Free Trials

Download a free trial to find out which Altium software best suits your needs

How to Buy

Contact your local sales office to get started on improving your design environment


Download the latest in PCB design and EDA software

  • Altium Designer

    Complete Environment for Schematic + Layout

  • CircuitStudio

    Entry Level, Professional PCB Design Tool

  • CircuitMaker

    Community Based PCB Design Tool


    Agile PCB Design For Teams

  • Altium 365

    Connecting PCB Design to the Manufacturing Floor

  • Altium Concord Pro

    Complete Solution for Library Management

  • Octopart

    Extensive, Easy-to-Use Component Database

  • PDN Analyzer

    Natural and Effortless Power Distribution Network Analysis

  • See All Extensions

    World-Renowned Technology for Embedded Systems Development

  • Live Courses

    Learn best practices with instructional training available worldwide

  • On-Demand Courses

    Gain comprehensive knowledge without leaving your home or office

  • Altium 365 Viewer

    View & Share electronic designs in your browser

  • Altium Designer 20

    The most powerful, modern and easy-to-use PCB design tool for professional use


    Annual PCB Design Summit

    • Forum

      Where Altium users and enthusiasts can interact with each other

    • Blog

      Our blog about things that interest us and hopefully you too

    • Ideas

      Submit ideas and vote for new features you want in Altium tools

    • Bug Crunch

      Help make the software better by submitting bugs and voting on what's important

    • Wall

      A stream of events on AltiumLive you follow by participating in or subscribing to

    • Beta Program

      Information about participating in our Beta program and getting early access to Altium tools

    All Resources

    Explore the latest content from blog posts to social media and technical white papers gathered together for your convenience


    Take a look at what download options are available to best suit your needs

    How to Buy

    Contact your local sales office to get started improving your design environment

    • Documentation

      The documentation area is where you can find extensive, versioned information about our software online, for free.

    • Training & Events

      View the schedule and register for training events all around the world and online

    • Design Content

      Browse our vast library of free design content including components, templates and reference designs

    • Webinars

      Attend a live webinar online or get instant access to our on demand series of webinars

    • Support

      Get your questions answered with our variety of direct support and self-service options

    • Technical Papers

      Stay up to date with the latest technology and industry trends with our complete collection of technical white papers.

    • Video Library

      Quick and to-the-point video tutorials to get you started with Altium Designer

    Clearing Up Trace Impedance Calculators and Formulas

    Zachariah Peterson
    |  May 19, 2019

    Calculator on electronic schematics

    Be careful when using a trace impedance calculator

    While it might not be obvious to the casual or to those who think the mathematics underlying PCB design is largely settled, there is plenty of disagreement regarding the right formula to calculate trace impedance. This disagreement extends to online trace impedance calculators, and designers should make themselves aware of the limitations of these tools.


    The Problem with a Trace Impedance Calculator

    If you use your favorite search engine to find a trace impedance calculator, you’ll find several. Some of these online calculators are  freeware programs from different companies Others just list formulas without citing sources. Some of these calculators will produce results without any context, without listing specific assumptions, and without detailing the relevant approximations their formulas used.

    These points are very important when working with, say, designing an impedance matching network for a printed trace antenna. Some calculators will allow you to calculate trace impedance in a number of geometries, e.g., broadside coupled, embedded microstrips, symmetric or asymmetric stripline, or regular microstrips. Other calculators are like a black box; you have no idea which formulas they are using and no way to check the accuracy of these calculations without comparing with a number of other calculators.

    To quote Douglas Brooks in an October 2011 article, “In the opinion of many designers, there are no impedance formulas that are now considered adequate.” Breaking down the mathematics of every trace impedance formula and providing a full solution for trace impedance is beyond the scope of this article. Instead, let’s take a look at the empirical trace impedance formulas often specified by the IPC and the more accurate equations provided by Brian Wadell and Rick Hartley, which are based on Wheeler’s methodology.

    IPC-2141 vs. Wadell’s Equations for Microstrips

    The IPC-2141 standard is just one source of empirical equations for microstrip and stripline impedance. However, the IPC-2141 formulas for microstrip traces actually produce less accurate results than the equations presented by Wadell. Polar Instruments provides a brief overview of this topic, and the IPC-2141 equation and Wadell’s equations are listed in this article.

    IPC-2141 equation for characteristic trace impedance

    IPC-2141 equation for characteristic trace impedance

    The accuracy of these equations for microstrip traces with different impedances is also compared in the Polar Instruments article. When the analytic results are compared with numerically calculated results in a given geometry, the results from Wadell’s equations have a factor ~10 higher accuracy (less than 0.7% error) than the results from the IPC-2141 equation for a microstrip. Despite the higher accuracy provided by Wadell’s equations, the IPC-2141 equation is still used in many online calculators.

    Hartley’s Equations for Embedded Microstrips

    Hartley derived a set of impedance equations for embedded microstrip traces that explicitly includes the effective dielectric constant and an incremental trace width adjustment due to the effective dielectric constant; these factors are not explicit in the Polar Instruments article, although they can be found in the references to Wadell’s work. Hartley’s method appears to be based on Wheeler’s method, although this was not explicitly stated.

    One can easily see that Hartley’s embedded microstrip traces reduce to Wadell’s surface microstrip equations. However, the Polar Instruments article contains an apparent error inside Wadell’s characteristic impedance equation: there appears to be a redundant square root inside the logarithm function. One should take note of this and check the equations against the original references when designing a trace impedance calculator for embedded and surface microstrips.

    Hartley’s equations for microstrip trace impedance

    Hartley’s method appears to be the most accurate method for calculating microstrip trace impedance for both embedded and surface traces. However, there is still an approximation enforced on the ratio of the microstrip width to the height above the conducting plane. This makes Hartley’s equations discontinuous and brings their accuracy into question when the microstrip width is similar to the height of the microstrip above the conducting plane.


    Going Forward with a Trace Impedance Calculator

    Before, working with a trace impedance calculator, one should be aware of which equations the calculation uses. Not all calculators will explicitly state this. Some calculators opt for Hartley’s results, yet they simply state that they are based on Wheeler’s method without providing references. Others simply present the IPC-2141 equation without stating from where the equation was taken.

    HDI routing on blue PCB

    Complicating things further, some RF calculators will present other trace impedance equations without citing sources. These equations appear to be an amalgamation of various factors from Hartley’s equations, while other factors are omitted or simply reduced through approximations.

    One final note regarding online calculators: these calculators may allow you to enter values that fall outside the valid range of their approximation. This produces inaccurate impedance values, yet you wouldn’t know that they are incorrect because the approximation is not listed, nor does the calculator check the inputs for validity.

    The right design software will allow you to incorporate the impedance equation you need as part of your design rules. With high speed and high frequency controlled impedance design, you need design tools that allow you to define the proper impedance for your specific trace configuration on surface layers or on internal signal layers. Altium Designer includes a layer stack manager with an extensive stackup materials that helps you control impedance throughout your design. These features integrate directly with your layout tools and run on top of a unified design engine, allowing you to create top quality boards for any application.

    If you’re interested in learning more about Altium , you can contact us or download a free trial and get access to the industry’s best layout, routing, and simulation tools. Talk to an Altium expert today to learn more.

    About Author

    About Author

    Zachariah Peterson has an extensive technical background in academia and industry. Prior to working in the PCB industry, he taught at Portland State University. He conducted his Physics M.S. research on chemisorptive gas sensors and his Applied Physics Ph.D. research on random laser theory and stability.His background in scientific research spans topics in nanoparticle lasers, electronic and optoelectronic semiconductor devices, environmental systems, and financial analytics. His work has been published in several peer-reviewed journals and conference proceedings, and he has written hundreds of technical blogs on PCB design for a number of companies.

    most recent articles

    Back to Home