{"id":18833,"date":"2023-12-20T10:10:36","date_gmt":"2023-12-20T10:10:36","guid":{"rendered":"https:\/\/imperix.com\/doc\/?p=18833"},"modified":"2026-03-06T13:41:29","modified_gmt":"2026-03-06T13:41:29","slug":"llc-converter-control","status":"publish","type":"post","link":"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control","title":{"rendered":"LLC converter operation with resistive load"},"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\/llc-converter-control\/#What-is-an-LLC-converter\" >What is an LLC converter?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Modeling-of-the-LLC-converter\" >Modeling of the LLC converter<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Fundamental-Harmonic-Approximation\" >Fundamental Harmonic Approximation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Transfer-function-of-the-LLC-converter\" >Transfer function of the LLC converter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#LLC-converter-parameter-selection\" >LLC converter parameter selection<\/a><\/li><\/ul><\/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\/llc-converter-control\/#Operation-of-the-LLC-converter\" >Operation of the LLC converter<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Operation-at-resonance-omega-n-1\" >Operation at resonance (\\(\\omega_n = 1\\))<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Operation-above-resonance-omega-n-%3E-1\" >Operation above resonance (\\(\\omega_n &gt; 1\\))<\/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\/llc-converter-control\/#Operation-below-resonance-omega-n-%3C-1\" >Operation below resonance (\\(\\omega_n &lt; 1\\))<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#LLC-converter-prototype-example\" >LLC converter prototype example<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Experimental-setup\" >Experimental setup<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Simulink-model\" >Simulink model<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#Experimental-results\" >Experimental results<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/imperix.com\/doc\/implementation\/llc-converter-control\/#References\" >References<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>This technical note provides an introduction to the LLC converter, which is an isolated DC-DC converter, popular in a multitude of fields. It is the first in a family of articles discussing the LLC converter:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/imperix.com\/doc\/implementation\/llc-resonant-converter-for-battery-charging-applications\">TN126 &#8211; LLC resonant converter for battery charging applications<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/doc\/implementation\/resonant-tank-circuit-design-for-an-llc-converter\">TN127 &#8211; Tank circuit design for an LLC resonant converter<\/a><\/li>\n<\/ul>\n\n\n\n<p>The fundamental harmonic approximation is presented as a modeling technique before the operation of the LLC converter is discussed above resonance, at resonance, and below resonance.<\/p>\n\n\n\n<p>Following that, this technical note demonstrates how to build and operate an LLC converter using imperix hardware and software, and compares the physical implementation with the theory and the simulated plant.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-is-an-llc-converter\"><span class=\"ez-toc-section\" id=\"What-is-an-LLC-converter\"><\/span>What is an LLC converter?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Most applications of LLC converters are characterized by the use of a resonant tank to induce a lag between the current and the voltage while exciting its isolation transformer with a near-sinusoidal current. This lagging current allows the LLC converter to operate in Zero Voltage Switching (ZVS) mode, while the sinusoidal current allows the isolation transformer to operate efficiently. On the secondary side of the transformer, rectification of the voltage can be done using diodes, or using synchronous rectifiers. This rectification occurs in Zero Current Switching (ZCS) mode. The resulting high efficiency allows the designer to increase the frequency of the LLC converter, reducing the size of all passives. <\/p>\n\n\n\n<p>Figure 1 is a schematic of a full-bridge LLC converter. The switches on the secondary of the transformer are present to perform rectification. In a unidirectional application such as in this technical note, they can also be replaced with diodes.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"751\" height=\"181\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2023\/12\/LLC_schematic_Rload_v1-1.png\" alt=\"Figure 1: Schematic of an LLC converter with a resistive load  \" class=\"wp-image-19110\" title=\"Figure 1: Bidirectional LLC converter Schematic\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2023\/12\/LLC_schematic_Rload_v1-1.png 751w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2023\/12\/LLC_schematic_Rload_v1-1-300x72.png 300w\" sizes=\"auto, (max-width: 751px) 100vw, 751px\" \/><figcaption class=\"wp-element-caption\">Figure 1: Schematic of an LLC converter with a resistive load  <\/figcaption><\/figure>\n\n\n\n<p>Multiple modulation schemes exist for controlling LLC converters [1]. The modulation strategy considered in this technical note is Pulse Frequency Modulation (PFM). PFM changes the frequency of voltage \\(V_1\\), which changes the magnitude of current \\(I_{Lr}\\). The change of the current in the resonant tank affects voltages \\(V_2\\) and \\(V_{load}\\). <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-modeling-of-the-llc-converter\"><span class=\"ez-toc-section\" id=\"Modeling-of-the-LLC-converter\"><\/span>Modeling of the LLC converter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Resonant converters such as the LLC converter operate by exciting a tank circuit near its resonant frequency. As a result, a different set of assumptions have to be made, compared to the ones made for PWM converters, to derive a model that can be used to predict the behavior of the LLC converter. <\/p>\n\n\n\n<p> The next sections discuss the Fundamental Harmonic Approximation (FHA) and how it can be used to derive a transfer function for the LLC converter when driving a resistive load [2]. An extension of this discussion for constant voltage loads can be found in <a href=\"https:\/\/imperix.com\/doc\/implementation\/llc-resonant-converter-for-battery-charging-applications\">TN126 &#8211; LLC resonant converter for battery charging applications<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-fundamental-harmonic-approximation\"><span class=\"ez-toc-section\" id=\"Fundamental-Harmonic-Approximation\"><\/span>Fundamental Harmonic Approximation <span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Despite \\(V_1\\) being a square wave, when the resonant tank is excited at its resonant frequency, the resonant current \\(I_{Lr}\\) is sinusoidal with negligible harmonic content. As a result, FHA supposes that \\(V_1\\) can be approximated by considering only its fundamental harmonic when the resonant tank is excited near its resonant frequency. Consequently, power transfer through the resonant tank and the transformer can be analyzed and the relationship between \\(V_2\\) and \\(V_1\\) can be derived. <\/p>\n\n\n\n<p>The derivation of \\(\\frac{V_2}{V_1}\\) requires the replacement of the full-bridge rectifier and \\(R_{load}\\) with an equivalent resistance \\(R_{ac}\\). Due to the FHA, it is assumed that the current flowing through the transformer is purely sinusoidal. Therefore, by equating the DC component of the rectified current flowing through the resistor with the load current, an expression can be found for \\(R_{ac}\\) [2].<\/p>\n\n\n\n<p>Note that \\(R_{ac}\\) is referred to the primary side of the isolation transformer.<\/p>\n\n\n\n<p>\\begin{equation}<br>R_{ac} = \\frac{n V_{2_{RMS}}}{\\frac{1}{n} I_{2_{RMS}}} = \\frac{8n^2}{\\pi^2} R_{load}<br>\\end{equation}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-transfer-function-of-the-llc-converter\"><span class=\"ez-toc-section\" id=\"Transfer-function-of-the-LLC-converter\"><\/span>Transfer function of the LLC converter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Having referred the load to the primary side, the resonant tank, shown in Figure 2, can be  analyzed:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"105\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2023\/12\/resonant_tank_schematic_v1.png\" alt=\"Figure 2: Schematic of the resonant tank of the LLC converter, after referring the load across the transformer\" class=\"wp-image-19111\" title=\"Figure 2: Resonant Tank Analysis\"\/><figcaption class=\"wp-element-caption\">Figure 2: Resonant tank schematic after referring the load across the transformer<\/figcaption><\/figure>\n<\/div>\n\n\n<p>A frequency-dependent gain function can be defined for the circuit in Figure 2 [3].<\/p>\n\n\n\n<p>$$<br>V_2 = \\frac{V_1}{n} \\frac{-\\omega^2 R_{ac} L_m}{R_{ac} (\\frac{1}{C_r}-\\omega^2(L_m+L_r)) + j \\omega L_m (\\frac{1}{C_r}-\\omega^2 L_r L_m)}<br>$$<br>This function can be normalized after making the following substitutions:<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\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 style=\"font-size:18px\">$$<br>\\begin{align}<br>L_n &amp;= \\frac{L_m}{L_r} \\\\<br>\\\\<br>\\omega_n &amp;= \\frac{\\omega}{\\omega_r} \\\\<br>\\end{align}<br>$$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p style=\"font-size:18px\">$$<br>\\begin{align}<br>\\omega_r &amp;= \\frac{1}{\\sqrt{L_r C_r}} \\\\<br>\\\\<br>Q &amp;= \\frac{\\sqrt{\\frac{L_r}{C_r}}}{R_{ac}} \\\\<br>\\end{align}<br>$$<\/p>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><strong>\\(Q\\)<\/strong> <\/strong>is defined as the<strong> quality factor <\/strong>of the circuit. It is the ratio between the characteristic impedance \\(\\sqrt{\\frac{L_r}{C_r}}\\) , and \\(R_{ac}\\) <\/li>\n\n\n\n<li><strong>\\(L_n\\) <\/strong>is defined as<strong> <\/strong>the <strong>normalized inductance<\/strong>.<strong> <\/strong>It is the ratio between the magnetizing inductance and resonant inductance.<\/li>\n\n\n\n<li><strong>\\(\\omega_n\\)<\/strong> is the <strong>normalized switching frequency <\/strong>of the LLC converter.<\/li>\n\n\n\n<li><strong>\\(\\omega_r\\)<\/strong> is considered the <strong>resonant frequency <\/strong>of the LLC converter even though the location of the peak gain of the LLC converter can vary based on operating conditions.<\/li>\n<\/ul>\n\n\n\n<p>The equation, after making the relevant substitutions, is shown below. It has been rearranged to show the gain of the resonant tank.<\/p>\n\n\n\n<p>$$<br>\\frac{V_2}{V_1} = \\frac{1}{n} \\frac{-\\omega_n^2 L_n}{1-\\omega_n^2 (L_n + 1) + j L_n \\omega_n Q (1 &#8211; \\omega_n^2)}<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-llc-converter-parameter-selection\"><span class=\"ez-toc-section\" id=\"LLC-converter-parameter-selection\"><\/span>LLC converter parameter selection<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The influence of the main design parameters, namely \\(L_n\\) and \\(Q\\), can be analyzed from the graphs below. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/LLC_param_plot.png\" alt=\"Figure 3: Plots of the possible gain curves of the LLC converter when varying resonant tank parameters Q and Ln \" class=\"wp-image-24343\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/LLC_param_plot.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/LLC_param_plot-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/LLC_param_plot-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 3: Possible gain curves of the LLC converter when varying Q factor (left) and when varying \\(L_n\\) (right)<\/figcaption><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-quality-factor-latex-q\">Quality factor \\(Q\\) <br><\/h4>\n\n\n\n<p>The left plot in Figure 3 shows how the gain curve of the LLC converter varies as the \\(Q\\) factor is modulated for a fixed \\(L_n\\).<\/p>\n\n\n\n<p>By definition, a larger \\(Q\\) factor means that the characteristic impedance of the resonant tank is considerably larger than the loading effect imposed by \\(R_{load}\\). Therefore, a larger \\(Q\\) factor implies that the resonant current magnitude will not greatly change as the load impedance varies. This is advantageous in ensuring that the circulating current in the resonating tank stays within desired limits during operation.<\/p>\n\n\n\n<p>However, due to the same reason, a high \\(Q\\) factor limits the maximum achievable gain (shown in Figure 3). The designer will therefore have to balance the effect of increased circulating current in the resonant tank versus the ability to reach the required peak gain, which is often a design constraint.  <\/p>\n\n\n\n<p>Note that, for all quality factors, the gain at \\(\\omega_n = 1\\) is always 1. This is an interesting property of the LLC converter as the insensitivity to changes in the load impedance at this operating point allows the LLC converter to have excellent transient performance when operating at resonance. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-normalized-inductance-latex-l_n\">Normalized inductance \\(L_n\\) <\/h4>\n\n\n\n<p>The right plot in Figure 3 shows how the gain curve for the LLC converter changes for various normalized inductances.<\/p>\n\n\n\n<p>If the \\(Q\\) factor and \\(\\omega_r\\) are considered fixed, then a larger \\(L_n\\) implies that the transformer part of the LLC converter&#8217;s resonant tank has a larger magnetizing inductance \\(L_m\\). Therefore, when comparing two designs operating at resonance, the LLC converter with a larger \\(L_n\\) will have less magnetizing current due to its transformer. The reduction in this current increases the efficiency of the LLC converter at this operating point.<\/p>\n\n\n\n<p>On the other hand, an increased \\(L_n\\) results in a decrease in the dynamic range of the possible gain of the resonant tank. Additionally, even if the required gains are achievable in two competing designs, the LLC converter with the larger \\(L_n\\) will require a greater shift in operating frequency to change the gain of the LLC converter. <\/p>\n\n\n\n<p>The larger required change in frequency affects all aspects of LLC converter design:     <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a lower minimum operating frequency will require larger filters to ensure the current ripple remains within specification<\/li>\n\n\n\n<li>a higher maximum operating frequency will result in higher switching losses and the typical EMC concerns associated with higher-frequency switching<\/li>\n\n\n\n<li>a large deviation in frequency would complicate the design of the magnetics as they would be operating in a larger range of frequencies<\/li>\n<\/ul>\n\n\n\n<p>As a result, just as with the \\(Q\\) factor, the designer will have to balance the desire to reduce the converter magnetizing current with the disadvantages that a large \\(L_n\\) creates.<\/p>\n\n\n\n<p>The LLC converter is often designed iteratively to ensure that all constraints are effectively met.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-operation-of-the-llc-converter\"><span class=\"ez-toc-section\" id=\"Operation-of-the-LLC-converter\"><\/span>Operation of the LLC converter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-operation-at-resonance-latex-omega_n-1\"><span class=\"ez-toc-section\" id=\"Operation-at-resonance-omega-n-1\"><\/span>Operation at resonance (\\(\\omega_n = 1\\))<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>When operating the LLC converter at resonance, the gain of the resonant tank is one. Furthermore, the ZVS (at turn-on of the primary switches) &amp; ZCS (for the rectification diodes) conditions are fulfilled and the resonant tank current is sinusoidal. <\/p>\n\n\n\n<p>Figure 4 shows a plot from a simulated LLC converter operating at resonance. The excitation voltage is plotted alongside to show the switching transitions. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/at_resonance-1.png\" alt=\"Figure 4: Simulated LLC converter resonant tank current at resonance\" class=\"wp-image-24345\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/at_resonance-1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/at_resonance-1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/at_resonance-1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 4: Simulated resonant current when the LLC converter is operating at resonance <\/figcaption><\/figure>\n\n\n\n<p>The reduced switching losses, coupled with the reduced losses in the magnetics due to the sinusoidal current, make this operating point the most efficient. The high efficiency at this operating point has given rise to converter topologies where the LLC converter remains at resonance at all times [4].<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-operation-above-resonance-latex-omega_n-1\"><span class=\"ez-toc-section\" id=\"Operation-above-resonance-omega-n-%3E-1\"><\/span>Operation above resonance (\\(\\omega_n &gt; 1\\))<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>When operating the LLC converter above resonance, the gain of the resonant tank is below 1. As the resonant tank impedance is always inductive above the resonant frequency, ZVS on the primary side switches is guaranteed at turn-on. <\/p>\n\n\n\n<p>Operating above resonance is characterized by a tank current like the one shown in Figure 5 below. The current begins to naturally oscillate at \\(\\omega_r\\) before the earlier switching changes the shape of the current as shown in the figure.  <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/above_resonance-1.png\" alt=\"Figure 5: Simulated resonant tank current above resonance\" class=\"wp-image-24346\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/above_resonance-1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/above_resonance-1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/above_resonance-1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 5: Simulated resonant current when the LLC converter is operating above resonance<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-operation-below-resonance-latex-omega_n-1\"><span class=\"ez-toc-section\" id=\"Operation-below-resonance-omega-n-%3C-1\"><\/span>Operation below resonance (\\(\\omega_n &lt; 1\\))<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>When operating the LLC converter below resonance, the gain of the resonant tank can be either above or below 1 depending on the frequency of operation. <\/p>\n\n\n\n<p>When switching the LLC converter below the resonant frequency, while remaining in the ZVS region, the shape of the current is as shown in Figure 6.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/below_resonance-1.png\" alt=\"Figure 6: Simulated resonant tank current below resonance\" class=\"wp-image-24347\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/below_resonance-1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/below_resonance-1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/below_resonance-1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 6: Simulated resonant current when the LLC converter is operating below resonance in the ZVS region<\/figcaption><\/figure>\n\n\n\n<p>As mentioned for other operating modes,  the current starts to naturally oscillate at \\(\\omega_r\\). In this case, the later switching, compared to resonant operation, results in the magnetizing inductance of the transformer maintaining the polarity of the current until the next switching instance.<\/p>\n\n\n\n<p>When switching below resonance, the LLC converter can operate either in ZVS mode or in ZCS mode, depending on the operating frequency. The boundary between the ZVS mode operating region and the ZCS mode operating region can be found by substituting the expression below into the equation of the resonant tank gain.<\/p>\n\n\n\n<p> $$<br>Q = \\sqrt{\\frac{1}{(1-\\omega_n^2)L_n} &#8211; \\frac{1}{\\omega_n^2 L_n^2}}<br>$$<\/p>\n\n\n\n<p>Figure 7 shows the boundary between the two areas, and how the LLC converter gain is split between the ZVS mode region and the ZCS mode region.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/ZVS_vs_ZCS_region_LLC.png\" alt=\"Figure 7: ZVS and ZCS regions according to FHA for two different load cases\" class=\"wp-image-24348\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/ZVS_vs_ZCS_region_LLC.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/ZVS_vs_ZCS_region_LLC-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/ZVS_vs_ZCS_region_LLC-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 7: ZVS and ZCS operating regions for two load cases<\/figcaption><\/figure>\n\n\n\n<p>In the case of high-frequency converters such as the LLC converter, generally, the switch of choice tends to be Si(C) MOSFETs or GaN HEMTs. For these devices, turn-on losses are greater than turn-off losses, therefore choosing the ZVS mode of operation is favorable because the ZVS mode results in no turn-on losses.<\/p>\n\n\n\n<p>Since the ZVS\/ZCS boundary crosses close to the peak of the gain-frequency plot, and there is a desire to remain in the ZVS mode zone, the lower limit of the switching frequency is limited to the frequency corresponding to the ZVS boundary.  <\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-llc-converter-prototype-example\"><span class=\"ez-toc-section\" id=\"LLC-converter-prototype-example\"><\/span>LLC converter prototype example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Imperix products can be used to easily implement a laboratory-scale prototype of the LLC converter. Figure 8 shows a possible implementation, made using the following products:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a B-Box RCP controller<\/li>\n\n\n\n<li>2x PEB 8024 are used to create a SiC H-bridge that is capable of switching at up to 200 kHz<\/li>\n\n\n\n<li>2x PEB 4050 are used, without any gate signals, as diodes since the IGBT technology has excellent body diodes in comparison to the SiC-based modules<\/li>\n\n\n\n<li>A custom resonant tank (as discussed in <a href=\"https:\/\/imperix.com\/doc\/implementation\/resonant-tank-circuit-design-for-an-llc-converter\">TN127<\/a>), with the following parameters:\n<ul class=\"wp-block-list\">\n<li>L<sub>r<\/sub> = 21 \u00b5H<\/li>\n\n\n\n<li>L<sub>m<\/sub> = 90 \u00b5H<\/li>\n\n\n\n<li>C<sub>r<\/sub> = 110 nF<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>A transformer with n = \\(\\frac{8}{9}\\)<\/li>\n\n\n\n<li>A resistive  load of either 99 \u03a9 or 50 \u03a9<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"493\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780_w_osc.png\" alt=\"Figure 8: LLC converter set up in the imperix laboratory\" class=\"wp-image-22754\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780_w_osc.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780_w_osc-300x190.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780_w_osc-768x485.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 8: LLC converter set up in the imperix laboratory<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-experimental-setup\"><span class=\"ez-toc-section\" id=\"Experimental-setup\"><\/span>Experimental setup<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=\"780\" height=\"209\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780.png\" alt=\"Figure 9: Labeled visual of the laboratory setup\" class=\"wp-image-22749\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780-300x80.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/setup_picture_Rload_cropped_780-768x206.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 9: Labeled visual of the laboratory setup<\/figcaption><\/figure>\n\n\n\n<p>Figure 9 shows a picture of the setup used to validate the provided Simulink file. The analog measurements and gate-driving optical fibers are wired such that they match the example model that can be downloaded below. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-practical-advice\">Practical advice<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since the LLC converter is a resonant converter that can be switched faster than the control frequency, it is essential that the hardware protections on the B-Box are correctly set to protect the equipment.<\/li>\n\n\n\n<li>Imperix modules require the de-rating of allowable RMS current as a function of the switching frequency. The derating curves can be found in the datasheets.<\/li>\n\n\n\n<li>The ratings of the capacitor bank in the resonant tank must be carefully observed to ensure that it can withstand both the maximum voltage across the capacitors and the maximum RMS current flowing through them.<\/li>\n\n\n\n<li>The recommendations outlined in <a href=\"https:\/\/imperix.com\/doc\/implementation\/safety-and-protection-in-the-lab\" type=\"link\" id=\"https:\/\/imperix.com\/doc\/implementation\/safety-and-protection-in-the-lab\">TN181<\/a> should be followed to maximize safety when performing experiments in the lab.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-simulink-model\"><span class=\"ez-toc-section\" id=\"Simulink-model\"><\/span>Simulink model<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=\"780\" height=\"250\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/simulink_screenshot_llc.png\" alt=\"Figure 10: Simulink model for the open loop control of the LLC converter\" class=\"wp-image-22727\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/simulink_screenshot_llc.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/simulink_screenshot_llc-300x96.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/simulink_screenshot_llc-768x246.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 10: Simulink model for the open loop control of the LLC converter<\/figcaption><\/figure>\n\n\n\n<p>Installing the imperix block set from the <a href=\"https:\/\/imperix.com\/doc\/help\/getting-started-acg-sdk-simulink\">ACG SDK<\/a> gives the user access to custom blocks which facilitate using Simulink to program the B-Box. Figure 10 shows how the Simulink block set is used to implement the open loop control of the LLC converter in the downloadable file below.<\/p>\n\n\n\n<div style=\"height:37px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a href=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2023\/12\/TN125_LLC_converter_passive_load.zip\" class=\"wp-block-file__button wp-element-button\" download>Download <strong>TN125_LLC_converter_passive_load<\/strong><\/a><\/div>\n\n\n\n<p><br>When controlling the LLC converter using PFM, the following blocks from the block set are essential:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/imperix.com\/doc\/software\/config-control-task-configuration\">Configuration block<\/a>: CLOCK_0 is set to 20 kHz<\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/doc\/software\/analog-data-acquisition\">ADC block<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/doc\/software\/carrier-based-pwm\">CB-PWM generator<\/a>: 2 blocks are needed to drive the primary-side H-bridge, with a duty ratio of 0.5 and a 0.5 offset in phase <\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/doc\/software\/probe-variable\">Probe block<\/a>\n<ul class=\"wp-block-list\">\n<li>The signals plotted in <a href=\"https:\/\/imperix.com\/doc\/help\/cockpit-user-guide\">Cockpit<\/a> will have the sampling frequency configured in the configuration block (using CLOCK_0). An external measurement using higher bandwidth equipment will be required to capture \\(V_1\\) and \\(I_{L_r}\\)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><a href=\"https:\/\/imperix.com\/doc\/software\/tunable-parameter\">Tunable parameter<\/a>\n<ul class=\"wp-block-list\">\n<li>The ability to set limits in the tunable parameter is particularly useful in the case of the LLC converter because it ensures that the frequency of the converter remains within the ZVS mode limits<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>For additional information regarding the soft-start state machine included in the model, additional information can be found in the following article: <a href=\"https:\/\/imperix.com\/doc\/implementation\/dab-converter-control\">TN115 &#8211; DAB converter control using phase-shift modulation<\/a>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h-clock-block\">CLOCK block<\/h4>\n\n\n\n<p>Most imperix examples use the clock output from the configuration block to drive both the ADC and CB PWM blocks. However, to implement PFM, a separate <a href=\"https:\/\/imperix.com\/doc\/software\/clock-generators\">clock block<\/a> (CLOCK_1) must be inserted into the model. There, by changing its configuration, its frequency input can be enabled. <\/p>\n\n\n\n<h3 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><\/h3>\n\n\n\n<p>As expected from the LLC converter, when exciting the resonant tank at its resonant frequency (\\(\\omega_n = 1\\)), the current is sinusoidal, as can be seen in Figure 11. It is very similar to the simulated current and voltage in Figure 4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_at_resonance.png\" alt=\"Figure 11: Measured resonant tank current of the LLC converter at resonance\" class=\"wp-image-24349\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_at_resonance.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_at_resonance-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_at_resonance-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 11: Measurement of tank current in the test setup at 105 kHz<\/figcaption><\/figure>\n\n\n\n<p>As shown in Figure 12, measuring the resonant current of the LLC converter above resonance shows a current waveform very similar to the simulated current in Figure 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_above_resonance-1.png\" alt=\"Figure 12: Measured resonant tank current above resonance\" class=\"wp-image-24350\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_above_resonance-1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_above_resonance-1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_above_resonance-1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 12: Measurement of the tank current in the test setup at 160 kHz<\/figcaption><\/figure>\n\n\n\n<p>As shown in Figure 13, measuring the resonant current of the LLC converter below resonance shows a current waveform very similar to the simulated current in Figure 7.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_below_resonance-1.png\" alt=\"Figure 13: Measured resonant tank current of the LLC converter below resonance\" class=\"wp-image-24353\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_below_resonance-1.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_below_resonance-1-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/HW_below_resonance-1-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 13: Measurement of the tank current in the test setup at 70 kHz<\/figcaption><\/figure>\n\n\n\n<p>Figure 14 compares using the FHA model of the LLC converter for gain estimation with a physical measurement.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"780\" height=\"300\" src=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/FHA_vs_results_plots.png\" alt=\"Figure 14: Comparison of measured output voltages with output voltages predicted using FHA\" class=\"wp-image-24355\" srcset=\"https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/FHA_vs_results_plots.png 780w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/FHA_vs_results_plots-300x115.png 300w, https:\/\/imperix.com\/doc\/wp-content\/uploads\/2024\/02\/FHA_vs_results_plots-768x295.png 768w\" sizes=\"auto, (max-width: 780px) 100vw, 780px\" \/><figcaption class=\"wp-element-caption\">Figure 14: Comparison between measured gain and designed gain using FHA<\/figcaption><\/figure>\n\n\n\n<p> Calculating the gain using the FHA model underestimates the gain near its peak, and overestimates the gain at higher frequencies. The theoretical curve should match the physical measurement at \\(\\omega_r\\) (or \\(\\omega_n = 1\\)), however since the series resistance and other non-idealities were not accurately modeled, the actual crossover point occurs at a lower switching frequency.<\/p>\n\n\n\n<p>While the results in Figure 14 show that there are differences between the predicted output voltage and the measured output voltage, FHA is still reasonably accurate for designing an LLC converter. Additionally, other modeling techniques for the LLC converter exist even if the accuracy of the FHA prediction is not sufficient for a given application [5].<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-references\"><span class=\"ez-toc-section\" id=\"References\"><\/span>References<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1109\/TPEL.2020.2975392\">[1]<\/a> Y. Wei, Q. Luo and A. Mantooth, &#8220;Overview of Modulation Strategies for LLC Resonant Converter,&#8221; in IEEE Transactions on Power Electronics, Oct. 2020<br>[2] R. W. Erickson, D. Maksimovi\u0107,<em>&nbsp;Fundamentals of Power Electronics<\/em>, 3rd ed.,&nbsp;Springer Cham, Cham, Switzerland, 2020,&nbsp;pp. 940\u2013945.<br>[3] C. Adragna,&nbsp;<em>LLC Resonant Converters: An Overview of Modeling, Control and Design Methods and Challenges<\/em>, now, 2022.&nbsp;pp. 160\u2013168.<br><a href=\"https:\/\/doi.org\/10.1109\/JESTPE.2019.2956240\">[4]<\/a> Q. Liu, Q. Qian, B. Ren, S. Xu, W. Sun and L. Yang, &#8220;A Two-Stage Buck\u2013Boost Integrated LLC Converter With Extended ZVS Range and Reduced Conduction Loss for High-Frequency and High-Efficiency Applications,&#8221; in IEEE Journal of Emerging and Selected Topics in Power Electronics, Feb. 2021<br><a href=\"https:\/\/doi.org\/10.1109\/APEC.2001.912451\">[5]<\/a> J. F. Lazar and R. Martinelli, &#8220;Steady-state analysis of the LLC series resonant converter,&#8221; in<em> Proc. of<\/em> APEC 2001, Anaheim, CA, USA, 2001, pp. 728-735 vol.2<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This technical note provides an introduction to the LLC converter, which is an isolated DC-DC converter, popular in a multitude of fields. <\/p>\n<p>The fundamental harmonic approximation is presented as a modeling technique before the operation of the LLC converter is discussed above resonance, at resonance, and below resonance.<\/p>\n<p>Following that, this technical note demonstrates how to build and operate an LLC converter using imperix hardware and software, and compares the physical implementation with the theory and the simulated plant.<\/p>\n","protected":false},"author":16,"featured_media":24569,"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],"provided-results":[108,107],"related-products":[50,32,92,166,51,111],"guidedreadings":[],"tutorials":[],"user-manuals":[],"coauthors":[83],"class_list":["post-18833","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-implementation","software-environments-matlab","provided-results-experimental","provided-results-simulation","related-products-acg-sdk","related-products-b-box-rcp","related-products-b-box-micro","related-products-b-box-rcp-3-0","related-products-cpp-sdk","related-products-pm"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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