{"id":6521,"date":"2021-09-27T14:38:40","date_gmt":"2021-09-27T09:08:40","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=5639"},"modified":"2021-09-27T14:38:40","modified_gmt":"2021-09-27T09:08:40","slug":"what-are-bode-plots","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-bode-plots\/","title":{"rendered":"What are Bode Plots?"},"content":{"rendered":"\n<p>As proposed by Hendrik W. Bode a\u00a0 Bode Plot is simply a graphical representation used to design and analyze any control system. Here a logarithmic scale is used which helps in the graphical representation of frequency response of any system.\u00a0<\/p>\n\n\n\n<p>In these plots we plot separate magnitude and phase plots on the logarithmic scale for logarithmic value of frequencies. The basic difference between the polar plots and these plots is that in polar plots normal linear scales are used and in bode plots we use logarithmic scale.<\/p>\n\n\n\n<p>By using these plots we represent any sinusoidal transfer function by two different plots. One of the plots is of magnitude versus frequency and the other one of phase angle vs frequency response of the system.<\/p>\n\n\n\n<p>The detailed description of the magnitude and phase plot is discussed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Magnitude Plot<\/strong><\/h2>\n\n\n\n<p>Here the logarithmic scale values of magnitude versus logarithmic values of frequency are plotted.\u00a0 The magnitude of any transfer function G(s)H(s) is found as<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"36\" src=\"https:\/\/lh4.googleusercontent.com\/BSYCrwpvnsWJtD59MtlIcHLp9fqZHOuvbpNyg8OZvfK-gqGIs0N6IH3U6WoOFF1UVZhcYeiTB5bao8Q_aMxy6DPmwC08cmmSyhb4dz3Zfuxd9C3k-_5VPcdO5fTg8Yc4oj9uIL36=s0\"><\/p>\n\n\n\n<p>The plot for logarithmic values of magnitude on the log axis is below.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"256\" src=\"https:\/\/lh3.googleusercontent.com\/CQCsCkC5MNri5DjDaFTiAo4qmPBW7uXg-2yGLf3OI_xlBEtyfuRszNVSfxxuEFgqOPfhywxg7GHFvo6aKJHA1qNLEgAtjn_U3VthBaaIyBIskIiANk6OmR1LHk1clpgEMSRFZg37=s0\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Phase Plot<\/strong><\/h2>\n\n\n\n<p>In this the logarithmic values of frequencies and the phase angle is plotted on log scale. The basic scale for representing these phase plots is below.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" width=\"408\" height=\"237\" src=\"https:\/\/lh6.googleusercontent.com\/2urF49kdVMz-zC2X1yttK4ePLKRpeBOnVzMsD1vplRccqmUAHu3_yiGig3tG7YiYmxq21p-alH6uSsiCIeM92j0hxGa3p5RnQXNK9mhiyaw3ysjQKjfYhUBdZW3gJupRJ-T1QZNd=s0\"><\/p>\n\n\n\n<p>In order to plot these magnitude and phase plots semi-log papers are used. They have one linear axis and the other one is the logarithmic axis.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Steps for plotting Bode Plot<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>For any given open loop transfer function G(s)H(s) replace s with j\u2375 so that the transfer function is now represented in frequency domain.<\/li><li>Then we calculate the magnitude in decibels by formula<\/li><\/ul>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"36\" src=\"https:\/\/lh4.googleusercontent.com\/BSYCrwpvnsWJtD59MtlIcHLp9fqZHOuvbpNyg8OZvfK-gqGIs0N6IH3U6WoOFF1UVZhcYeiTB5bao8Q_aMxy6DPmwC08cmmSyhb4dz3Zfuxd9C3k-_5VPcdO5fTg8Yc4oj9uIL36=s0\"><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Therefore, the phase angle in degrees for phase plot is calculated as<\/li><\/ul>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"236\" height=\"64\" src=\"https:\/\/lh3.googleusercontent.com\/navRAQ7DgltuiX721WWCHCg6COoNxOiUdSeYBzsmQnOE75l9Tbt_arMbAazf1DKHocXIvPC6AuwSJRYGPOLw9PklN2-fgkoz2MgA9vR2qUxVVtFBU-Xqth7ScNbxGT2QFwLsb9nu=s0\"><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Lastly we plot magnitude and phase plot for different values of \u2375 from 0 to \u221e.<\/li><li>Then system gain is calculated as\u00a0<\/li><\/ul>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"163\" height=\"40\" src=\"https:\/\/lh3.googleusercontent.com\/j1dMwEvYs_MRrbq3LEZB76y6ysnAnCMID5uFWBCmTeUQtq8V7rc6t_vy-876Q4gmRkWf3o5_8lxHzZTp-4MNMmCKGr4sH5kW8rO8jFo-lcBQDkW0BAI93debejZccf--LOEYnRw3=s0\"><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Since, the value of k is always constant the magnitude will also be constant\u00a0 for different values of \u2375 from 0 to \u221e.\u00a0<\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" width=\"430\" height=\"250\" src=\"https:\/\/lh4.googleusercontent.com\/Xjn4q4IEn5UmmQLjPjnryE2uIX0SrSrSqGYpTOT9w1HyRsxGi7e66_omGUie2dOqibg6_3FvEfDoNAXAZGWBwpiGIaEmJYN-ZeQJEacjgjagtnGCwe-ymuWYaxjlaJKgyACFZJKY=s0\"><\/p>\n\n\n\n<p>Then we have, for K>1 straight line is above 0dB<\/p>\n\n\n\n<p>Also for K&lt;1 straight line is below 0dB<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Approximation of Bode Plot<\/strong><\/h2>\n\n\n\n<p>If <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pole%E2%80%93zero_plot\" target=\"_blank\" rel=\"noreferrer noopener\">poles<\/a> and zeros are not located at origin then the transfer function will be <\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"200\" src=\"https:\/\/lh3.googleusercontent.com\/eE5OuiaApdHc4zTUjqcDlsAIUZC88xfv4dWIJGO3XjKikHT6ZbStJUB25yUm1SxN0LJOlopZ_4js9ghow3iSKWVJDS5lBiNneIUWaHtTnRIO6TdCf_RAT_x15n9aNXyvj7bLBaSR=s0\"><\/p>\n\n\n\n<p>Approximation: T >> 1. so, we can neglect 1.<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"62\" src=\"https:\/\/lh5.googleusercontent.com\/UYwe0dfbARyHdaZjAsvOEExwV_P4Qml-XJSGVZDDMWbmAiCGavjHR6KaOSLbMam0IUCpilw_qdOP_SJixE2NoQng5wS5SNI-MDMhhsFvZpn8PO9iaOlBW0CXUUQXfEYmIAbnC9Mw=s0\"><\/p>\n\n\n\n<p>Also due to the Approximation: T &lt;&lt; 1. so, we can neglect T.<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"172\" height=\"31\" src=\"https:\/\/lh6.googleusercontent.com\/fhGYlwcrldW-zPmlKCDprJEppC067l2nxyPbOpkE130Rbz4ITOxK1VTswoZSRVdhXDpc_xe5lC786B3nXvWrVu2IFVMBGpVYxNzVJmUAyu999XwhvyigjnOn4MvYBezTai8ryOyW=s0\"><\/p>\n\n\n\n<p>At a point both meet so equal i.e a time will come hence both approx become equal<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"93\" src=\"https:\/\/lh4.googleusercontent.com\/O-ts47K3IzrNYxk3dUyJd-bWJtbFc0C6mVtjlZ9eCPx2W21Qj3cI3N5FKz6EiNrNOABhmk2_i5zl0kQNgryO_TqnRrBvikkn7oMvmgNOLBx-sJmHrwMbq3_XtpjeypMqt2aG8qSa=s0\"><\/p>\n\n\n\n<p>At this frequency both the cases are equal<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"213\" src=\"https:\/\/lh5.googleusercontent.com\/zFiiBi7H7_uicrgqcisjGAgfLaiAM3byTh_WBrKmj8UaTEmXKnNKHYHJluPwIWW5grD1PwWr83vjIj094SnZZxzHeL8gq9dBtu_rO4WsP1BQtP0fw9O26TODFu74zP5LHWrAotrY=s0\"><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" width=\"371\" height=\"265\" src=\"https:\/\/lh3.googleusercontent.com\/FxjnYk7X91bTcfznNHkeCaXYFIAj6yJIXn2XtZluvZUYEEN37ZVji8knGca1kj5cjWx1UO6wR2V4ssJFAnLHhNdMIhligGQg8YbC_ihQNVMYJRjPreywoIrbdELcVm1Geid0czz3=s0\"><\/p>\n\n\n\n<p>When we increase the value of&nbsp; in approximation 2 and decrease the&nbsp; of approximation 1 so a RT comes when both cases are equal and hence for that value of&nbsp; where both approximations are equal gives max. error we found above and is equal to 3dB<\/p>\n\n\n\n<p>Then at corner frequency we have max error of -3dB<\/p>\n\n\n\n<p><strong>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-are-logic-gates\/\" target=\"_blank\" rel=\"noreferrer noopener\">Basic Logic Gates<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-aloha\/\" target=\"_blank\" rel=\"noreferrer noopener\">What is ALOHA?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-switched-mode-power-supply\/\" target=\"_blank\" rel=\"noreferrer noopener\">Working of SMPS<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-are-plcs\/\" target=\"_blank\" rel=\"noreferrer noopener\">What are PLCs?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-stepper-motor\/\" target=\"_blank\" rel=\"noreferrer noopener\">Working principle of Stepper Motor<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>As proposed by Hendrik W. Bode a  Bode Plot is simply a graphical representation used to design and analyze any control system. <\/p>\n","protected":false},"author":28,"featured_media":5641,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37],"tags":[],"class_list":["post-6521","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What are Bode Plots? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"As proposed by Hendrik W. 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