{"id":64446,"date":"2025-05-12T09:30:45","date_gmt":"2025-05-12T06:30:45","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64446"},"modified":"2026-09-30T18:28:06","modified_gmt":"2026-09-30T15:28:06","slug":"microstrip-transmission-line-impedance","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/microstrip-transmission-line-impedance\/","title":{"rendered":"Microstrip Transmission Lines Impedance 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 Line Characteristic Impedance Tool<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64446\" data-favorite-title=\"Microstrip Transmission Lines Impedance\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-transmission-line-impedance\/\" data-favorite-excerpt=\"Estimate the characteristic impedance of a microstrip transmission line from the dielectric constant, substrate height, trace width and copper thickness. Enter your PCB stack-up values to get Z0 in ohms for RF and high-speed design.\" 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-transmission-line-impedance\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64446\" data-post=\"64446\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">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-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"4.5\"\/><small id=\"calc-info-1\">Relative permittivity of the PCB material<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">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-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"1.6\"\/><div class=\"unit\" id=\"calc-unit-2\">mm<\/div><small id=\"calc-info-2\">Height of dielectric layer between trace and ground<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Trace width<\/label><div class=\"term\">w<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"trace_width\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"1\"\/><div class=\"unit\" id=\"calc-unit-3\">mm<\/div><small id=\"calc-info-3\">Width of the transmission line trace<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Trace thickness<\/label><div class=\"term\">t<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"trace_thickness\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0.035\"\/><div class=\"unit\" id=\"calc-unit-4\">mm<\/div><small id=\"calc-info-4\">Copper thickness of the trace<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64446\">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>Characteristic Impedance<\/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><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=\"64446\" 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 Transmission Line Impedance 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\\[ \\varepsilon_{\\mathrm{eff}} = \\frac{\\varepsilon_r + 1}{2} + \\frac{\\varepsilon_r - 1}{2} \\cdot \\frac{1}{\\sqrt{1 + 12h\/w}} \\\\ \\text{If } \\frac{w}{h} \\leq 1: \\quad Z_0 = \\frac{60}{\\sqrt{\\varepsilon_{\\mathrm{eff}}}} \\cdot \\ln\\!\\left( \\frac{8h}{w + t \\cdot \\ln\\!\\left( 1 + \\dfrac{4e}{t\/w} \\right)} \\right) \\\\ \\text{If } \\frac{w}{h} &gt; 1: \\quad Z_0 = \\frac{120\\pi}{\\sqrt{\\varepsilon_{\\mathrm{eff}}} \\cdot \\left( \\dfrac{w}{h} + 1.393 + 0.667 \\cdot \\ln\\!\\left( \\dfrac{w}{h} + 1.444 \\right) \\right)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(Z_0\\) \u2014 characteristic impedance (\u03a9)<\/li>\n<li>\\(\\varepsilon_r\\) \u2014 relative permittivity (dielectric constant) of the substrate<\/li>\n<li>\\(\\varepsilon_{\\mathrm{eff}}\\) \u2014 effective permittivity seen by the line<\/li>\n<li>\\(h\\) \u2014 substrate height between trace and ground plane (mm)<\/li>\n<li>\\(w\\) \u2014 trace width (mm)<\/li>\n<li>\\(t\\) \u2014 trace (copper) thickness (mm)<\/li>\n<li>\\(e \\approx 2.71828\\) \u2014 Euler's number<\/li>\n<\/ul>\n<p>Because part of the field propagates in air above the board, the line behaves as if it were filled by a dielectric with \\(\\varepsilon_{\\mathrm{eff}}\\), which always lies between 1 and \\(\\varepsilon_r\\). The trace-thickness term in the narrow-trace formula accounts for the extra copper that effectively widens the line.<\/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 Transmission Line Impedance \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 1 mm wide trace on a 1.6 mm thick substrate with \\(\\varepsilon_r = 4.5\\) and 0.035 mm (1 oz) copper \u2014 the calculator's default values.<\/p>\n<p>\\[ \\frac{w}{h} = \\frac{1}{1.6} = 0.625 \\leq 1 \\quad \\Rightarrow \\quad \\text{use the narrow-trace formula} \\]<\/p>\n<p>\\[ \\varepsilon_{\\mathrm{eff}} = 2.75 + 1.75 \\cdot \\frac{1}{\\sqrt{1 + 12 \\cdot 1.6 \/ 1}} = 2.75 + \\frac{1.75}{\\sqrt{20.2}} \\approx 3.139 \\]<\/p>\n<p>\\[ t \\cdot \\ln\\!\\left(1 + \\frac{4e}{t\/w}\\right) = 0.035 \\cdot \\ln(311.66) \\approx 0.201 \\text{ mm} \\]<\/p>\n<p>\\[ Z_0 = \\frac{60}{\\sqrt{3.139}} \\cdot \\ln\\!\\left( \\frac{8 \\cdot 1.6}{1 + 0.201} \\right) \\approx 33.86 \\cdot \\ln(10.66) \\approx 33.86 \\cdot 2.366 \\approx 80.09 \\, \\Omega \\]<\/p>\n<p><strong>Result:<\/strong> the characteristic impedance is approximately <strong>80.09 \u03a9<\/strong>.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Dielectric constant<\/strong> of your PCB material (e.g. 4.5 for typical FR-4).<\/li>\n<li>Enter the <strong>Substrate height<\/strong> \u2014 the thickness of the dielectric layer between the trace and the ground plane.<\/li>\n<li>Enter the <strong>Trace width<\/strong> of the copper trace.<\/li>\n<li>Enter the <strong>Trace thickness<\/strong> \u2014 the copper weight of the trace (0.035 mm for 1 oz copper, 0.07 mm for 2 oz).<\/li>\n<li>Read the <strong>Characteristic Impedance<\/strong> in ohms; use the result to adjust the width until you hit your target impedance.<\/li>\n<\/ol>\n<h2>What Is Microstrip Impedance and Why It Matters<\/h2>\n<p>A microstrip transmission line is a flat conductor on the surface of a printed circuit board, with a ground plane on the opposite side of the dielectric layer. It is the most common controlled-impedance structure in modern PCBs because it is easy to fabricate, easy to probe, and gives reasonable performance from DC into the lower gigahertz range.<\/p>\n<p>The characteristic impedance \\(Z_0\\) is the ratio of voltage to current for a wave travelling along the line. When a high-speed or high-frequency signal encounters a change in impedance \u2014 at a driver output, a connector, or a trace of the wrong width \u2014 part of the signal is reflected back toward the source. These reflections cause ringing, overshoot, timing errors, and EMI, and they can corrupt data on digital buses just as they detune RF amplifiers and filters.<\/p>\n<p>Most systems standardise on 50 \u03a9 (RF and test equipment) or 90\u2013100 \u03a9 (differential pairs such as USB, LVDS, and Ethernet). To hit these targets you must set the trace geometry correctly: wider traces lower the impedance, thicker substrates raise it, and higher dielectric constants lower it. A trace of about 3 mm width on 1.6 mm FR-4 comes close to 50 \u03a9; on the same board a 1 mm trace, as in the example above, sits near 80 \u03a9.<\/p>\n<p>If you work with embedded traces between two ground planes instead, use the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-impedance\/\">Stripline Impedance calculator<\/a>; for a similar surface-trace geometry solved differently, see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-pcb-impedance\/\">Microstrip PCB Impedance calculator<\/a>. Keeping uncoupled traces apart also matters \u2014 the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pcb-microstrip-crosstalk\/\">PCB Microstrip Crosstalk calculator<\/a> helps you check spacing, and the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pi-network-impedance-matching\/\">PI Network Impedance Matching calculator<\/a> can help when a source and line simply cannot be made equal.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Quasi-static model:<\/strong> the formulas are accurate for electrically thin substrates (typically up to a few GHz for ordinary FR-4 thicknesses). At higher frequencies, dispersion makes \\(Z_0\\) frequency-dependent and full-wave tools are more reliable.<\/li>\n<li><strong>Isolated trace:<\/strong> the calculation assumes a single trace over an infinite ground plane. Neighbouring traces, planes on the same layer, and via fences all pull the impedance down.<\/li>\n<li><strong>Trace thickness edge case:<\/strong> enter a nonzero copper thickness. Setting \\(t = 0\\) makes the thickness-correction term undefined in the narrow-trace branch; use at least the foil thickness of your stack-up (0.035 mm for 1 oz copper).<\/li>\n<li><strong>Solder mask:<\/strong> the coating above the trace has a dielectric constant near 3\u20134 and typically lowers \\(Z_0\\) by 1\u20133 \u03a9. This calculator ignores it, so budget for the drop on mask-covered traces.<\/li>\n<li><strong>Manufacturing tolerances:<\/strong> etching narrows or widens traces by 10\u201320% of the copper thickness, and both \\(\\varepsilon_r\\) and \\(h\\) vary board to board. A \u00b110% impedance tolerance on the drawing is realistic for standard FR-4; tighter tolerances require controlled-impedance fabrication.<\/li>\n<\/ul>\n<h2>Typical Dielectric Constants<\/h2>\n<table>\n<thead>\n<tr>\n<th>Material<\/th>\n<th>Approx. \\(\\varepsilon_r\\) (1 MHz \u2013 1 GHz)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>FR-4 (standard glass epoxy)<\/td>\n<td>4.3 \u2013 4.7<\/td>\n<\/tr>\n<tr>\n<td>High-Tg \/ low-Dk FR-4 blends<\/td>\n<td>3.8 \u2013 4.2<\/td>\n<\/tr>\n<tr>\n<td>Rogers RO4350B<\/td>\n<td>3.48<\/td>\n<\/tr>\n<tr>\n<td>PTFE (Teflon) \/ RT\/duroid 5880<\/td>\n<td>2.1 \u2013 2.2<\/td>\n<\/tr>\n<tr>\n<td>Alumina (Al<sub>2<\/sub>O<sub>3<\/sub>, hybrid circuits)<\/td>\n<td>9.8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Manufacturers specify \\(\\varepsilon_r\\) at a particular frequency \u2014 always use the value quoted for your design frequency, since FR-4 in particular loses dielectric constant noticeably above a few GHz.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Estimate the characteristic impedance of a microstrip transmission line from the dielectric constant, substrate height, trace width and copper thickness. Enter your PCB stack-up values to get Z0 in ohms for RF and high-speed design.<\/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-64446","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\/64446","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=64446"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64446\/revisions"}],"predecessor-version":[{"id":65993,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64446\/revisions\/65993"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64446"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64446"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}