{"id":3109,"date":"2024-12-12T14:13:10","date_gmt":"2024-12-12T13:13:10","guid":{"rendered":"https:\/\/www.dk8pp.de\/blog\/?page_id=3109"},"modified":"2025-04-17T15:59:10","modified_gmt":"2025-04-17T13:59:10","slug":"formelsammlung","status":"publish","type":"page","link":"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/","title":{"rendered":"For\u00admel\u00adsamm\u00adlung"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 ez-toc-wrap-right counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Inhalts\u00adver\u00adzeich\u00adnis<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class><span class=\"eztoc-hide\" style=\"display:none;\">Togg\u00adle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\" \/><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\" \/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class=\"ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default\"><li class=\"ez-toc-page-1 ez-toc-heading-level-2\"><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#konventionen_bei_der_komplexen_wechselstromrechnung\">Kon\u00adven\u00adtio\u00adnen bei der kom\u00adple\u00adxen Wechselstromrechnung<\/a><ul class=\"ez-toc-list-level-3\"><li class=\"ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#imaginaere_einheit\">Ima\u00adgi\u00adn\u00e4\u00adre Einheit<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#impedanz\">Impe\u00addanz<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#scheinwiderstand\">Schein\u00adwi\u00adder\u00adstand<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#admittanz\">Admit\u00adtanz<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#scheinleitwert\">Schein\u00adleit\u00adwert<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#identitaeten\">Iden\u00adti\u00adt\u00e4\u00adten<\/a><\/li><\/ul><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-2\"><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#das_smith-diagramm\">Das Smith-Dia\u00adgramm<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-2\"><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#das_stehwellenverhaeltnis\">Das Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis<\/a><\/li><li class=\"ez-toc-page-1 ez-toc-heading-level-2\"><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#guete\">G\u00fcte<\/a><ul class=\"ez-toc-list-level-3\"><li class=\"ez-toc-heading-level-3\"><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/#schwingkreisguete\">Schwing\u00adkreis\u00adg\u00fc\u00adte<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n\n<p class=\"has-text-align-left wp-block-paragraph\">In meh\u00adre\u00adren Bei\u00adtr\u00e4\u00adgen habe ich For\u00admeln benutzt und sie manch\u00admal auch erkl\u00e4rt oder auf wei\u00adter\u00adge\u00adhen\u00adde Erkl\u00e4\u00adrun\u00adgen andern\u00adorts ver\u00adwie\u00adsen. Man\u00adche die\u00adser For\u00admeln brau\u00adche ich immer wie\u00adder mal und mu\u00df sie mit\u00adun\u00adter selbst wie\u00adder her\u00adaus\u00adsu\u00adchen, weil ich mir lei\u00adder vie\u00adles nicht mer\u00adken&nbsp;kann.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mit die\u00adser Sei\u00adte will ich nun eine zen\u00adtra\u00adle For\u00admel\u00adsamm\u00adlung erstel\u00adlen, auf die ich bei Bedarf immer wie\u00adder ver\u00adwei\u00adsen kann. Das bedeu\u00adtet, da\u00df die\u00adse Sei\u00adte lebt und bei Bedarf upge\u00adda\u00adted wird. Ich star\u00adte mit copy&amp;paste, also bit\u00adte nicht wun\u00addern, wenn hier Tei\u00adle aus fr\u00fc\u00adhe\u00adren Bei\u00adtr\u00e4\u00adgen auf\u00adtau\u00adchen. Das soll so sein und ich wer\u00adde auch nicht die alten Bei\u00adtr\u00e4\u00adge dahin\u00adge\u00adhend ver\u00ad\u00e4n\u00addern, da\u00df sie nun auf die\u00adse For\u00admel\u00adsamm\u00adlung verweisen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline;\"><strong>Hin\u00adweis:<\/strong><\/span> <s>Wenn For\u00admeln nume\u00adriert sind, star\u00adtet die\u00adse Nume\u00adrie\u00adrung bei jedem Kapi\u00adtel von vor\u00adne. Das erleich\u00adtert mir das hin- und her\u00adschie\u00adben der Kapi\u00adtel.<\/s><br><strong><span style=\"text-decoration: underline;\">Update:<\/span><\/strong> Die Idee ist Mist! Ich habe jetzt doch alles von oben nach unten durch\u00adnum\u00adme\u00adriert, dann kann ich leich\u00adter auf eine For\u00admel ver\u00adwei\u00adsen. Bei Ver\u00adwei\u00adsen f\u00fcge ich dann ein # vor der Zahl ein, damit ich die Stel\u00adlen bes\u00adser fin\u00adden&nbsp;kann.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"konventionen-bei-der-komplexen-wechselstromrechnung\"><span class=\"ez-toc-section\" id=\"konventionen_bei_der_komplexen_wechselstromrechnung\"><\/span>Kon\u00adven\u00adtio\u00adnen bei der kom\u00adple\u00adxen Wechselstromrechnung<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Hier eine kur\u00adze Auf\u00adli\u00adstung der \u00fcbli\u00adcher\u00adwei\u00adse ver\u00adwen\u00adde\u00adten Bezeich\u00adnun\u00adgen, in Klam\u00admern die eng\u00adli\u00adschen Begrif\u00adfe, die einem ja auch immer wie\u00adder mal begegnen.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"imagin\u00e4re-einheit\"><span class=\"ez-toc-section\" id=\"imaginaere_einheit\"><\/span>Ima\u00adgi\u00adn\u00e4\u00adre Einheit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_imagin\u00e4re-einheit\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_imag.svg\" alt class=\"wp-image-3118\" style=\"width:173px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[1]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">j ist die ima\u00adgi\u00adn\u00e4\u00adre Ein\u00adheit (ima\u00adgi\u00adna\u00adry unit). Um Ver\u00adwechs\u00adlun\u00adgen mit der Strom\u00adst\u00e4r\u00adke zu ver\u00admei\u00adden, wird die ima\u00adgi\u00adn\u00e4\u00adre Ein\u00adheit (anders als in der Mathe\u00adma\u00adtik und der Phy\u00adsik) in der Elek\u00adtro\u00adtech\u00adnik \u00fcbli\u00adcher\u00adwei\u00adse mit \u201ej\u201c statt mit \u201ei\u201c gekennzeichnet.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"impedanz\"><span class=\"ez-toc-section\" id=\"impedanz\"><\/span>Impe\u00addanz<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_impedanz\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_impedance.svg\" alt class=\"wp-image-3125\" style=\"width:250px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[2]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline;\">Z<\/span> ist der kom\u00adple\u00adxe Wider\u00adstand, die Impe\u00addanz (impe\u00addance). Sein Real\u00adteil R ist der reel\u00adle Wirk\u00adwider\u00adstand (resi\u00adstance) und sein Ima\u00adgi\u00adn\u00e4r\u00adteil X ist der Blind\u00adwi\u00adder\u00adstand (reac\u00adtance). Als Kom\u00adpo\u00adnen\u00adte einer kom\u00adple\u00adxen Zahl ist auch X selbst eine reel\u00adle Zahl. Der Kehr\u00adwert der Impe\u00addanz ist der kom\u00adple\u00adxe Leit\u00adwert, die Admit\u00adtanz <span style=\"text-decoration: underline;\">Y<\/span>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"scheinwiderstand\"><span class=\"ez-toc-section\" id=\"scheinwiderstand\"><\/span>Schein\u00adwi\u00adder\u00adstand<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_scheinwiderstand\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_scheinwiderstand.svg\" alt class=\"wp-image-3128\" style=\"width:250px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[3]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Der Betrag der Impe\u00addanz ist der Scheinwiderstand.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"admittanz\"><span class=\"ez-toc-section\" id=\"admittanz\"><\/span>Admit\u00adtanz<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_admittanz\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_admittance.svg\" alt class=\"wp-image-3126\" style=\"width:250px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[4]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline;\">Y<\/span> ist der kom\u00adple\u00adxe Leit\u00adwert, die Admit\u00adtanz (admit\u00adtance). Sein Real\u00adteil G ist der reel\u00adle Wirk\u00adleit\u00adwert (con\u00adduc\u00adtance) und sein Ima\u00adgi\u00adn\u00e4r\u00adteil B ist der Blind\u00adleit\u00adwert (sus\u00adcep\u00adtance). Als Kom\u00adpo\u00adnen\u00adte einer kom\u00adple\u00adxen Zahl ist auch B eine reel\u00adle Zahl. Der Kehr\u00adwert der Admit\u00adtanz ist die kom\u00adple\u00adxe Impe\u00addanz <span style=\"text-decoration: underline;\">Z<\/span>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"scheinleitwert\"><span class=\"ez-toc-section\" id=\"scheinleitwert\"><\/span>Schein\u00adleit\u00adwert<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_scheinleitwert\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_scheinleitwert.svg\" alt class=\"wp-image-3129\" style=\"width:250px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[5]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Der Betrag der Admit\u00adtanz ist der Scheinleitwert.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Genau\u00adso wie bei Wider\u00adstands\u00adnetz\u00adwer\u00adken unter Gleich\u00adspan\u00adnung addie\u00adren sich auch bei Wech\u00adsel\u00adspan\u00adnung die Impe\u00addan\u00adzen, wenn kom\u00adplex\u00adwer\u00adti\u00adge Wider\u00adst\u00e4n\u00adde in Serie geschal\u00adtet wer\u00adden. Bei par\u00adal\u00adlel\u00adge\u00adschal\u00adte\u00adten Ele\u00admen\u00adten addie\u00adren sich ihre Admittanzen.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"identitaeten\"><\/span>Iden\u00adti\u00adt\u00e4\u00adten<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Durch Umfor\u00admen der oben genann\u00adten Glei\u00adchun\u00adgen unter Anwen\u00addung der Rechen\u00adre\u00adgeln f\u00fcr kom\u00adple\u00adxe Zah\u00adlen erge\u00adben sich fol\u00adgen\u00adde Identit\u00e4ten:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_wirkwiderstand\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<p class=\"wp-block-paragraph\"><br><strong>Wirk\u00adwider\u00adstand<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:40%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/03\/20250319_complex_r.svg\" alt class=\"wp-image-3470\" style=\"width:146px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:5.18%\">\n<p class=\"wp-block-paragraph\"><strong>[6]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_wirkleitwert\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<p class=\"wp-block-paragraph\"><br><strong>Wirk\u00adleit\u00adwert<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:40%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/03\/20250319_complex_g.svg\" alt class=\"wp-image-3468\" style=\"width:146px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:5.18%\">\n<p class=\"wp-block-paragraph\"><strong>[7]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_blindwiderstand\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<p class=\"wp-block-paragraph\"><br><strong>Blind\u00adwi\u00adder\u00adstand<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:40%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/03\/20250319_complex_x.svg\" alt class=\"wp-image-3469\" style=\"width:146px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:5.18%\">\n<p class=\"wp-block-paragraph\"><strong>[8]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_blindleitwert\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<p class=\"wp-block-paragraph\"><br><strong>Blind\u00adleit\u00adwert<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:40%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/03\/20250319_complex_b.svg\" alt class=\"wp-image-3467\" style=\"width:146px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:5.18%\">\n<p class=\"wp-block-paragraph\"><strong>[9]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"das-smith-diagramm\"><span class=\"ez-toc-section\" id=\"das_smith-diagramm\"><\/span>Das Smith-Dia\u00adgramm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Das Smith-Dia\u00adgramm zeigt den kom\u00adple\u00adxen Refle\u00adxi\u00adons\u00adfak\u00adtor Gam\u00adma (<span style=\"text-decoration: underline;\">\u0393<\/span>). Gam\u00adma ist defi\u00adniert als das Ver\u00adh\u00e4lt\u00adnis der kom\u00adple\u00adxen r\u00fcck\u00adlau\u00adfen\u00adden zur kom\u00adple\u00adxen vor\u00adlau\u00adfen\u00adden Spannung:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_gamma\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:70%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Gamma_Ur_Uf.svg\" alt class=\"wp-image-2825\" style=\"width:146px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[10]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Der kom\u00adple\u00adxe Refle\u00adxi\u00adons\u00adfak\u00adtor Gam\u00adma ist damit genau das, was ein vek\u00adto\u00adri\u00adel\u00adler Netz\u00adwerk\u00adana\u00adly\u00adsa\u00adtor als s11-Para\u00adme\u00adter misst. Die Wech\u00adsel\u00adspan\u00adnun\u00adgen k\u00f6n\u00adnen als kom\u00adple\u00adxe Gr\u00f6\u00ad\u00dfen geschrie\u00adben werden:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_ufur\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:95%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Uf_Ur.svg\" alt class=\"wp-image-2824\" style=\"width:560px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[11]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Das Dach (Zir\u00adkum\u00adflex) bezeich\u00adnet dabei die Ampli\u00adtu\u00adde der jewei\u00adli\u00adgen Span\u00adnung, \u03c9 die Kreis\u00adfre\u00adquenz, t den Zeit\u00adpunkt und \u03c6 die Pha\u00adsen\u00adver\u00adschie\u00adbung bei\u00adder Signa\u00adle. Bei\u00adde Kreis\u00adfre\u00adquen\u00adzen sind not\u00adwen\u00addi\u00adger\u00adwei\u00adse gleich, denn bei der Refle\u00adxi\u00adon tritt kei\u00adne Fre\u00adquenz\u00ad\u00e4n\u00adde\u00adrung auf. Damit k\u00fcr\u00adzen sich bei der Divi\u00adsi\u00adon zwei Ter\u00adme im Z\u00e4h\u00adler und Nen\u00adner und Gam\u00adma errech\u00adnet sich&nbsp;zu:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_gammaur\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:95%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Gamma_Ur_Uf_e.svg\" alt class=\"wp-image-2822\" style=\"width:602px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[12]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Mit Hil\u00adfe der <a href=\"https:\/\/de.wikipedia.org\/wiki\/Eulersche_Formel\" target=\"_blank\" rel=\"noreferrer noopener\">Euler\u00adschen For\u00admel<\/a> wird daraus:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_gammaeuler\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:95%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Gamma_Cos.svg\" alt class=\"wp-image-2823\" style=\"width:534px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[13]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Damit ist Gam\u00adma eine \u201eganz gew\u00f6hn\u00adli\u00adche\u201c kom\u00adple\u00adxe Zahl im Ein\u00adheits\u00adkreis der kom\u00adple\u00adxen Zah\u00adlen\u00adebe\u00adne, wie im oben ver\u00adlink\u00adten Wiki\u00adpe\u00addia-Arti\u00adkel gezeigt wird. Das Smith-Dia\u00adgramm stellt in die\u00adsem Ein\u00adheits\u00adkreis die Refle\u00adxi\u00adons\u00adfak\u00adto\u00adren dar. Das Smith-Dia\u00adgramm zeigt also die Reflexionsfaktorebene.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Der Refle\u00adxi\u00adons\u00adfak\u00adtor Gam\u00adma l\u00e4sst sich auch aus den Impe\u00addan\u00adzen berech\u00adnen. Damit wer\u00adden die Impe\u00addan\u00adzen aus der kar\u00adthe\u00adsi\u00adschen Impe\u00addanz\u00adebe\u00adne in die pola\u00adre Refle\u00adxi\u00adons\u00adfak\u00adtor\u00adebe\u00adne transformiert:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_gammaz\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:95%\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Gamma_Zl_Z0.svg\" alt class=\"wp-image-2832\" style=\"width:436px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[14]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Die\u00adse Trans\u00adfor\u00adma\u00adti\u00adon ist bili\u00adne\u00adar. Aus der Refle\u00adxi\u00adons\u00adfak\u00adtor\u00adebe\u00adne kann man auch wie\u00adder die Impe\u00addanz berechnen:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_zgamma\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/08\/20240804_Z_Gamma.svg\" alt class=\"wp-image-2833\" style=\"width:215px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[15]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Das Smith-Dia\u00adgramm wird kon\u00adstru\u00adiert, indem man den Refle\u00adxi\u00adons\u00adfak\u00adtor Gam\u00adma im kar\u00adthe\u00adsi\u00adschen Koor\u00addi\u00adna\u00adten\u00adsy\u00adstem dar\u00adstellt. Als Beschrif\u00adtung wird dann aber nor\u00adma\u00adler\u00adwei\u00adse die ein\u00addeu\u00adtig zu jedem Gam\u00adma geh\u00f6\u00adren\u00adde Last\u00adim\u00adpe\u00addanz <span style=\"text-decoration: underline;\">Z<\/span><sub>L<\/sub> gezeigt, die sich aus <a href=\"#eq_zgamma\">[#15]<\/a> errechnet.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"das-stehwellenverh\u00e4ltnis\"><span class=\"ez-toc-section\" id=\"das_stehwellenverhaeltnis\"><\/span>Das Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Das Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis errech\u00adnet sich aus dem Betrag des kom\u00adple\u00adxen Reflexionsfaktors:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_das-stehwellenverh\u00e4ltnis\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/07\/20240804_SWR.svg\" alt class=\"wp-image-2839\" style=\"width:200px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[16]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Damit wird das Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis zu einer reel\u00adlen Zahl, der die Pha\u00adsen\u00adin\u00adfor\u00adma\u00adti\u00adon fehlt. Durch ein\u00adfa\u00adche Umfor\u00admung kann man aus dem Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis auch den Betrag des Refle\u00adxi\u00adons\u00adfak\u00adtors berechnen:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_gammaswr\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241219_Gamma_SWR-1.svg\" alt class=\"wp-image-3221\" style=\"width:200px\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[17]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Alle Punk\u00adte glei\u00adchen Steh\u00adwel\u00adlen\u00adver\u00adh\u00e4lt\u00adnis\u00adses lie\u00adgen im Smith-Dia\u00adgramm auf kon\u00adzen\u00adtri\u00adschen Krei\u00adsen um des\u00adsen Mittelpunkt.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aus <a href=\"#eq_gamma\" data-type=\"internal\" data-id=\"#eq_gamma\">[#10]<\/a> und <a href=\"#eq_das-stehwellenverh\u00e4ltnis\">[#16]<\/a> ergibt sich auch fol\u00adgen\u00adder Zusammenhang:<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_swru\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/02\/20250228_SWR_U.svg\" alt class=\"wp-image-3431\" style=\"width:329px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[18]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_swrp\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2025\/02\/20250228_SWR_P.svg\" alt class=\"wp-image-3432\" style=\"width:338px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"wp-block-paragraph\"><strong>[19]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sie\u00adhe auch: <a href=\"https:\/\/de.wikipedia.org\/wiki\/Stehwellenverh%C3%A4ltnis\" target=\"_blank\" rel=\"noreferrer noopener\">Wiki\u00adpe\u00addia<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"g\u00fcte\"><span class=\"ez-toc-section\" id=\"guete\"><\/span>G\u00fcte<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Als G\u00fcte Q einer rea\u00adlen und ver\u00adlust\u00adbe\u00adhaf\u00adte\u00adten Impe\u00addanz (Spu\u00adle oder Kon\u00adden\u00adsa\u00adtor) bezeich\u00adnet man den Quo\u00adti\u00aden\u00adten ihres Blind\u00adwi\u00adder\u00adstan\u00addes und ihres Wirkwiderstandes.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_g\u00fcte\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_quality.svg\" alt class=\"wp-image-3133\" style=\"width:113px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[20]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Da der Blind\u00adwi\u00adder\u00adstand X fre\u00adquenz\u00adab\u00adh\u00e4n\u00adgig ist, ist auch die G\u00fcte frequenzabh\u00e4ngig.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Die G\u00fcte Q eines Schwing\u00adkrei\u00adses im Reso\u00adnanz\u00adfall errech\u00adnet sich aus der G\u00fcte Q<sub>C<\/sub> des Kon\u00adden\u00adsa\u00adtors und der G\u00fcte Q<sub>L<\/sub> der Spu\u00adle nach fol\u00adgen\u00adder Formel:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"schwingkreisg\u00fcte\"><span class=\"ez-toc-section\" id=\"schwingkreisguete\"><\/span>Schwing\u00adkreis\u00adg\u00fc\u00adte<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\" id=\"eq_schwingkreisg\u00fcte\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:20%\">\n<p class=\"has-text-align-center wp-block-paragraph\"><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image formel\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.dk8pp.de\/blog\/wp-content\/uploads\/2024\/12\/20241213_quality_lc.svg\" alt class=\"wp-image-3135\" style=\"width:193px;height:auto\"><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:8%\">\n<p class=\"has-text-align-right wp-block-paragraph\"><br><strong>[21]<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u00dcbli\u00adcher\u00adwei\u00adse ist die G\u00fcte des Kon\u00adden\u00adsa\u00adtors eines Schwing\u00adkrei\u00adses deut\u00adlich h\u00f6her, als die G\u00fcte der Spu\u00adle. Dann n\u00e4hert sich die Gesamt\u00adg\u00fc\u00adte Q der G\u00fcte der Spu\u00adle Q<sub>L<\/sub> an. Typi\u00adsche Wer\u00adte f\u00fcr Q<sub>C<\/sub> lie\u00adgen in der Gr\u00f6\u00ad\u00dfen\u00adord\u00adnung 1000, w\u00e4h\u00adrend typi\u00adsche Spu\u00adlen\u00adg\u00fc\u00adten Q<sub>L<\/sub> bei 100 liegen.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In meh\u00adre\u00adren Bei\u00adtr\u00e4\u00adgen habe ich For\u00admeln benutzt und sie manch\u00admal auch erkl\u00e4rt oder auf wei\u00adter\u00adge\u00adhen\u00adde Erkl\u00e4\u00adrun\u00adgen andern\u00adorts ver\u00adwie\u00adsen. Man\u00adche die\u00adser For\u00admeln brau\u00adche ich immer wie\u00adder mal und mu\u00df sie mit\u00adun\u00adter selbst wie\u00adder her\u00adaus\u00adsu\u00adchen, weil ich mir lei\u00adder vie\u00adles nicht mer\u00adken&nbsp;kann. Mit die\u00adser Sei\u00adte will ich nun eine zen\u00adtra\u00adle For\u00admel\u00adsamm\u00adlung erstel\u00adlen, auf die ich bei Bedarf \u2026 <a href=\"https:\/\/www.dk8pp.de\/blog\/formelsammlung\/\" class=\"more-link\"><span class=\"screen-reader-text\">For\u00admel\u00adsamm\u00adlung<\/span> weiterlesen<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"wp_typography_post_enhancements_disabled":false,"footnotes":""},"class_list":["post-3109","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/pages\/3109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/comments?post=3109"}],"version-history":[{"count":46,"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/pages\/3109\/revisions"}],"predecessor-version":[{"id":3551,"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/pages\/3109\/revisions\/3551"}],"wp:attachment":[{"href":"https:\/\/www.dk8pp.de\/blog\/wp-json\/wp\/v2\/media?parent=3109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}