{"id":64440,"date":"2025-05-12T09:21:24","date_gmt":"2025-05-12T06:21:24","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64440"},"modified":"2026-09-30T18:26:27","modified_gmt":"2026-09-30T15:26:27","slug":"microstrip-from-zo","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/microstrip-from-zo\/","title":{"rendered":"Microstrip Impedance From Zo 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\">Microstrip Geometry Estimator from Target Zo<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64440\" data-favorite-title=\"Microstrip Impedance From Zo\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-from-zo\/\" data-favorite-excerpt=\"Find the microstrip trace width needed to hit a target characteristic impedance (Zo). Enter the target impedance, dielectric constant and substrate height, and get the required width in mm.\" 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\/microstrip-from-zo\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64440\" data-post=\"64440\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Characteristic impedance<\/label><div class=\"term\">Z_0<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"characteristic_impedance\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-1\">\u03a9<\/div><small id=\"calc-info-1\">Target characteristic impedance<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Dielectric constant<\/label><div class=\"term\">\u03b5r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"dielectric_constant\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"4.5\"\/><small id=\"calc-info-2\">Relative permittivity of the substrate<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Substrate height<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"substrate_height\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"1.6\"\/><div class=\"unit\" id=\"calc-unit-3\">mm<\/div><small id=\"calc-info-3\">Height of the substrate (dielectric layer)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64440\">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>Required Trace Width<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"mm\"><\/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=\"64440\" 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>Microstrip Width From Zo 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\\[ A = \\frac{Z_0}{60}\\sqrt{\\frac{\\varepsilon_r + 1}{2}} + \\frac{\\varepsilon_r - 1}{\\varepsilon_r + 1}\\left(0.23 + \\frac{0.11}{\\varepsilon_r}\\right) \\\\ \\frac{w}{h} = \\frac{8e^{A}}{e^{2A} - 2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(Z_0\\) \u2014 target characteristic impedance (\u03a9)<\/li>\n<li>\\(\\varepsilon_r\\) \u2014 relative permittivity (dielectric constant) of the substrate<\/li>\n<li>\\(h\\) \u2014 substrate height, i.e. the dielectric thickness between the trace and the ground plane (mm)<\/li>\n<li>\\(w\\) \u2014 required trace width (mm)<\/li>\n<li>\\(A\\) \u2014 dimensionless intermediate term<\/li>\n<\/ul>\n<p>This is Wheeler's synthesis equation for a microstrip line. It inverts the standard impedance analysis formulas, so instead of computing \\(Z_0\\) from a known geometry, it directly yields the width-to-height ratio \\(w\/h\\) that produces the desired impedance.<\/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>Microstrip Width From Zo \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 50 \u03a9 single-ended microstrip on 1.6 mm FR-4 with a dielectric constant of 4.5.<\/p>\n<p>\\[ A = \\frac{50}{60}\\sqrt{\\frac{4.5 + 1}{2}} + \\frac{4.5 - 1}{4.5 + 1}\\left(0.23 + \\frac{0.11}{4.5}\\right) = 1.382 + 0.162 = 1.544 \\]<\/p>\n<p>\\[ \\frac{w}{h} = \\frac{8e^{1.544}}{e^{2 \\cdot 1.544} - 2} = \\frac{8 \\cdot 4.683}{21.93 - 2} \\approx 1.880 \\]<\/p>\n<p>\\[ w = 1.880 \\times 1.6 = 3.01~\\text{mm} \\]<\/p>\n<p><strong>Result:<\/strong> the required trace width is approximately 3.01 mm.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Characteristic impedance<\/strong> \\(Z_0\\) you want to achieve, in ohms. For most RF and high-speed single-ended traces this is 50 \u03a9.<\/li>\n<li>Enter the <strong>Dielectric constant<\/strong> \\(\\varepsilon_r\\) of your substrate. Standard FR-4 is typically 4.3\u20134.7 depending on frequency and manufacturer; high-frequency laminates range from about 2.2 (PTFE) to 10 (alumina).<\/li>\n<li>Enter the <strong>Substrate height<\/strong> \\(h\\) in millimetres \u2014 the thickness of the dielectric layer between the copper trace and the ground plane, not the total board thickness.<\/li>\n<li>Read the <strong>Required Trace Width<\/strong> in the result field. The calculation updates instantly as you change any input.<\/li>\n<\/ol>\n<h2>What Is Microstrip Impedance Synthesis?<\/h2>\n<p>A microstrip is a flat conductor on the outer layer of a printed circuit board, referenced to a ground plane beneath the dielectric. Because the field lines are split between the substrate below and air above, a microstrip behaves as a transmission line with a characteristic impedance \\(Z_0\\) determined by the trace width \\(w\\), the substrate height \\(h\\), and the dielectric constant \\(\\varepsilon_r\\).<\/p>\n<p>Most textbook formulas run in the \u201canalysis\u201d direction: you know the geometry and compute the impedance. This calculator solves the inverse, more practical problem \u2014 <em>synthesis<\/em>: given the impedance your system requires, what trace width should you draw? If you need to check an existing trace instead, use the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-pcb-impedance\/\">Microstrip PCB Impedance calculator<\/a>, which runs the calculation in the forward direction.<\/p>\n<p>Controlling \\(Z_0\\) matters because every driver, receiver, and connector in a high-speed link is designed around a specific impedance. If the trace impedance deviates from it \u2014 typically beyond about \u00b110 % \u2014 part of the signal reflects at each discontinuity, causing ringing, overshoot, EMI, and bit errors. This is why controlled-impedance routing is standard for USB, HDMI, Ethernet, PCIe, DDR memory, and RF circuits. The 50 \u03a9 target is the near-universal convention for single-ended RF work because it is a good compromise between power handling and loss in coaxial systems.<\/p>\n<p>The result is best interpreted as a starting point: the calculator gives the width for an ideal, infinitely thin copper trace. Real boards add effects (trace thickness, solder mask, etch back) that shift the impedance by a few percent, so treat the output as a first-pass value to refine before fabrication.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Valid range:<\/strong> the synthesis formula used here is accurate for \\(w\/h \\lt 2\\), which covers the common cases (impedances below roughly 60\u201370 \u03a9 on typical FR-4). For very narrow, high-impedance traces where \\(w\/h \\gt 2\\) would be needed in the alternate branch of Wheeler's equations, results become less reliable.<\/li>\n<li><strong>Zero trace thickness:<\/strong> copper thickness (e.g. 35 \u00b5m for 1 oz copper) is ignored. Thicker copper lowers the impedance slightly, so the actual impedance will be a few ohms lower than the target; many fab houses provide corrections.<\/li>\n<li><strong>Solder mask:<\/strong> a conformal coating over the trace raises the effective dielectric constant and typically lowers the impedance by 2\u20135 \u03a9. Many stackup tools let you model this explicitly.<\/li>\n<li><strong>Frequency dependence:<\/strong> \\(\\varepsilon_r\\) of FR-4 falls with frequency (roughly 4.5 at low frequency to about 4.2 in the GHz range). Use the value quoted for your operating frequency.<\/li>\n<li><strong>Single-ended only:<\/strong> this calculator handles single-ended traces. Differential pairs (USB, HDMI, LVDS) need coupled-line models \u2014 see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-pcb-differential-impedance\/\">Stripline PCB Differential Impedance calculator<\/a>.<\/li>\n<li><strong>Inner layers differ:<\/strong> traces sandwiched between two dielectric layers are striplines, not microstrips, and follow different equations \u2014 use the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-impedance\/\">Stripline Impedance calculator<\/a> for those.<\/li>\n<li><strong>Final verification:<\/strong> before committing a design, confirm the width with your PCB manufacturer's stackup data or a 2D field solver, since resin content, glass weave, and etch tolerances all play a role.<\/li>\n<\/ul>\n<p>Keep in mind that impedance control is only one part of signal integrity. Spacing to neighbouring traces affects crosstalk, which you can estimate with the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pcb-microstrip-crosstalk\/\">PCB Microstrip Crosstalk calculator<\/a>, and source\/load mismatches may still require matching networks.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the microstrip trace width needed to hit a target characteristic impedance (Zo). Enter the target impedance, dielectric constant and substrate height, and get the required width in mm.<\/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-64440","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\/64440","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=64440"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64440\/revisions"}],"predecessor-version":[{"id":65989,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64440\/revisions\/65989"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64440"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64440"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}