{"id":64549,"date":"2025-05-12T10:14:39","date_gmt":"2025-05-12T07:14:39","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64549"},"modified":"2026-09-30T18:38:59","modified_gmt":"2026-09-30T15:38:59","slug":"t-matching-network","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/t-matching-network\/","title":{"rendered":"T 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\">T-Network Impedance Matching Estimator<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64549\" data-favorite-title=\"T Matching Network\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/t-matching-network\/\" data-favorite-excerpt=\"Computes the capacitor and inductor values for a T impedance matching network from frequency, source and load impedance, and Q factor \u2014 for RF, antenna and amplifier matching.\" 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\/t-matching-network\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64549\" data-post=\"64549\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">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=\"frequency\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"1000000\"\/><div class=\"unit\" id=\"calc-unit-1\">Hz<\/div><small id=\"calc-info-1\">Operating frequency<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">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-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-2\">\u03a9<\/div><small id=\"calc-info-2\">Real part of source impedance<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Source Reactance<\/label><div class=\"term\">Xs<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"source_reactance\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0\"\/><div class=\"unit\" id=\"calc-unit-3\">\u03a9<\/div><small id=\"calc-info-3\">Imaginary part of source impedance<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">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-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"100\"\/><div class=\"unit\" id=\"calc-unit-4\">\u03a9<\/div><small id=\"calc-info-4\">Real part of load impedance<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Load Reactance<\/label><div class=\"term\">Xl<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"load_reactance\" id=\"field-5\" aria-describedby=\"calc-unit-5 calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0\"\/><div class=\"unit\" id=\"calc-unit-5\">\u03a9<\/div><small id=\"calc-info-5\">Imaginary part of load impedance<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">Q Factor<\/label><div class=\"term\">Q<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"q_factor\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"2\"\/><small id=\"calc-info-6\">Quality factor of the matching network<\/small><\/div><div class=\"field is-single\" id=\"input-7\"><label for=\"field-7\">Circuit DC Current<\/label><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"circuit_dc_current\"><option value=\"1\">Pass DC Current<\/option><option value=\"0\">Block DC Current<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64549\">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>Capacitor (C)<\/span><\/span><span class=\"field-value\" id=\"result-1\" 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-2\"><span class=\"field-title\"><span>Series Inductor (Ls)<\/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>Shunt Inductor (Ll)<\/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><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=\"64549\" 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\">1<\/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\">1<\/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>T 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\\[ X = Q \\, R_s \\\\ B = \\frac{Q}{R_s} \\\\ L_s = L_l = \\frac{X}{2\\pi f} \\\\ C = \\frac{B}{2\\pi f} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(f\\) \u2014 operating frequency (Hz)<\/li>\n<li>\\(R_s\\) \u2014 source resistance (\u03a9)<\/li>\n<li>\\(Q\\) \u2014 loaded quality factor of the network<\/li>\n<li>\\(X\\) \u2014 required series reactance (\u03a9)<\/li>\n<li>\\(B\\) \u2014 required shunt susceptance (S)<\/li>\n<li>\\(L_s, L_l\\) \u2014 series inductances (H)<\/li>\n<li>\\(C\\) \u2014 shunt capacitance (F)<\/li>\n<\/ul>\n<p>Each series arm of the T network needs a reactance of \\(X = QR_s\\), and the shunt branch needs a susceptance of \\(B = Q\/R_s\\). Dividing by \\(2\\pi f\\) converts the reactance into an inductance and the susceptance into a capacitance at the operating frequency.<\/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>T Matching Network \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> match a 50 \u03a9 source to a 100 \u03a9 load at 1 MHz with a quality factor of 2 \u2014 the calculator's default values.<\/p>\n<p>\\[ X = Q R_s = 2 \\times 50 = 100~\\Omega \\]<\/p>\n<p>\\[ B = \\frac{Q}{R_s} = \\frac{2}{50} = 0.04~\\text{S} \\]<\/p>\n<p>\\[ L_s = L_l = \\frac{100}{2\\pi \\times 1\\,000\\,000} \\approx 15.92~\\mu\\text{H} \\]<\/p>\n<p>\\[ C = \\frac{0.04}{2\\pi \\times 1\\,000\\,000} \\approx 6.37~\\text{nF} \\]<\/p>\n<p><strong>Result:<\/strong> two series inductors of 15.92 \u00b5H and a shunt capacitor of 6.37 nF.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the operating <strong>Frequency<\/strong> in hertz (for example, 1000000 for 1 MHz).<\/li>\n<li>Enter the <strong>Source Resistance<\/strong> and <strong>Source Reactance<\/strong> in ohms \u2014 the real and imaginary parts of the impedance driving the network.<\/li>\n<li>Enter the <strong>Load Resistance<\/strong> and <strong>Load Reactance<\/strong> in ohms \u2014 the impedance the network must match to.<\/li>\n<li>Set the <strong>Q Factor<\/strong>. Higher Q gives stronger harmonic attenuation but narrower bandwidth; typical values are 1\u20135.<\/li>\n<li>Choose <strong>Circuit DC Current<\/strong>: \u201cPass DC Current\u201d keeps the series inductors so DC flows through the network, while \u201cBlock DC Current\u201d indicates series capacitors that isolate the DC path.<\/li>\n<li>Read the three component values from the results: the shunt capacitor \\(C\\) and the two inductors \\(L_s\\) and \\(L_l\\).<\/li>\n<\/ol>\n<h2>What Is a T Matching Network?<\/h2>\n<p>A T matching network is a three-element impedance transformation circuit named after its shape: two reactive elements in series (one in each arm of the signal path) and a third reactive element connected as a shunt between them. In the low-pass configuration computed here, the series arms are inductors and the shunt element is a capacitor. It is widely used in radio-frequency design \u2014 between a transmitter and an antenna, an amplifier and a filter, or a source and a transmission line \u2014 to transform one impedance into another.<\/p>\n<p>Matching matters because of the maximum power transfer theorem: when the impedance seen by the source equals the complex conjugate of the source impedance, the largest possible fraction of power is delivered and reflections vanish. Without a match, part of the signal reflects back toward the source, producing standing waves (a high VSWR), reduced transmitted power, inaccurate measurements, and \u2014 in transmitters \u2014 stress on the output stage.<\/p>\n<p>The quality factor \\(Q\\) sets how aggressive the transformation is. A higher Q means larger reactances, a steeper impedance transformation, and stronger attenuation of harmonics; the low-pass T with series inductors and a shunt capacitor passes the fundamental while attenuating higher frequencies. The trade-off is bandwidth: higher Q narrows the frequency range over which the match holds and makes the circuit more sensitive to component tolerances and frequency drift.<\/p>\n<p>Compared with the two-element L network, whose Q is fixed by the impedance ratio, the T network lets you choose the Q \u2014 and therefore the bandwidth \u2014 independently. Its close relative, the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pi-network-impedance-matching\/\">PI network impedance matching calculator<\/a>, uses two shunt elements and one series element and is often preferred when a shunt capacitor at the load is more convenient.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li>The calculation assumes ideal, lossless components. Real inductors have winding resistance and self-capacitance, which shift the match at higher frequencies; use RF-grade components and verify with a network analyzer if accuracy is critical.<\/li>\n<li>The component values are derived from the resistive part of the source impedance. If your source or load has significant reactance, cancel it first \u2014 for example, a capacitive load reactance can be absorbed by reducing the adjacent series inductive reactance by the same amount.<\/li>\n<li>Both series arms use the same reactance \\(X = QR_s\\), which produces an exact conjugate match when \\(R_l = R_s(1+Q^2)\\). For other load resistances the result is an approximation; check the final impedance with a Smith chart or circuit simulator and adjust Q or the load-side component if needed.<\/li>\n<li>The \u201cBlock DC Current\u201d option changes the component types rather than the required reactances: series capacitors of \\(1\/(2\\pi f X)\\) farads replace the series inductors, so DC is isolated while the RF match is preserved.<\/li>\n<li>All component values scale inversely with frequency \u2014 the same reactances at 10 MHz need one-tenth the inductance and capacitance as at 1 MHz.<\/li>\n<li>When building the network, keep leads short and account for parasitic inductance; the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/straight-wire-inductor\/\">straight wire inductance calculator<\/a> helps estimate how much a lead or trace adds. If an exact value is unavailable, combine stock parts using the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/series-inductance\/\">series inductance<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-inductance\/\">parallel inductance<\/a> calculators.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Computes the capacitor and inductor values for a T impedance matching network from frequency, source and load impedance, and Q factor \u2014 for RF, antenna and amplifier matching.<\/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-64549","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\/64549","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=64549"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64549\/revisions"}],"predecessor-version":[{"id":66023,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64549\/revisions\/66023"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}