{"id":949,"date":"2026-04-01T10:02:00","date_gmt":"2026-04-01T01:02:00","guid":{"rendered":"https:\/\/www.muratasoftware.com\/en_wacul_new\/fwp-new-wacul\/?post_type=case&#038;p=949"},"modified":"2026-08-24T16:43:23","modified_gmt":"2026-08-24T07:43:23","slug":"her011","status":"publish","type":"case","link":"https:\/\/www.muratasoftware.com\/en\/case\/her011\/","title":{"rendered":"Designing a Low-Pass Filter with Lumped-Constant Boundary Condition"},"content":{"rendered":"\n<figure class=\"wp-block-table blockPattern__table\"><table><thead><tr><th>General<\/th><th>An electromagnetic solver of Femtet assists you to design electronic components like resistor, inductor, and capacitor utilizing lumped-constant boundary condition.<\/th><\/tr><\/thead><tbody><tr><td>Analysis Model<\/td><td>The specifications of the low-pass filter and the circuit are as shown in Fig. 1.<br>The lumped constant is set on the microstrip line as shown in Fig. 2. The inductor elements are in series with the signal line and the capacitor elements are used as shunts on the reverse side of the substrate.<br>Fig. 3 shows the setting of the lumped constant as a boundary condition. Resistor, inductor, and capacitor can be defined inn parallel. S-parameter can be defined as well.<\/td><\/tr><tr><td>Result<\/td><td>As the result in Fig. 4 shows, the characteristics specified in Fig. 1 are obtained.<\/td><\/tr><tr><td>Keywords<\/td><td>Low-Pass Filters, Lumped-Element Circuits, Resistors, Inductors, Capacitors, Microstrip Lines, S-Parameters<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-columns blockPattern__column is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Fig. 1: Specifications of Low-Pass Filter and Equivalent Circuit<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6abb6ba50b50b&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6abb6ba50b50b\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"823\" height=\"485\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" data-id=\"3096\" src=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig1e-3.png\" alt=\"\" class=\"wp-image-3096\" srcset=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig1e-3.png 823w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig1e-3-300x177.png 300w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig1e-3-768x453.png 768w\" sizes=\"auto, (max-width: 823px) 100vw, 823px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"\u62e1\u5927\u3059\u308b\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Fig. 2: Analysis Model<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6abb6ba50bf04&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6abb6ba50bf04\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" data-id=\"3097\" src=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_02.jpg\" alt=\"\" class=\"wp-image-3097\" srcset=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_02.jpg 960w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_02-300x169.jpg 300w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_02-768x432.jpg 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"\u62e1\u5927\u3059\u308b\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns blockPattern__column is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Fig. 3: Boundary Condition Setup<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"712\" height=\"558\" data-id=\"3098\" src=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig3e-2.png\" alt=\"\" class=\"wp-image-3098\" srcset=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig3e-2.png 712w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/fig3e-2-300x235.png 300w\" sizes=\"auto, (max-width: 712px) 100vw, 712px\" \/><\/figure>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Fig. 4: Result<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6abb6ba50c43d&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6abb6ba50c43d\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" data-id=\"3099\" src=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_04.jpg\" alt=\"\" class=\"wp-image-3099\" srcset=\"https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_04.jpg 960w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_04-300x169.jpg 300w, https:\/\/www.muratasoftware.com\/en\/fwp\/wp-content\/uploads\/2026\/08\/figure_04-768x432.jpg 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"\u62e1\u5927\u3059\u308b\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n","protected":false},"featured_media":3099,"template":"","meta":{"_acf_changed":false},"case_category":[26],"class_list":["post-949","case","type-case","status-publish","has-post-thumbnail","hentry","case_category-hertz"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/case\/949","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/case"}],"about":[{"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/types\/case"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/media\/3099"}],"wp:attachment":[{"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/media?parent=949"}],"wp:term":[{"taxonomy":"case_category","embeddable":true,"href":"https:\/\/www.muratasoftware.com\/en\/wp-json\/wp\/v2\/case_category?post=949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}