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

Downloads

Download the latest in PCB design and EDA software

  • PCB DESIGN SOFTWARE
  • Altium Designer

    Complete Environment for Schematic + Layout

  • CircuitStudio

    Entry Level, Professional PCB Design Tool

  • CircuitMaker

    Community Based PCB Design Tool

  • NEXUS

    Agile PCB Design For Teams

  • CLOUD PLATFORM
  • Altium 365

    Connecting PCB Design to the Manufacturing Floor

  • COMPONENT MANAGEMENT
  • Altium Concord Pro

    Complete Solution for Library Management

  • Octopart

    Extensive, Easy-to-Use Component Database

  • PRODUCT EXTENSIONS
  • PDN Analyzer

    Natural and Effortless Power Distribution Network Analysis

  • See All Extensions
  • EMBEDDED
  • TASKING

    World-Renowned Technology for Embedded Systems Development

  • TRAININGS
  • Live Courses

    Learn best practices with instructional training available worldwide

  • On-Demand Courses

    Gain comprehensive knowledge without leaving your home or office

  • ONLINE VIEWER
  • 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

    ALTIUMLIVE

    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

    Downloads

    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

    Pole-Zero Analysis and Transient Analysis in High Speed Design

    Zachariah Peterson
    |  August 18, 2019

    Measurements for transient analysis on an oscilloscope readout

    Overshoot and ringing in transient analysis. Image credit.

    As part of high speed design, transmission line effects in traces and impedance matching normally receive a lot of attention. This is understandable, as switching speed in a digital IC is the primary factor that determines whether termination needs to be considered in a transmission line. However, any RLC circuit can exhibit a transient response, which appears as overshoot or undershoot and a subsequent damped oscillation during switching. This can even propagate into the power bus in a PCB. This is shown in the above graph, where the output from a switching IC is compared with the voltage on a power bus.

     

    When Transients Become Important

    The transient response in a circuit becomes more problematic as the switching speed increases; the voltage induced in an RLC network or in a transmission line due to parasitic capacitance/inductance is larger when the switching speed is faster. Impedance matching in a system with transmission lines is important for suppressing reflections, but the transient response can still appear as an underdamped oscillation in the voltage/current seen at the receiver.

    The behavior of transients becomes important in any circuit that contains an equivalent RLC portion or is itself an equivalent RLC network (this is essentially every circuit thanks to parasitics). This includes impedance matching networks, circuits with capacitive and/or inductive loads, and many other circuits. In low-level circuits with narrow noise margin, or on clock pulse trains, this can produce unintended switching in a downstream IC. If a circuit is over-terminated at the source (i.e., the transient response is overdamped), the current takes a longer amount of time to rise to full scale, effectively increasing the propagation delay.

    When designing an impedance matching network or decoupling network, you should try to aim for critical damping, although this is not always possible. As part of transient analysis, pole-zero analysis is a great tool you can use to quickly understand the transient behavior of your system. This allows you to identify whether a given circuit or model is overdamped/underdamped, and you can use the results to reach critical damping using series termination.

     

    Pole-Zero Analysis in Transient Analysis

    If you are working with a lumped transmission line model or with simpler circuits, it is rather easy to determine the damping constant in your circuit using Kirchoff’s laws and/or the Telegrapher's equations. With more complicated circuits, it can be more difficult to determine the damping constant in your circuit. This is where pole-zero analysis can aid transient analysis of your circuit. This allows you to identify the damping constant and the oscillation frequency in a circuit when it is driven with digital or analog pulses.

    If you are familiar with transfer functions and Laplace transforms, then you are already familiar with the idea of poles and zeroes in a circuit’s response. Pole analysis is based on calculating the damping constant and oscillation frequency in a circuit, effectively showing you maxima in the transfer function. As most circuits are purely involve first order or second order derivatives of the charge in the circuit, the output from a pole-zero simulation will generally reveal two possible poles in your circuit. Higher order circuits may have many more poles and/or zeroes (3 or more). Calculating these values by hand directly from the transfer function for very complex circuit can be difficult as it may require solving a third degree or higher polynomial, and the problem can become intractable.

    Pole-zero analysis automates this process for you. The example below shows the output from pole-zero analysis. If we look at the graph, we see there are two poles and one zero. Note that the real parts of these values are negative. The two poles are complex conjugates of each other (as they should be), and the zero lies along the real axis.

    Real and imaginary parts of the poles in a circuit

    Example output from pole-zero analysis as part of transient analysis

     

    What Does This Mean in Transient Analysis?

    The location of the poles tells us two things in transient analysis. First, the real part of the pole is the damping constant in the circuit. In the above plot, the real part of the poles is negative (about -315 rad/sec), meaning the transient response decays over time. The imaginary part is the frequency at which the transient response will oscillate (about 1 kHz). In this case, the transient response will produce an underdamped oscillation. Note that, if the poles were located on the right half of the graph (i.e., the real part of the poles was positive), then this system would be unstable, and the transient response would grow over time.

    The zeroes of a transfer function refer to specific frequencies that produce a zero output in the circuit. In the above example, the zero is located at the origin, meaning that a DC driver will not pass a current into the circuit. If the zero were located elsewhere along the imaginary axis, then the value on the imaginary axis corresponds to a particular frequency that will not produce a current in the circuit.

    Pole-zero analysis is just one of many tools you can use for transient analysis in that it tells you two aspects of a given circuit:

    • Stability: this is important in circuits with feedback and it tells you the limits of the driving frequency you should use in your circuit.

    • Damping: you can immediately determine whether the response is overdamped, underdamped, or critically damped.

    Note that this does not tell you the resonance frequency of the circuit; this is best done by looking at the transfer function for your circuit, or you can calculate it manually from the real and imaginary parts of a pole, just as you would for any oscillator. Note that some circuits with multiple complex conjugate pair poles will have multiple resonances.

    If you complete pole-zero analysis and you find that your circuit exhibits an undesired response (i.e., an underdamped response in an impedance matching network), you can iterate through different component values in your circuit to determine the component values that produce the desired response. This allows you to critically damp the response in your circuit such that you can eliminate overshoot/undershoot.

    Transient responses in different impedance matching networks

    You can examine multiple transients when optimizing an impedance matching network

    When you work with the comprehensive set of signal integrity tools in Altium Designer®, you won’t have to conduct transient analysis by hand. The industry-standard layout and simulation tools are ideal for high speed design and high frequency analog design. These tools are integrated into a single platform, allowing them to be quickly incorporated into your workflow.

    Contact us or download a free trial if you’re interested in learning more about Altium Designer. You’ll have access to the industry’s best layout, simulation, and data management tools in a single program. 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