{"id":89,"date":"2025-02-26T10:03:11","date_gmt":"2025-02-26T15:03:11","guid":{"rendered":"https:\/\/blogs.mathworks.com\/semiconductors\/?p=89"},"modified":"2025-07-21T12:20:00","modified_gmt":"2025-07-21T16:20:00","slug":"enhancing-mixed-signal-ic-design-with-symbolic-state-space-models","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/semiconductors\/2025\/02\/26\/enhancing-mixed-signal-ic-design-with-symbolic-state-space-models\/","title":{"rendered":"Enhancing Mixed-Signal IC Design with Symbolic State-Space Models"},"content":{"rendered":"<p>&nbsp;<\/p>\n<p>In the world of Analog\/Mixed-Signal Integrated Circuit (IC) design, <strong>transfer functions<\/strong> have long been the go-to method for representing and analyzing linear time-invariant (LTI) circuits. However, this traditional approach comes with its own set of limitations:<\/p>\n<ul>\n<li><strong>Single-Input-Single-Output (SISO) Limitation<\/strong>: Transfer functions are only applicable to SISO systems, leaving out the complexity of Multiple-Input-Multiple-Output (MIMO) systems.<\/li>\n<li><strong>Lack of Internal State Description<\/strong>: They do not describe internal system states, limiting the depth of analysis.<\/li>\n<\/ul>\n<h2><\/h2>\n<h2>State-Space vs. Transfer Function and Symbolic vs. Numerical<\/h2>\n<p>To address these shortcomings, the state-space representation is often considered. However, it requires extensive <strong>manual calculations<\/strong>, which are <strong>time-consuming<\/strong> and <strong>error-prone<\/strong>, especially when circuit topologies change.<\/p>\n<p>Moreover, both state-space models and transfer functions, when taken into their numerical form, can suffer from <strong>numerical truncations<\/strong> and potentially lead to ill-conditioned system representations.<\/p>\n<p>&nbsp;<\/p>\n<pre> Learn more about <a href=\"https:\/\/www.mathworks.com\/solutions\/semiconductors.html\">MathWorks Solutions for Semiconductors<\/a>, or register to our <a href=\"https:\/\/www.mathworks.com\/content\/mathworks\/www\/en\/company\/events\/seminars\/series\/na-semiconductor-design-and-verification-2025.html\">Semiconductor Webinar Series<\/a><\/pre>\n<p>&nbsp;<\/p>\n<h2>Auto-Generated Symbolic State-Space<\/h2>\n<p>The automatic generation of symbolic state-space models effectively overcomes these limitations effectively by providing:<\/p>\n<ul>\n<li><strong>Symbolic Nature<\/strong>: Allows for the introduction of numerical values later in the process, minimizing issues related to numerical truncations.<\/li>\n<li><strong>Automation<\/strong>: Eliminates the need for manual calculations, enhancing efficiency and reducing errors.<\/li>\n<\/ul>\n<p>Symbolic representations offer other significant advantages, as they support <strong>advanced analytical methodologies<\/strong>, such as robust control techniques. These methodologies can often provide closed form results, in contrast to statistical outcomes typically produced by methods like Monte Carlo simulations.<\/p>\n<p>&nbsp;<\/p>\n<h2>More about Symbolic State-Space Generation<\/h2>\n<p>To delve deeper into the automatic extraction of symbolic state-space representations, refer to the paper titled \u201c<em>Automating the Use of State-Space Representations in Mixed-Signal IC Design and Verification<\/em>\u201d authored by Francesco Stilgenbauer from STMicroelectronics and other contributors that has been presented last October at DVCON Europe 2024.<\/p>\n<p>I had the honor of co-authoring this paper and learned a great deal from Francesco.<\/p>\n<p>&nbsp;<\/p>\n<p><div id=\"attachment_53\" style=\"width: 562px\" class=\"wp-caption aligncenter\"><img aria-describedby=\"caption-attachment-53\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-53\" src=\"http:\/\/blogs.mathworks.com\/semiconductors\/files\/2025\/02\/Picture2.jpg\" alt=\"Figure 1: Modified schematic of the differential audio LC filter taken as a case study in Francesco\u2019s paper\" width=\"552\" height=\"97\" \/><p id=\"caption-attachment-53\" class=\"wp-caption-text\">Figure 1: Modified schematic of the differential audio LC filter taken as a case study in Francesco\u2019s paper<\/p><\/div><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/ieeexplore.ieee.org\/document\/10830778\"><strong>Read the full paper on IEEEXplore<\/strong><\/a><\/p>\n<h2>Leveraging MATLAB and Simulink Capabilities<\/h2>\n<p>Being based on MATLAB and Simulink, workflows like the one described by Francesco allow to fully exploit a wide range of features:<\/p>\n<ul>\n<li><strong>Advanced Analysis<\/strong>: MATLAB and Simulink control design and signal processing tools allow for a sophisticated analysis of circuit behavior.<\/li>\n<li><strong>Digital Filter Design<\/strong>: MATLAB discretization, system inversion, and signal processing capabilities facilitate the design of digital filters, for instance, to compensate for analog behaviors.<\/li>\n<li><strong>Integration with Logic Simulators<\/strong>: MATLAB and Simulink models can be exported as SystemVerilog components, enabling their reuse in logic simulators and digital verification environments.<\/li>\n<li><strong>Reuse within Analog Simulators<\/strong>: As detailed in the paper, Verilog-A models can be generated from MATLAB discrete-time state-space models, allowing for reuse in analog simulators.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>For those interested in exploring this innovative methodology further, I highly recommend reading the full paper. It offers a guide on automatically extracting symbolic state-space models and leveraging them for efficient mixed-signal IC design and verification.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/ieeexplore.ieee.org\/document\/10830778\"><strong>Read the full paper on IEEEXplore<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>For more information on how MATLAB and Simulink can enhance semiconductor design and verification, visit MathWorks <strong><a href=\"https:\/\/www.mathworks.com\/solutions\/semiconductors.html\">Semiconductor Design and Verification solutions page<\/a><\/strong>, or<strong> <a href=\"https:\/\/www.mathworks.com\/content\/mathworks\/www\/en\/company\/events\/seminars\/series\/na-semiconductor-design-and-verification-2025.html\">register to our upcoming Semiconductor Webinar Series<\/a><\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>Please share your thoughts and experiences in the comments below!<\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/semiconductors\/files\/2025\/02\/Picture2.jpg\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div>\n<p>&nbsp;<br \/>\nIn the world of Analog\/Mixed-Signal Integrated Circuit (IC) design, transfer functions have long been the go-to method for representing and analyzing linear time-invariant (LTI) circuits&#8230;. <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/semiconductors\/2025\/02\/26\/enhancing-mixed-signal-ic-design-with-symbolic-state-space-models\/\">read more >><\/a><\/p>\n","protected":false},"author":209,"featured_media":98,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/posts\/89"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/users\/209"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/comments?post=89"}],"version-history":[{"count":17,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":464,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/posts\/89\/revisions\/464"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/media\/98"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/media?parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/categories?post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/semiconductors\/wp-json\/wp\/v2\/tags?post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}