{"id":6824,"date":"2021-08-30T06:39:08","date_gmt":"2021-08-30T06:39:08","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=6824"},"modified":"2025-05-07T10:43:06","modified_gmt":"2025-05-07T10:43:06","slug":"buck-boost-converter","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter","title":{"rendered":"Buck-boost converter"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-right-text counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#What-is-a-buck-boost-converter\" >What is a buck-boost converter?<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Continuous-and-discontinuous-conduction-mode\" >Continuous and discontinuous conduction mode<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Buck-boost-converter-implementation-with-imperix-power-modules\" >Buck-boost converter implementation with imperix power modules<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Effect-of-parasitic-components\" >Effect of parasitic components<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Passive-component-selection\" >Passive component selection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Academic-Reference\" >Academic Reference<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#B-Box-and-B-Board-implementation\" >B-Box and B-Board implementation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Software-resources\" >Software resources<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Simulink\" >Simulink<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#PLECS\" >PLECS<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/imperix.com\/doc\/implementation\/buck-boost-converter\/#Experimental-results\" >Experimental results<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>This technical note describes the operating principles of a buck-boost converter. A possible open-loop control implementation of this converter, targeting the&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bbox\">B-Box RCP<\/a>&nbsp;or&nbsp;<a href=\"https:\/\/imperix.com\/products\/control\/bboard\">B-Board PRO<\/a>&nbsp;with both&nbsp;<a href=\"https:\/\/imperix.com\/software\/cpp-sdk\">C\/C++<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">automated code generation<\/a>&nbsp;approaches, as well as experimental results are presented.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"419\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Complete-testbench-1.png\" alt=\"Buck-boost converter testbench\" class=\"wp-image-7927\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Complete-testbench-1.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Complete-testbench-1-300x157.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Complete-testbench-1-768x402.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption>Buck-boost converter testbench<br>(Passive components and power supply not sold by imperix)<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-a-buck-boost-converter\"><span class=\"ez-toc-section\" id=\"What-is-a-buck-boost-converter\"><\/span>What is a buck-boost converter?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A step-down buck converter is a type of DC to DC switched-mode power converter like the&nbsp;<a href=\"https:\/\/imperix.com\/doc\/implementation\/step-down-buck-converter\">Step-down buck converter<\/a> and the <a href=\"https:\/\/imperix.com\/doc\/implementation\/step-up-boost-converter\">Step-up boost converter.<\/a> It can be considered as the combination of a buck and a boost converter since it is able to step down and step up the input voltage according to [1]. In an ideal buck-boost converter, the output voltage ranges from 0 to \\(\\infty\\). The specificity of this converter is the inverted polarity of the output voltage.<\/p>\n\n\n\n<p>The converter&#8217;s schematic is presented below.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"397\" height=\"125\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_basic_schematic.png\" alt=\"Buck-boost converter generic schematic\" class=\"wp-image-7934\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_basic_schematic.png 397w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_basic_schematic-300x94.png 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><figcaption>Buck-boost converter schematic<\/figcaption><\/figure><\/div>\n\n\n\n<p>The input to output voltage relation for a buck-boost converter is described by the following equation: $$V_{out} = -\\frac{D}{1-D} V_{in}$$<\/p>\n\n\n\n<p>The minus sign on the equation&#8217;s left side explains the inverting property.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-continuous-and-discontinuous-conduction-mode\"><span class=\"ez-toc-section\" id=\"Continuous-and-discontinuous-conduction-mode\"><\/span>Continuous and discontinuous conduction mode<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Similar to the buck and boost converter, the buck-boost converter can also operate in continuous and discontinuous conduction mode, depending on the inductor current. For more information on the conduction modes please refer to the <a href=\"https:\/\/imperix.com\/doc\/implementation\/step-down-buck-converter\">Step-down buck converter<\/a>&nbsp;note. Also, a plot of the operating mode boundaries can be found in [2].<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-buck-boost-converter-implementation-with-imperix-power-modules\"><span class=\"ez-toc-section\" id=\"Buck-boost-converter-implementation-with-imperix-power-modules\"><\/span>Buck-boost converter implementation with imperix power modules<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The implementation of the converter using imperix&#8217;s power modules is illustrated by the schematic below.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"434\" height=\"244\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_schematic_imperix-5.png\" alt=\"Buck-boost converter schematic with IGBT\" class=\"wp-image-7935\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_schematic_imperix-5.png 434w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/Buck-boost_schematic_imperix-5-300x169.png 300w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><figcaption>Buck-boost converter with an IGBT based imperix module<\/figcaption><\/figure><\/div>\n\n\n\n<p>Only the high side IGBT is driven in this case. However, if a MOSFET power module is used, it is recommended to drive both transistors for synchronous rectification. This subject is further detailed in <a href=\"https:\/\/imperix.com\/doc\/implementation\/step-down-buck-converter\">Step-down buck converter<\/a>.<\/p>\n\n\n\n<p>Note that the power module&#8217;s capacitor, highlighted in red on the schematic, is connected between \\(V_{in}\\) and \\(V_{out}\\). This capacitor does not affect the correct behavior of the circuit. However, several practical details are to be kept in mind when doing experiments.<\/p>\n\n\n\n<p>First, since the output voltage polarity is inverted, the voltage across the module&#8217;s capacitor is \\(V_{in} &#8211; V_{out} = V_{in} + |V_{out}|\\). The designer should then be careful not to exceed the maximum DC bus voltage rating. Second, a protection diode should be placed after the power supply. Indeed, when the converter is turned off, the output voltage goes back to zero. Since the VDC+ terminal of the module is floating, its voltage will rise to V_{in} + |V_{out}| resulting in potential reverse current flow in the power supply.<\/p>\n\n\n\n<p>Last but not least, if a polarized capacitor is used at the output, make sure to connect it in the correct way, meaning the plus terminal to ground, since the output voltage polarity is inverted!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-effect-of-parasitic-components\"><span class=\"ez-toc-section\" id=\"Effect-of-parasitic-components\"><\/span>Effect of parasitic components<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Having similar characteristics to the boost, the buck-boost also suffers from non-idealities [2]. Taking the inductor&#8217;s parasitics resistance into acount, the new transfer function becomes: $$V_{out} = -V_{in}* \\frac{D}{1-D} \\frac{1}{1+\\frac{R_L}{R(1-D)^2}} $$<\/p>\n\n\n\n<p>For more information, please look at the <a href=\"https:\/\/imperix.com\/doc\/implementation\/step-up-boost-converter\">Step-up boost converter<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-passive-component-selection\"><span class=\"ez-toc-section\" id=\"Passive-component-selection\"><\/span>Passive component selection<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The switching of the transistors induces inductor current and output voltage ripples. The current ripples\u2019 amplitude&nbsp;\\(\\Delta I_{L}\\)&nbsp;are determined by the following equation: $$ \\Delta I_{L} = V_{in} \\frac{D}{Lf_{sw}}$$<\/p>\n\n\n\n<p>The voltage ripple\u2019s amplitude follows the equation: $$ \\Delta V_{out} = V_{in} \\frac{D^2}{RCf_{sw}(1-D)}$$<\/p>\n\n\n\n<p>Defining an acceptable value for the ripple\u2019s amplitude, for a given input voltage, frequency, and duty cycle allows for the computation of the passive components.<\/p>\n\n\n\n<p>For instance, with an input voltage of 100 [V], an output voltage of 150[V], and a frequency of 20 [kHz], using an off-the-shelf inductor of 2.36 [mH], the current ripple would have a magnitude of&nbsp;\\(\\Delta I_{out}  = 1.27\\)&nbsp;[A]. Adding an output capacitance of 2 [mF] and a resistor of 60[\u03a9] would then result in an output voltage ripple magnitude of&nbsp;\\(\\Delta V_{out} = 37.5\\) [mV].<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-academic-reference\"><span class=\"ez-toc-section\" id=\"Academic-Reference\"><\/span>Academic Reference<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>[1] Mohan, Undeland, Robbins: \u201cPower Electronics\u201d, 2002<br>[2] Texas Instrument: &#8220;<a href=\"https:\/\/www.ti.com\/lit\/an\/slva059b\/slva059b.pdf?ts=1630278830832&amp;ref_url=https%253A%252F%252Fwww.ti.com%252Fproduct%252FUC3844\">Understanding Inverting Buck-Boost Power Stages in Switch Mode Power Supplies<\/a>&#8220;, Application Report SLVA059B, March 1999 revised March 2019<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-b-box-and-b-board-implementation\"><span class=\"ez-toc-section\" id=\"B-Box-and-B-Board-implementation\"><\/span>B-Box and B-Board implementation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-software-resources\"><span class=\"ez-toc-section\" id=\"Software-resources\"><\/span>Software resources<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>Simulink model<\/em><\/p>\n\n\n\n<div class=\"wp-block-file\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoost_Openloop.slx\">BuckBoost_Openloop<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoost_Openloop.slx\" class=\"wp-block-file__button\" download>Download<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p><em>PLECS model<\/em><\/p>\n\n\n\n<div class=\"wp-block-file\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoost_Openloop.plecs\">BuckBoost_Openloop<\/a><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoost_Openloop.plecs\" class=\"wp-block-file__button\" download>Download<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<p>The provided Simulink and PLECS model implements a simple open-loop control for the converter using the&nbsp;<a href=\"https:\/\/imperix.com\/software\/acg-sdk\/\">ACG SDK<\/a>&nbsp;for simulation and code generation. Isolating the duty cycle from the aforementioned CCM transfer function gives $$ D = \\frac{V_{out}}{V_{out}-V_{in}}$$ The duty cycle for the PWM is then computed with the measured input voltage and the reference output voltage, in a feedforward fashion. The figure below shows an overview of the Simulink algorithm.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"h-simulink\"><span class=\"ez-toc-section\" id=\"Simulink\"><\/span>Simulink<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"682\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlSimulink-1024x682.png\" alt=\"\" class=\"wp-image-8158\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlSimulink-1024x682.png 1024w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlSimulink-300x200.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlSimulink-768x511.png 768w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlSimulink.png 1299w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Buck-boost converter control Simulink implementation<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<h3 class=\"wp-block-heading\" id=\"h-plecs\"><span class=\"ez-toc-section\" id=\"PLECS\"><\/span>PLECS<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"643\" height=\"404\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlPlecs.png\" alt=\"\" class=\"wp-image-8159\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlPlecs.png 643w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/09\/BuckBoostCtrlPlecs-300x188.png 300w\" sizes=\"auto, (max-width: 643px) 100vw, 643px\" \/><figcaption>Buck-boost converter control PLECS implementation<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-experimental-results\"><span class=\"ez-toc-section\" id=\"Experimental-results\"><\/span>Experimental results<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The two following plots show the voltage step-up and step-down capabilities of the buck-boost converter as well as the inductor current ripples. The buck-boost is, in this case, able to change its output voltage from -50 [V] to -150 [V]. Note that the absolute value of the output voltage is plotted here.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"300\" src=\"https:\/\/cdn.imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Experimental_results_v2.png\" alt=\"Buck-boost converter experimental results\" class=\"wp-image-10390\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Experimental_results_v2.png 800w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Experimental_results_v2-300x113.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2021\/08\/Experimental_results_v2-768x288.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><figcaption>Buck-boost converter experimental results<\/figcaption><\/figure><\/div>\n\n\n\n<p>The perturbation seen on the input voltage is most probably due to oscillations in the circuit since it is operating in open-loop. Also, the output voltage in boost mode does not fully reach 150 [V] due to the parasitic resistance of the inductor, as previously explained. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>This technical note describes the operating principles of a buck-boost converter. A possible open-loop control implementation of this converter, targeting the&nbsp;B-Box RCP&nbsp;or&nbsp;B-Board PRO&nbsp;with both&nbsp;C\/C++&nbsp;and&nbsp;automated code&#8230;<\/p>\n","protected":false},"author":11,"featured_media":8143,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[4],"tags":[],"software-environments":[103,104],"provided-results":[108],"related-products":[50,32,92,166,112,111],"guidedreadings":[],"tutorials":[],"user-manuals":[],"coauthors":[64],"class_list":["post-6824","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","software-environments-matlab","software-environments-plecs","provided-results-experimental","related-products-acg-sdk","related-products-b-box-rcp","related-products-b-box-micro","related-products-b-box-rcp-3-0","related-products-peb","related-products-pm"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Buck-boost converter - imperix<\/title>\n<meta name=\"description\" content=\"This note details the working principle of a buck-boost converter. 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