{"id":3036,"date":"2024-08-26T11:19:32","date_gmt":"2024-08-26T11:19:32","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=3036"},"modified":"2024-08-26T11:19:32","modified_gmt":"2024-08-26T11:19:32","slug":"first-order-filters","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/26\/first-order-filters\/","title":{"rendered":"First-Order Filters"},"content":{"rendered":"\n

The first-order filter is the simplest type and forms the basis of all other filters. Normally, what is called the\u00a0Butterworth<\/em>\u00a0type is analyzed. We will look at the low-pass filter first, a circuit for which is shown in\u00a0Figure 17.9.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 17.9<\/strong> Low-pass Butterworth filter<\/p>\n\n\n\n

In this circuit note that the op-amp is ideal, i.e., it draws no current, and also it is used in the noninverting mode in order to prevent loading down of the RC<\/em> network. R<\/em> and C<\/em> act as a voltage-dividing network, and hence we have that:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Simplifying this expression gives:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

The output voltage is given as:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Hence,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

<\/a>or,<\/p>\n\n\n\n

\"image\"(17.3)<\/strong><\/p>\n\n\n\n

Note that;<\/p>\n\n\n\n

\"image\"(17.4)<\/strong><\/p>\n\n\n\n

This has the characteristics of a first-order low-pass filter. When \u03c9=0 then the pass-band gain is:<\/p>\n\n\n\n

\"image\"(17.5)<\/strong><\/p>\n\n\n\n

This is simply the amplifier gain. Note also that when:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

the gain has dropped by 3\u00a0dB after which the gain falls off at the rate of 20\u00a0dB\/decade. A typical response for this filter is shown in\u00a0Figure 17.10.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 17.10<\/strong> Typical filter response for low-pass<\/p>\n\n\n\n

A similar analysis may be carried out for the first-order high-pass filter, which is shown in\u00a0Figure 17.11. Note that these two filters are identical except that R and C have been interchanged. The output voltage is given by:<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

or,<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Note that:<\/p>\n\n\n\n

\"image\"(17.6)<\/strong><\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 17.11<\/strong> First-order high-pass filter<\/p>\n\n\n\n

The response for this filter is shown below in\u00a0Figure 17.12.<\/p>\n\n\n\n

\"image\"\/<\/figure>\n\n\n\n

Figure 17.12<\/strong> Response for high-pass filter<\/p>\n","protected":false},"excerpt":{"rendered":"

The first-order filter is the simplest type and forms the basis of all other filters. Normally, what is called the\u00a0Butterworth\u00a0type is analyzed. We will look at the low-pass filter first, a circuit for which is shown in\u00a0Figure 17.9. Figure 17.9 Low-pass Butterworth filter In this circuit note that the op-amp is ideal, i.e., it draws no […]<\/p>\n","protected":false},"author":1,"featured_media":3037,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[422],"tags":[],"class_list":["post-3036","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\/F000172gr9.jpg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3036","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=3036"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3036\/revisions"}],"predecessor-version":[{"id":3038,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/3036\/revisions\/3038"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/3037"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=3036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=3036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=3036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}