{"id":3031,"date":"2024-08-26T11:16:06","date_gmt":"2024-08-26T11:16:06","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3031"},"modified":"2024-08-26T11:16:06","modified_gmt":"2024-08-26T11:16:06","slug":"passive-filters","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/26\/passive-filters\/","title":{"rendered":"Passive Filters"},"content":{"rendered":"\n<p id=\"P0260\">The most elementary types of filters are constructed from\u00a0<em>RC<\/em>\u00a0networks and are known as\u00a0<em>passive filters<\/em>\u00a0as they dissipate part of the signal power and pass the rest.\u00a0Figure 17.3(a)\u00a0shows a passive low-pass filter, while\u00a0Figure 17.3(b)\u00a0shows a passive high-pass filter. These form the basis of more sophisticated filters. Each has a cut-off frequency, which may be derived by considering the high-pass filter as a voltage divider. From\u00a0Figure 17.3(b)\u00a0we have:<\/p>\n\n\n\n<p id=\"EQN1\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781856175289\/files\/images\/F000172si1.png\" alt=\"image\" width=\"104\" height=\"39\"><strong>(17.1)<\/strong><\/p>\n\n\n\n<p>and at the cut-off frequency the gain falls by 3&nbsp;dB or&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781856175289\/files\/images\/F000172si2.png\" alt=\"image\" width=\"33\" height=\"16\">. Also at this frequency&nbsp;<em>R<\/em>=<em>X<\/em><sub>c<\/sub>, which gives:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781856175289\/files\/images\/F000172si3.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p><a><\/a>Hence,<\/p>\n\n\n\n<p id=\"EQN2\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781856175289\/files\/images\/F000172si4.png\" alt=\"image\" width=\"71\" height=\"31\"><strong>(17.2)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9781856175289\/files\/images\/F000172gr3.jpg\" alt=\"image\"\/><\/figure>\n\n\n\n<p><strong>Figure 17.3<\/strong>&nbsp;(a) Passive low-pass filter; (b) passive high-pass filter<\/p>\n\n\n\n<p id=\"P0270\">A similar result can be derived for the low pass filter, but for both first-order filters the following points should be considered.<\/p>\n\n\n\n<p id=\"O0190\">(a)\u00a0Cascading or connecting these networks in series causes the roll-off of the frequency response to increase by 20\u00a0dB\/decade for each filter, where \u201cdecade\u201d refers to a one-to-ten range of frequencies, such as 1\u201310\u00a0Hz, 10\u2013100\u00a0Hz, etc.: observe that on a logarithmic scale, such ranges span an equal distance (see\u00a0Figures 17.42\u00a0and\u00a017.43).<\/p>\n\n\n\n<p id=\"O0200\">(b)&nbsp;<a><\/a>A low-pass filter causes a phase lag between the output and input voltages, while a high-pass filter causes a phase lead between the output and input voltages. This has an important bearing on filters used in certain oscillators.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The most elementary types of filters are constructed from\u00a0RC\u00a0networks and are known as\u00a0passive filters\u00a0as they dissipate part of the signal power and pass the rest.\u00a0Figure 17.3(a)\u00a0shows a passive low-pass filter, while\u00a0Figure 17.3(b)\u00a0shows a passive high-pass filter. These form the basis of more sophisticated filters. Each has a cut-off frequency, which may be derived by considering [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3032,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[422],"tags":[],"class_list":["post-3031","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-filter-design"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/picture.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3031","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=3031"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3031\/revisions"}],"predecessor-version":[{"id":3033,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3031\/revisions\/3033"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3032"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}