j 20 log 1 j 1 3 20 log H j dB 20 log j 1 j 5 2 10 Recall log of products is sum of logs Department of EECS z z Breaking Down the Magnitude EECS 105 Fall 2003 Lecture 3 Prof A Niknejad University of California Berkeley Let s plot each factor separately and add them graphically 1 j 1 j 1 3 j H j 5 1 j 10 2 10 5 j 1 j 2 H j 1 j 1 1 j 3 Since a b a b Breaking Down the Phase Department of EECS z z EECS 105 Fall 2003 Lecture 3 80 60 40 20 20 40 60 80 Department of EECS 104 j 5 10 105 0 dB 106 107 108 109 1011 Prof A Niknejad University of California Berkeley 1010 Magnitude Bode Plot DC Zero EECS 105 Fall 2003 Lecture 3 180 135 90 45 45 90 135 180 Department of EECS 105 106 107 108 109 1011 Prof A Niknejad University of California Berkeley 1010 Phase Bode Plot DC Zero 104 j 5 10 EECS 105 Fall 2003 Lecture 3 80 60 40 20 20 40 60 80 Department of EECS 104 105 1 10 Mrad s 106 107 108 1 j 107 1 109 1011 University of California Berkeley 1010 dB dB j 105 Prof A Niknejad Magnitude Bode Plot Add First Pole EECS 105 Fall 2003 Lecture 3 180 135 90 45 45 90 135 180 Department of EECS 104 j 5 10 105 106 107 108 109 107 1011 University of California Berkeley 1 j 1 1010 Prof A Niknejad Phase Bode Plot Add First Pole EECS 105 Fall 2003 Lecture 3 80 60 40 20 20 40 60 80 Prof A Niknejad Department of EECS 104 105 2 100 Mrad s 106 107 108 109 1011 108 dB University of California Berkeley 1010 1 j Magnitude Bode Plot Add 2nd Zero EECS 105 Fall 2003 Lecture 3 180 135 90 45 45 90 135 180 Department of EECS 104 105 106 107 108 109 1011 108 University of California Berkeley 1010 1 j Prof A Niknejad Phase Bode Plot Add 2nd Zero EECS 105 Fall 2003 Lecture 3 80 60 40 20 20 40 60 80 Department of EECS 104 105 3 10 Grad s 106 107 108 109 University of California Berkeley dB 1011 1010 1 1 j 1010 Prof A Niknejad Magnitude Bode Plot Add 2nd Pole EECS 105 Fall 2003 Lecture 3 180 135 90 45 45 90 135 180 Department of EECS 104 105 106 107 108 1011 Prof A Niknejad University of California Berkeley 1010 1010 1 j 109 Phase Bode Plot Add 2nd Pole EECS 105 Fall 2003 Lecture 3 Prof A Niknejad Department of EECS University of California Berkeley Comparison to Actual Mag Plot EECS 105 Fall 2003 Lecture 3 Prof A Niknejad Department of EECS University of California Berkeley Comparison to Actual Phase Plot EECS 105 Fall 2003 Lecture 3 Why do I say actual Prof A Niknejad University of California Berkeley 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 I plotted the transfer characteristics with Mathematica 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 Department of EECS z z z EECS 105 Fall 2003 Lecture 3 Prof A Niknejad Department of EECS University of California Berkeley Don t always believe a computer EECS 105 Fall 2003 Lecture 3 University of California Berkeley The physics describes not only physical LCR circuits but also approximates mechanical resonance mass spring pendulum molecular resonance microwave cavities transmission lines buildings bridges The series resonant circuit is one of the most important elementary circuits Department of EECS z z Prof A Niknejad Second Order Transfer Function EECS 105 Fall 2003 Lecture 3 Series LCR Analysis Vs V0 I R R 1 j L R j C Vs I IR j C 1 j L R j C Vs I j L I 1 Vo Prof A Niknejad University of California Berkeley With phasor analysis this circuit is readily analyzed Department of EECS z EECS 105 Fall 2003 Lecture 3 Vo V0 R H j Vs j L 1 R j C University of California Berkeley One zero at DC frequency can t conduct DC due to capacitor V0 j CR H j Vs 1 2 LC j RC To find the poles zeros let s put the H in canonical form So we have Department of EECS z z z Prof A Niknejad Second Order Transfer Function EECS 105 Fall 2003 Lecture 3 H j Q 0 2 j j 2 0 …
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