{"id":4603,"date":"2021-01-18T17:43:44","date_gmt":"2021-01-18T16:43:44","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=4603"},"modified":"2024-04-23T15:37:14","modified_gmt":"2024-04-23T14:37:14","slug":"how-to-calculate-and-solve-for-transfer-function-sensitivity-first-order-instruments-dynamic-characteristics-of-instruments","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2021\/01\/18\/how-to-calculate-and-solve-for-transfer-function-sensitivity-first-order-instruments-dynamic-characteristics-of-instruments\/","title":{"rendered":"How to Calculate and Solve for Transfer Function (Sensitivity) | First Order Instruments | Dynamic Characteristics of Instruments"},"content":{"rendered":"<p><img decoding=\"async\" class=\"alignnone size-full wp-image-4615\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Sensitivity.png\" alt=\"\" width=\"277\" height=\"182\" \/><\/p>\n<p>The image above represents transfer function. To calculate transfer function (sensitivity) | First Order Instruments, three essential parameters are needed, and these parameters are Static Sensitivity (k), Time Constant (u), and Differentiation Value (d \/ dt) (D).<\/p>\n<h3><strong>The formula for calculating transfer function:<\/strong><\/h3>\n<p>c =\u00a0<sup>k<\/sup>\u00a0\/\u00a0<sub>1 + uD<\/sub><\/p>\n<p>Where:<\/p>\n<p>c = Sensitivity<br \/>\nk = Static Sensitivity<br \/>\nu = Time Constant<br \/>\nD = Differentiation Value<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the sensitivity when the static sensitivity is 24, the time constant is 16 and the differentiation value is 10.<\/p>\n<p>This implies that;<\/p>\n<p>k = Static Sensitivity = 24<br \/>\nu = Time Constant = 16<br \/>\nD = Differentiation Value = 10<\/p>\n<p>c =\u00a0<sup>k<\/sup>\u00a0\/\u00a0<sub>1 + uD<\/sub><br \/>\nc =\u00a0<sup>24<\/sup>\u00a0\/\u00a0<sub>1 + 16 x 10<\/sub><br \/>\nThat is, c = <sup>24<\/sup>\u00a0\/\u00a0<sub>1 + 160<\/sub><br \/>\nc =\u00a0<sup>24<\/sup>\u00a0\/\u00a0<sub>161<\/sub><br \/>\nc = 0.149<\/p>\n<p>Therefore, the\u00a0<strong>transfer function (sensitivity)\u00a0<\/strong>is\u00a0<strong>0.149.<\/strong><\/p>\n<h3><strong>Calculating for the Static Sensitivity when the Transfer Function (Sensitivity), the Time Constant and the Differentiation Value are Given<\/strong><\/h3>\n<p>k = c (1 + uD)<\/p>\n<p>Where;<\/p>\n<p>k = Static Sensitivity<br \/>\nc = Sensitivity<br \/>\nu = Time Constant<br \/>\nD = Differentiation Value<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the static sensitivity when the transfer function (sensitivity) is 12, the time constant is 8 and the differentiation value is 4.<\/p>\n<p>This implies that;<\/p>\n<p>c = Sensitivity = 12<br \/>\nu = Time Constant = 8<br \/>\nD = Differentiation Value = 4<\/p>\n<p>k = c (1 + uD)<br \/>\nk = 12 (1+ (8)(4))<br \/>\nSo, k = 12 (1 + 32)<br \/>\nk = 12 (33)<br \/>\nk = 396<\/p>\n<p>Therefore, the\u00a0<strong>static sensitivity\u00a0<\/strong>is <strong>396.<\/strong><\/p>\n<h3><strong>Calculating for the Time Constant when the Transfer Function (Sensitivity), the Static Sensitivity and the Differentiation Value are Given<\/strong><\/h3>\n<p>u = <sup>(<sup>k<\/sup> \/ <sub>c<\/sub> &#8211; 1)<\/sup> \/ <sub>D<\/sub><\/p>\n<p>Where;<\/p>\n<p>u = Time Constant<br \/>\nc = Sensitivity<br \/>\nk = Static Sensitivity<br \/>\nD = Differentiation Value<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the time constant when the transfer function (sensitivity) is 8, the static sensitivity is 40 and the differentiation value is 2.<\/p>\n<p>This implies that;<\/p>\n<p>c = Sensitivity = 8<br \/>\nk = Static Sensitivity = 40<br \/>\nD = Differentiation Value = 2<\/p>\n<p>u = <sup>(<sup>k<\/sup> \/ <sub>c<\/sub> &#8211; 1)<\/sup> \/ <sub>D<\/sub><br \/>\nu = <sup>(<sup>40<\/sup> \/ <sub>8<\/sub> &#8211; 1)<\/sup> \/ <sub>2<\/sub><br \/>\nSo, u = <sup>(5 &#8211; 1)<\/sup> \/ <sub>2<\/sub><br \/>\nu = <sup>4<\/sup> \/ <sub>2<\/sub><br \/>\nu = 2<\/p>\n<p>Therefore, the\u00a0<strong>time constant\u00a0<\/strong>is\u00a0<strong>2.<\/strong><\/p>\n<p>Read more:\u00a0<a href=\"https:\/\/www.nickzom.org\/blog\/2021\/01\/18\/how-to-calculate-and-solve-for-time-constant-first-order-instruments-dynamic-characteristics-of-instruments\/\">How to Calculate and Solve for Time Constant | First Order Instruments | Dynamic Characteristics of Instruments<\/a><\/p>\n<h3><strong>Calculating for the Differentiation Value when the Transfer Function (Sensitivity), the Static Sensitivity and the Time Constant are Given<\/strong><\/h3>\n<p>D = <sup>(<sup>k<\/sup> \/ <sub>c<\/sub> &#8211; 1)<\/sup> \/ <sub>u<\/sub><\/p>\n<p>Where;<\/p>\n<p>D = Differentiation Value<br \/>\nc = Sensitivity<br \/>\nk = Static Sensitivity<br \/>\nu = Time Constant<\/p>\n<p>Let&#8217;s solve an example;<br \/>\nFind the differentiation value when the transfer function (sensitivity) is 12, the static sensitivity is 84, and the time constant is 6.<\/p>\n<p>This implies that;<\/p>\n<p>c = Sensitivity = 12<br \/>\nk = Static Sensitivity = 84<br \/>\nu = Time Constant = 6<\/p>\n<p>D = <sup>(<sup>k<\/sup> \/ <sub>c<\/sub> &#8211; 1)<\/sup> \/ <sub>u<\/sub><br \/>\nD = <sup>(<sup>84<\/sup> \/ <sub>12<\/sub> &#8211; 1)<\/sup> \/ <sub>6<\/sub><br \/>\nThat is, D = <sup>(7 &#8211; 1)<\/sup> \/ <sub>6<\/sub><br \/>\nD = <sup>6<\/sup> \/ <sub>6<\/sub><br \/>\nD = 1<\/p>\n<p>Therefore, the\u00a0<strong>differentiation value\u00a0<\/strong>is\u00a0<strong>1.<\/strong><\/p>\n<h3><strong>How to Calculate Transfer Function (Sensitivity) | First Order Instruments With Nickzom Calculator<\/strong><\/h3>\n<p>Nickzom Calculator \u2013\u00a0<strong>The Calculator Encyclopedia<\/strong> is capable of calculating the transfer function (sensitivity) | First Order Instruments.<\/p>\n<p>To get the answer and workings of the transfer function (sensitivity) | First Order Instruments using the <strong>Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n<p>You can get this app via any of these means:<\/p>\n<p><strong>Web<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator-plus\">https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n<p>To get access to the\u00a0<strong>professional\u00a0<\/strong>version via web, you need to\u00a0<strong>register<\/strong>\u00a0and\u00a0<strong>subscribe\u00a0<\/strong>for<strong>\u00a0NGN 2,000\u00a0<\/strong>per<strong>\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.<br \/>\nYou can also try the\u00a0<strong>demo\u00a0<\/strong>version via\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator\">https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n<p><strong>Android (Paid)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a><br \/>\n<strong>Android (Free)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><br \/>\n<strong>Apple (Paid)<\/strong>\u00a0\u2013\u00a0<a href=\"https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8\">https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><br \/>\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0<strong>Calculator Map,\u00a0<\/strong>then click on\u00a0<b>Materials and Metallurgical\u00a0<\/b>under\u00a0<strong>Engineering<\/strong><strong>.<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4494 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-3.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-3.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-3-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-3-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-3-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on\u00a0<strong>instrumentation\u00a0<\/strong>under\u00a0<strong>Materials and Metallurgical<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4495 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-4.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-4.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-4-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-4-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-4-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>So, Click on <strong>Dynamic Characteristics of Instruments\u00a0<\/strong>under\u00a0<strong>Instrumentation<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4609 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-1.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, Click on <strong>Transfer Function (sensitivity) | First Order Instruments\u00a0<\/strong>under\u00a0<strong>Dynamic Characteristics of Instruments<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4616 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-6-1.png\" alt=\"\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-6-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-6-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-6-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-6-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>The screenshot below displays the page or activity to enter your values, to get the answer for the transfer function (sensitivity) | First Order Instruments according to the respective parameters which is the <strong>Static Sensitivity (k), Time Constant (u)<\/strong> and\u00a0<strong>Differentiation Value (<sup>d<\/sup>\u00a0\/\u00a0<sub>dt<\/sub>) (D).<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4617 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-7-1.png\" alt=\"How to Calculate and Solve for Transfer Function (Sensitivity) | First Order Instruments | Dynamic Characteristics of Instruments\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-7-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-7-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-7-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-7-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Now, enter the values appropriately and accordingly for the parameters as required by the <strong>Static Sensitivity (k)<\/strong> is <strong>24<\/strong>,<strong> Time Constant (u)\u00a0<\/strong>is\u00a0<strong>16,<\/strong> and\u00a0<strong>Differentiation Value (<sup>d<\/sup>\u00a0\/\u00a0<sub>dt<\/sub>) (D)<\/strong> is <strong>10<\/strong>.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4618 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-8.png\" alt=\"How to Calculate and Solve for Transfer Function (Sensitivity) | First Order Instruments | Dynamic Characteristics of Instruments\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-8.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-8-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-8-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-8-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>Finally, Click on Calculate<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-4619 size-full\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-9-1.png\" alt=\"How to Calculate and Solve for Transfer Function (Sensitivity) | First Order Instruments | Dynamic Characteristics of Instruments\" width=\"1366\" height=\"768\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-9-1.png 1366w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-9-1-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-9-1-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2021\/01\/Screenshot-9-1-768x432.png 768w\" sizes=\"(max-width: 1366px) 100vw, 1366px\" \/><\/p>\n<p>As you can see from the screenshot above,\u00a0<strong>Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the transfer function (sensitivity) | First Order Instruments and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents transfer function. To calculate transfer function (sensitivity) | First Order Instruments, three essential parameters&hellip;","protected":false},"author":5,"featured_media":14352,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Transfer Function Sensitivity","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn the steps and the formula on How to Calculate and Solve for Transfer Function (Sensitivity) in First Order Instruments","_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[47],"tags":[1351,1348,60,1329,543,1349,1350,1352],"class_list":["post-4603","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-differentiation-value","tag-dynamic-characteristics-of-instruments","tag-engineering","tag-instrumentation","tag-materials-and-metallurgical","tag-static-sensitivity","tag-time-constant","tag-transfer-function","cs-entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How to Calculate and Solve for 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