{"id":10597,"date":"2022-07-05T17:49:53","date_gmt":"2022-07-05T17:49:53","guid":{"rendered":"https:\/\/liquidinstruments.com\/?p=10597"},"modified":"2025-12-08T20:42:43","modified_gmt":"2025-12-08T20:42:43","slug":"s-parameter-measurement","status":"publish","type":"post","link":"https:\/\/liquidinstruments.com\/application-notes\/s-parameter-measurement\/","title":{"rendered":"S-parameter measurement with the Moku:Lab Frequency Response Analyzer","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p>Transmission and reflection signal information is vital when designing and validating RF components and systems. In this application note, Moku:Lab\u2019s Frequency Response Analyzer is used in conjunction with an RF directional coupler for a complete S-parameter characterization of a two port network.<\/p>\n<hr \/>\n<h2>Introduction<\/h2>\n<p>Imagine shouting into a long, endless hallway. The sound travels into the abyss with no discontinuity and eventually just fades into nothingness. Next, imagine doing the same thing, but the hallway is truncated with a wall. This time, when you shout your voice is reflected by the wall and echoes back at you. This phenomenon of reflection is analogous to dealing with high frequency signals (hundreds of MHz or GHz) in the RF world. Any mismatch in impedance along the transmission lines of an RF system will result in signal reflection. This reflection is suboptimal in RF design as it reduces transmission quality and efficiency. One useful parameter when designing at high frequencies is the S-parameter, or \u201cScattering parameter\u201d. It is used to describe the reflection\/transmission characteristics of a port network system. In other words, it helps describe how RF energy propagates through a multi-port network. We will be exploring this parameter in depth and showcasing its implementations when analyzing systems and filters at high frequencies using Moku:Lab\u2019s Frequency Response Analyzer. We will visualize transmission line problems and impedance matching with Smith charts.<\/p>\n<h2>Theory<\/h2>\n<p>S-parameters are complex numbers, meaning they have both imaginary and real parts, thus can represent both magnitude and phase. Since we care mainly about power gain or loss we will focus on the magnitude as a function of frequency.<\/p>\n<p>S-parameter characterization of a Device Under Test (DUT) treats that DUT as a black box with one or more ports, where signals can both enter and exit any port. This box can contain a multitude of system variables: resistors, filters, integrated circuits, or transmission lines, the details of which are hidden. The beauty of S-parameters is that we can fully understand a DUT by just analyzing the transmitted and reflected signals as described by its S-parameters. Below is a figure representing a 2-port DUT network along with all the signal paths captured by S-parameters.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone wp-image-10598 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure-1-1.png\" alt=\"S-parameter representation in a 2-port network\" width=\"738\" height=\"314\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure-1-1.png 738w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure-1-1-300x128.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure-1-1-600x255.png 600w\" sizes=\"(max-width: 738px) 100vw, 738px\" \/><br \/>\n<em>Figure 1: S-parameter representation in a 2-port network<\/em><\/p>\n<p>Notice that the four S-parameters for this 2-port network have subscripts relating the ports that are under consideration. The first number is the output port (emerging) and the second number is the input port (applied) as depicted in this figure below.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10602 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Picture1.png\" alt=\"S22 represents the reflected power (magnitude and phase) of the system from port 2 at a certain frequency\" width=\"190\" height=\"108\" \/><\/p>\n<p>For example, S<sub>22<\/sub> represents the reflected power (magnitude and phase) of the system from port 2 at a certain frequency. Moku:Lab\u2019s FRA is capable of driving a DUT with a swept sine wave into a system\u2019s input port and extracting the amplitude and phase response at a system\u2019s output port. On its own, Moku:Lab is capable of measuring S<sub>12<\/sub> or S<sub>21<\/sub> of a 2-port system, but not the S<sub>11<\/sub> and S<sub>22.<\/sub><\/p>\n<p>These complex numbers arise from a mathematical representation known as a scattering matrix. In this format the rows and columns represent the number of ports present. The matrix allows for a powerful and scalable linear tool that can be used to isolate and study certain port characteristics in an n-port network.<\/p>\n<h4>Directional coupler<\/h4>\n<p>A directional coupler is an analog device that is designed to couple a certain amount of power transmitted a certain direction (but not the other direction). The directional coupler we are going to use to measure S-parameters is a Mini-Circuits ZFDC-10-21. It has an input (In), an output (Out), and a coupling (CPL) port. For signals traveling from the input to output, a small portion of the power is coupled to the CPL port. For signals traveling in the reverse direction, almost no power is coupled. This means if we place a DUT at the input port of the RF coupler and drive the device from the output port, we can probe the reflected power by monitoring the CPL port. With the help of the directional coupler, Moku:Lab\u2019s FRA is able to measure all four S-parameters of a 2-port system.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone wp-image-10599 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure2.png\" alt=\"Power flow inside a directional coupler under different circumstances\" width=\"829\" height=\"554\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure2.png 829w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure2-300x200.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure2-768x513.png 768w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure2-600x401.png 600w\" sizes=\"(max-width: 829px) 100vw, 829px\" \/><br \/>\n<em>Figure 2: Power flow inside a directional coupler under different circumstances<\/em><\/p>\n<blockquote>\n<pre>&nbsp;<\/pre>\n<\/blockquote>\n<h2>Moku:Lab Set Up<\/h2>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10603 size-thumbnail\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Picture2-150x150.png\" alt=\"bandpass filter by Mini-Circuits (BBP-35A+)\" width=\"150\" height=\"150\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Picture2-150x150.png 150w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Picture2-100x100.png 100w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Picture2.png 274w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/p>\n<p>Our 2-port network will be a bandpass filter by Mini-Circuits (BBP-35A+) with a frequency range of 30-40MHz.<\/p>\n<p>Figure 3 shows the four arrangements of the Moku:Lab with respect to the 2-port filter (BPF) and RF coupler (Mini Circuits ZFDC-10-21). Notice that a 50\u03a9 terminator is connected in series with the filter to preserve impedance match when measuring S<sub>11<\/sub> and S<sub>22<\/sub> parameters.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10600 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3.jpg\" alt=\"Moku:Lab configurations for S-parameter measurements\" width=\"1485\" height=\"806\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3.jpg 1485w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3-300x163.jpg 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3-1024x556.jpg 1024w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3-768x417.jpg 768w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure3-600x326.jpg 600w\" sizes=\"(max-width: 1485px) 100vw, 1485px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure <\/em><em>3<\/em><em>: Moku:Lab configurations for S-parameter measurements<\/em><\/p>\n<h2>Measurement Validation<\/h2>\n<p>In this section we will validate the RF components by comparing FRA measurements over a large bandwidth to specifications (e.g., from datasheets).<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10601 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4.png\" alt=\"Moku:Lab FRA plots for bandpass filter\" width=\"1491\" height=\"1118\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4.png 1491w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4-300x225.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4-1024x768.png 1024w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4-768x576.png 768w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure4-600x450.png 600w\" sizes=\"(max-width: 1491px) 100vw, 1491px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure <\/em><em>4<\/em><em>: Moku:Lab FRA plots for bandpass filter<\/em><\/p>\n<p>The magnitude plot on the top of Figure 4 shows the approximate 30-40MHz bandpass that the filter is rated for while the bottom plot displays the phase. Both measurements are made with a 50\u03a9 input impedance setting, sweeping the frequency range from 1 to 120 MHz. We can now validate these results against known data to assure Moku:Lab\u2019s capability of accurately measuring all four S-parameters.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10604 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure5.png\" alt=\"Validation with Moku:Lab and mini-circuits\" width=\"498\" height=\"443\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure5.png 498w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure5-300x267.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure <\/em><em>5<\/em><em>: Measured and datasheet S<sub>12<\/sub> plots<\/em><\/p>\n<p>In order to validate our measurements we will compare the experimental data measuring the transmission signal (S<sub>12<\/sub>) from Moku:Lab\u2019s FRA to the spec sheet provided by Mini-Circuits.<\/p>\n<p>Comparing both the theoretical and experimental plots for S<sub>12<\/sub> it is clear that there is reasonable agreement, validating that Moku:Lab produces accurate S-parameters with FRA.<\/p>\n<p>Now that we have confidence in the results produced by this setup of the mini-circuits coupler with Moku:Lab\u2019s FRA, we can use the procedure above to record all four S-parameters of our two-port system.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10605 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6.png\" alt=\"S parameter magnitude plots\" width=\"1524\" height=\"1030\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6.png 1524w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6-300x203.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6-1024x692.png 1024w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6-768x519.png 768w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure6-600x406.png 600w\" sizes=\"(max-width: 1524px) 100vw, 1524px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure 6: S parameter magnitude plots<\/em><\/p>\n<p>Figure 6 depicts reflection signals (S<sub>11<\/sub> and S<sub>22<\/sub>) and transmission signals (S<sub>21<\/sub> and S<sub>12<\/sub>) in a frequency range from 1 MHz to 120 MHz as plotted from Moku:Lab measurements.<\/p>\n<h2>Further Analysis<\/h2>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10606 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7.png\" alt=\"Forward and reverse reflections for BPF\" width=\"2245\" height=\"1631\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7.png 2245w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-300x218.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-1024x744.png 1024w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-768x558.png 768w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-1536x1116.png 1536w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-2048x1488.png 2048w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure7-600x436.png 600w\" sizes=\"(max-width: 2245px) 100vw, 2245px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure 7: S<sub>11<\/sub> and S<sub>22<\/sub><\/em><\/p>\n<p>Isolating the forward and reverse signal reflections we notice significant drop offs around the bounds of the pass band (30-40 MHz). When dealing with sensitive systems, attenuations such as -6.66 dB, -7.86 dB can cause diminishing power transfers as most of the signal is reflected. Avoiding these limits and staying within the bounds of 28.6 MHz and 41.6 MHz will eliminate unwanted forward and reverse reflections, thus maximizing the signal\u2019s transmission throughout the system.<\/p>\n<h2>Smith Chart via MATLAB<\/h2>\n<p>With the help of the MATLAB RF TOOLBOX we are able to import magnitude and phase data into MATLAB following a .s2p file format. Here we will be comparing the S-parameters provided by Mini-Circuits to our experimental S-parameters captured by Moku:Lab.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10607 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure8.png\" alt=\"Smith chart\" width=\"682\" height=\"478\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure8.png 682w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure8-300x210.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure8-600x421.png 600w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure 8: Smith chart derived from datasheet<\/em><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-10608 size-full\" src=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure9.png\" alt=\"Smith chart derived from Moku:Lab measurements\" width=\"722\" height=\"504\" srcset=\"https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure9.png 722w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure9-300x209.png 300w, https:\/\/liquidinstruments.com\/wp-content\/uploads\/2022\/05\/Figure9-600x419.png 600w\" sizes=\"(max-width: 722px) 100vw, 722px\" \/><\/p>\n<p style=\"text-align: center;\"><em>Figure 9: Smith chart derived from Moku:Lab measurements<\/em><\/p>\n<p>Smith charts are an invaluable tool for RF engineers as they characterize S-parameters in a graphical and easy to read method, allowing for capacitive or inductive impedance matching.<\/p>\n<h2>Conclusion<\/h2>\n<p>In this application note we showcased the power of S-parameters when analyzing an RF network. By pairing the Frequency Response Analyzer with a RF coupler, accurate and repeatable S-parameter data of a n-port network can be produced. Furthermore, this reflection data can be exported and visualized via Smith Charts with MATLAB. This allows for deeper analysis on impedance mismatch as it relates to signal reflections within the system.<\/p>\n<h2>Reference<\/h2>\n<p>[1] <a href=\"https:\/\/www.microwaves101.com\/encyclopedias\/s-parameters\">https:\/\/www.microwaves101.com\/encyclopedias\/s-parameters&nbsp;<\/a><\/p>\n<p>[2] .s2p file format, <a href=\"https:\/\/cdn.macom.com\/applicationnotes\/AN3009.pdf\">Macom application note AN3009<\/a><\/p>\n<hr style=\"margin: 50px 0 50px 0 !important;\" \/>\n<h2>&nbsp;<\/h2>\n<h2>Have questions or want a printable version?<\/h2>\n<p>Please contact us at <a href=\"mailto:support@liquidinstruments.com\">support@liquidinstruments.com<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>Transmission and reflection signal information is vital when designing and validating RF components and systems. In this application note, Moku:Lab\u2019s Frequency Response Analyzer is used in conjunction with an RF directional coupler for a complete S-parameter characterization of a two port network. Introduction Imagine shouting into a long, endless hallway. The sound travels into the [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":22,"featured_media":11014,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"content-type":"","footnotes":""},"categories":[5],"tags":[312],"class_list":["post-10597","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-application-notes","tag-semiconductortest","site-category-frequency-response-analyzer","site-category-matlab","site-category-mokulab"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.0) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>S-Parameter Measurement for RF Systems | Liquid Instruments<\/title>\n<meta name=\"description\" content=\"Optimize RF (radio frequency) systems with precision S-parameter measurements using Moku&#039;s Frequency 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