{"id":64416,"date":"2025-05-12T09:13:33","date_gmt":"2025-05-12T06:13:33","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64416"},"modified":"2026-09-30T18:23:40","modified_gmt":"2026-09-30T15:23:40","slug":"l-matching-network","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/l-matching-network\/","title":{"rendered":"L Matching Network Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">L-Network Impedance Matching Tool<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64416\" data-favorite-title=\"L Matching Network\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/l-matching-network\/\" data-favorite-excerpt=\"Calculate the component values for an L-network that matches a low source resistance to a higher load resistance at a given RF frequency. Enter the two resistances and the operating frequency to get Q, the series inductance, and the parallel capacitance.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-engineering\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/l-matching-network\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64416\" data-post=\"64416\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Source resistance<\/label><div class=\"term\">Rs<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"source_resistance\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-1\">\u03a9<\/div><small id=\"calc-info-1\">Source resistance (input impedance)<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Load resistance<\/label><div class=\"term\">Rl<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"load_resistance\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"200\"\/><div class=\"unit\" id=\"calc-unit-2\">\u03a9<\/div><small id=\"calc-info-2\">Load resistance (output impedance)<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Operating frequency<\/label><div class=\"term\">f<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"operating_frequency\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><div class=\"unit\" id=\"calc-unit-3\">MHz<\/div><small id=\"calc-info-3\">Frequency in megahertz (MHz)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64416\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Quality Factor (Q)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Series Reactance<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"\u03a9\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Parallel Reactance<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"\u03a9\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Series Inductance<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"\u00b5H\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Parallel Capacitance<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"pF\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64416\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>L Matching Network Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ Q = \\sqrt{\\frac{R_L}{R_S} - 1} \\\\ X_S = Q \\cdot R_S \\\\ X_P = \\frac{R_L}{Q} \\]\n\\[ L = \\frac{X_S}{2\\pi f} \\qquad C = \\frac{1}{2\\pi f \\, X_P} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(R_S\\) \u2014 source resistance, the lower impedance to be matched (\u03a9)<\/li>\n<li>\\(R_L\\) \u2014 load resistance, the higher impedance to be matched (\u03a9)<\/li>\n<li>\\(Q\\) \u2014 loaded quality factor of the network<\/li>\n<li>\\(X_S\\) \u2014 series reactance (\u03a9)<\/li>\n<li>\\(X_P\\) \u2014 parallel reactance (\u03a9)<\/li>\n<li>\\(f\\) \u2014 operating frequency (Hz)<\/li>\n<li>\\(L\\) \u2014 series inductance (H)<\/li>\n<li>\\(C\\) \u2014 parallel capacitance (F)<\/li>\n<\/ul>\n<p>These formulas design the classic low-pass L-network that transforms a low source resistance \\(R_S\\) up to a higher load resistance \\(R_L\\): a series inductor on the low-impedance side and a shunt capacitor on the high-impedance side. The Q factor is set by the resistance ratio alone, so it cannot be chosen independently.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>L Matching Network \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 50 \u03a9 source must drive a 200 \u03a9 load at 10 MHz.<\/p>\n<p>\\[ Q = \\sqrt{\\frac{200}{50} - 1} = \\sqrt{3} \\approx 1.7321 \\]<\/p>\n<p>\\[ X_S = 1.7321 \\times 50 = 86.60~\\Omega \\qquad X_P = \\frac{200}{1.7321} \\approx 115.47~\\Omega \\]<\/p>\n<p>\\[ L = \\frac{86.60}{2\\pi \\times 10 \\times 10^6} \\approx 1.378~\\mu\\text{H} \\qquad C = \\frac{1}{2\\pi \\times 10 \\times 10^6 \\times 115.47} \\approx 137.8~\\text{pF} \\]<\/p>\n<p><strong>Result:<\/strong> a series inductor of <strong>1.378 \u00b5H<\/strong> on the 50 \u03a9 side and a shunt capacitor of <strong>137.8 pF<\/strong> across the 200 \u03a9 load match the two resistances at 10 MHz.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Source resistance<\/strong> \\(R_S\\) in ohms \u2014 for example, the 50 \u03a9 output of a transmitter or generator.<\/li>\n<li>Enter the <strong>Load resistance<\/strong> \\(R_L\\) in ohms. It must be greater than the source resistance; if it is not, swap the two values and flip the network orientation.<\/li>\n<li>Enter the <strong>Operating frequency<\/strong> in MHz \u2014 the frequency at which the match must hold.<\/li>\n<li>Read the results: the quality factor <strong>Q<\/strong>, the series and parallel reactances, and the practical component values \u2014 <strong>Series Inductance<\/strong> in \u00b5H and <strong>Parallel Capacitance<\/strong> in pF.<\/li>\n<\/ol>\n<h2>What is an L matching network?<\/h2>\n<p>An L-network is the simplest impedance matching circuit, named after the shape of its schematic: two reactive components \u2014 one in series, one in parallel (shunt) \u2014 arranged as an \"L\". Its purpose is to make a load appear to the source as a pure resistance equal to the source resistance, so that maximum power is transferred and virtually no signal is reflected at the interface.<\/p>\n<p>The version calculated here is the low-pass configuration for matching a <em>low<\/em> resistance \\(R_S\\) to a <em>high<\/em> resistance \\(R_L\\): the series inductor goes on the low-impedance (source) side and the shunt capacitor on the high-impedance (load) side. Because the two reactances are equal in magnitude and opposite in effect at the design frequency, the network presents exactly \\(R_S\\) to the source while the load sees a transformed impedance.<\/p>\n<p>A key property of the L-network is that its Q is not a free parameter. It is fixed by the resistance ratio: \\(Q = \\sqrt{R_L\/R_S - 1}\\). A 50 \u03a9-to-200 \u03a9 match, for instance, always has \\(Q \\approx 1.73\\). If you need a specific Q \u2014 for example, a narrow-band match with high selectivity, or a broad match with low Q \u2014 use a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/t-matching-network\/\">T matching network<\/a> or a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pi-network-impedance-matching\/\">PI network impedance matching<\/a> topology instead, where Q can be chosen independently of the transformation ratio.<\/p>\n<p>When reading the result, remember that the match is perfect only at the design frequency. The bandwidth over which the match stays acceptable is roughly \\(f\/Q\\); higher transformation ratios mean higher Q and therefore a narrower usable band.<\/p>\n<h2>Assumptions, limitations and practical tips<\/h2>\n<ul>\n<li><strong>Resistive impedances only.<\/strong> The calculator assumes both source and load are pure resistances. If the load is reactive (for example, an antenna with significant reactance), first cancel its reactance with a series or shunt component, then match the resistive part.<\/li>\n<li><strong>\\(R_L\\) must exceed \\(R_S\\).<\/strong> This tool only transforms upward (low to high). To match a high source to a low load, swap the two resistances and mirror the network: the inductor and capacitor swap roles on either side of the L.<\/li>\n<li><strong>Fixed Q.<\/strong> Since \\(Q\\) is determined by the resistance ratio, the L-network offers no control over bandwidth. Use T or \u03c0 networks when you need a specific Q.<\/li>\n<li><strong>Component self-resonance.<\/strong> At VHF and above, parasitic inductance and capacitance of real components shift the match. Choose inductors and capacitors whose self-resonant frequency is well above your operating frequency, and prefer high-Q, low-ESR capacitors (C0G\/NP0) for RF work.<\/li>\n<li><strong>Stray effects matter.<\/strong> PCB trace inductance and pad capacitance become part of the network. Keep the layout compact and account for trace impedance, which you can estimate with the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-pcb-impedance\/\">Microstrip PCB Impedance<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-impedance\/\">Stripline Impedance<\/a> calculators.<\/li>\n<li><strong>Verify with a VNA.<\/strong> Component tolerances and parasitics mean the built network rarely matches exactly on the first try; tune the inductor or capacitor experimentally for best return loss.<\/li>\n<\/ul>\n<h2>Typical L-network values for common matches<\/h2>\n<p>The table below shows series inductance and shunt capacitance for a 50 \u03a9 source at several transformation ratios, all at 10 MHz. Scale \\(L\\) and \\(C\\) inversely with frequency: halving the frequency doubles the inductance and the capacitance.<\/p>\n<table>\n<thead>\n<tr>\n<th>\\(R_L\\) (\u03a9)<\/th>\n<th>Q<\/th>\n<th>X_S (\u03a9)<\/th>\n<th>X_P (\u03a9)<\/th>\n<th>L at 10 MHz (\u00b5H)<\/th>\n<th>C at 10 MHz (pF)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>100<\/td>\n<td>1.000<\/td>\n<td>50.00<\/td>\n<td>100.00<\/td>\n<td>0.796<\/td>\n<td>159.2<\/td>\n<\/tr>\n<tr>\n<td>200<\/td>\n<td>1.732<\/td>\n<td>86.60<\/td>\n<td>115.47<\/td>\n<td>1.378<\/td>\n<td>137.8<\/td>\n<\/tr>\n<tr>\n<td>500<\/td>\n<td>3.000<\/td>\n<td>150.00<\/td>\n<td>166.67<\/td>\n<td>2.387<\/td>\n<td>95.5<\/td>\n<\/tr>\n<tr>\n<td>1000<\/td>\n<td>4.359<\/td>\n<td>217.94<\/td>\n<td>229.42<\/td>\n<td>3.469<\/td>\n<td>69.4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note how the required capacitance <em>falls<\/em> as the transformation ratio grows, while the inductance rises \u2014 and how Q climbs rapidly, narrowing the bandwidth of high-ratio matches.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the component values for an L-network that matches a low source resistance to a higher load resistance at a given RF frequency. Enter the two resistances and the operating frequency to get Q, the series inductance, and the parallel capacitance.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[92],"class_list":["post-64416","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-rf-microwave"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64416","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64416"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64416\/revisions"}],"predecessor-version":[{"id":65982,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64416\/revisions\/65982"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}