{"id":1508,"date":"2018-04-23T09:23:26","date_gmt":"2018-04-23T09:23:26","guid":{"rendered":"https:\/\/www.tina.com\/resources\/?page_id=1508"},"modified":"2018-06-21T11:07:26","modified_gmt":"2018-06-21T11:07:26","slug":"9-differential-summing","status":"publish","type":"page","link":"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/","title":{"rendered":"9. Differential Summing"},"content":{"rendered":"<div class=\"top-navigation\">\n<div class=\"current-page\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/people-location-30.png\" \/>CURRENT &#8211; 9. Differential Summing<\/div>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/8-inverting-amplifier\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 8. Inverting Amplifier<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/10-amplifiers-with-balanced-inputs-or-outputs\/\">NEXT- 10. Amplifiers with balanced inputs or outputs<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n<\/div>\n<p><script>\nfunction setStyle(){ \nheight = document.getElementsByClassName('entry-header')[0].clientHeight;\ndocument.getElementsByClassName('entry-header')[0].style.marginTop = height +\"px\";\ndocument.getElementsByClassName('top-navigation')[0].style.top = Math.round(-(height-20)*2) +\"px\";\n}\nsetStyle();\nwindow.onresize = function(event) {\nsetStyle();\n};\n<\/script><\/p>\n<div>\n<div id=\"attachment_1517\" style=\"width: 462px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1517\" class=\"wp-image-1517 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-40-1.png\" alt=\"Differential summing\" width=\"452\" height=\"384\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-40-1.png 452w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-40-1-300x255.png 300w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><p id=\"caption-attachment-1517\" class=\"wp-caption-text\">Figure 40 \u2013 Differential summing<\/p><\/div>\n<p>We have seen that an op-amp can be configured to produce an output that is a weighted sum of multiple inputs. If the sum includes both positive and negative signs, D<em>ifferential Summing <\/em>results.<br \/>\nThe op-amp configuration of Figure 40 produces an output voltage, <em>v<sub>out<\/sub><\/em>, given by<\/p>\n<div id=\"attachment_1519\" style=\"width: 310px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1519\" class=\"wp-image-1519 size-medium\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-90-1-300x43.png\" alt=\"\" width=\"300\" height=\"43\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-90-1-300x43.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-90-1.png 321w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-1519\" class=\"wp-caption-text\">(90)<\/p><\/div>\n<\/div>\n<div>\n<p>\u00a0where<\/p>\n<\/div>\n<div>\n<div id=\"attachment_1524\" style=\"width: 170px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1524\" class=\"wp-image-1524 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-91.png\" alt=\"\" width=\"160\" height=\"34\" \/><p id=\"caption-attachment-1524\" class=\"wp-caption-text\">(91)<\/p><\/div>\n<p>We choose the resistors to achieve bias balance, as follows:<\/p>\n<div id=\"attachment_1526\" style=\"width: 243px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1526\" class=\"wp-image-1526 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-92.png\" alt=\"\" width=\"233\" height=\"36\" \/><p id=\"caption-attachment-1526\" class=\"wp-caption-text\">(92)<\/p><\/div>\n<p>The input resistance for each inverting input, <em>v<sub>j<\/sub><\/em>, is <em>R<sub>j<\/sub><\/em>.<\/p>\n<p>If the inverting and non-inverting terminals each have only one input, the result is a <em>differencing amplifier. <\/em>This is illustrated in Figure 41.<\/p>\n<div id=\"attachment_1530\" style=\"width: 230px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1530\" class=\"wp-image-1530 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-41.png\" alt=\"Differencing amplifier\" width=\"220\" height=\"151\" \/><p id=\"caption-attachment-1530\" class=\"wp-caption-text\">Figure 41 \u2013 Differencing amplifier<\/p><\/div>\n<p>The output voltage for this configuration is<\/p>\n<div id=\"attachment_1527\" style=\"width: 216px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1527\" class=\"wp-image-1527 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-93.png\" alt=\"\" width=\"206\" height=\"45\" \/><p id=\"caption-attachment-1527\" class=\"wp-caption-text\">(93)<\/p><\/div>\n<p>Note that RA = Ra [see Equation 91]. To achieve bias balance, we choose<\/p>\n<div id=\"attachment_1532\" style=\"width: 113px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1532\" class=\"wp-image-1532 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-94.png\" alt=\"\" width=\"103\" height=\"24\" \/><p id=\"caption-attachment-1532\" class=\"wp-caption-text\">(94)<\/p><\/div>\n<\/div>\n<p>The input resistance for the <em>v<sub>a<\/sub><\/em> terminal is <em>R<sub>A<\/sub><\/em>. The input resistance for the <em>v<sub>1<\/sub><\/em> terminal is\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1533\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-94Equation.png\" alt=\"\" width=\"84\" height=\"28\" \/> , where <em>R<sub>in<\/sub><\/em> is found from Equation (56) to be<\/p>\n<div id=\"attachment_1535\" style=\"width: 208px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1535\" class=\"wp-image-1535 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-95.png\" alt=\"\" width=\"198\" height=\"86\" \/><p id=\"caption-attachment-1535\" class=\"wp-caption-text\">(95)<\/p><\/div>\n<p>Then <em>R<sub>in<\/sub><\/em>(at <em>V<sub>1<\/sub><\/em>) is approximately <em>R<sub>1<\/sub><\/em>+<em>R<sub>2<\/sub><\/em>. <em>R<sub>out<\/sub><\/em> is found in Equation (52) and is equal to<\/p>\n<div id=\"attachment_1538\" style=\"width: 140px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1538\" class=\"wp-image-1538 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-96.png\" alt=\"\" width=\"130\" height=\"45\" \/><p id=\"caption-attachment-1538\" class=\"wp-caption-text\">(96)<\/p><\/div>\n<p>To achieve unit-gain differencing, where the output is given by <em>v<sub>out<\/sub><\/em> = <em>v<sub>1<\/sub><\/em> &#8211; <em>v<sub>a<\/sub><\/em> we set <em>R<sub>A<\/sub><\/em> = <em>R<sub>F<\/sub><\/em> = <em>R<sub>1<\/sub><\/em> = <em>R<sub>x<\/sub>.<\/em> If a 741 op-amp is used, a typical value for these four resistors is 10 k\u03a9.<\/p>\n<p>The input resistance into <em>v<sub>out<\/sub><\/em> is then 10 k\u03a9 and into the <em>v<sub>1<\/sub><\/em> terminal the resistance is 20 k\u03a9.<\/p>\n<p>Suppose that equal-gain differencing is desired but that the gains need not be unity. We then set <em>R<sub>1<\/sub><\/em> = <em>R<sub>A<\/sub><\/em> and <em>R<sub>x<\/sub><\/em> = <em>R<sub>F<\/sub><\/em>. The output voltage is then<\/p>\n<div id=\"attachment_1541\" style=\"width: 115px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1541\" class=\"wp-image-1541 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-97.png\" alt=\"\" width=\"105\" height=\"45\" \/><p id=\"caption-attachment-1541\" class=\"wp-caption-text\">(97)<\/p><\/div>\n<p>The input resistance into the <em>v<sub>a<\/sub><\/em> terminal is <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1542\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-97-Equation.png\" alt=\"\" width=\"88\" height=\"28\" \/>, and into the non-inverting terminal it is , which is approximately <em>R<sub>A <\/sub><\/em>+ <em>R<sub>F<\/sub><\/em> since <em>R<sub>in <\/sub><\/em>&gt;&gt; <em>R<sub>F<\/sub><\/em>. Values for input resistance and\u00a0<em>R<sub>out<\/sub><\/em> are easily determined with the use of Equations (95) and (96).<\/p>\n<p>A useful modification of the differencing amplifier configuration of Figure 41 is the <em>sign switcher <\/em>as shown in Figure 42.<\/p>\n<div id=\"attachment_1548\" style=\"width: 461px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1548\" class=\"wp-image-1548 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-42-1.png\" alt=\"Sign switcher\" width=\"451\" height=\"161\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-42-1.png 451w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-42-1-300x107.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-42-1-450x161.png 450w\" sizes=\"auto, (max-width: 451px) 100vw, 451px\" \/><p id=\"caption-attachment-1548\" class=\"wp-caption-text\">Figure 42 &#8211; Sign switcher<\/p><\/div>\n<p>With the switch in the position shown in Figure 42(a), <em>v<sub>out <\/sub><\/em>= &#8211;<em>v<sub>in<\/sub><\/em>, and for the opposite switch position, <em>v<sub>out<\/sub><\/em> = 2<em>v<sub>in<\/sub><\/em> &#8211; <em>v<sub>in<\/sub><\/em> = <em>v<sub>in<\/sub><\/em>. The input resistance is 10 k\u03a9 for each position, and the bias is balanced in each position. Figure 42(a) shows a single-pole double-throw switch. Sign switching can also be accomplished with a single-throw switch as shown in Figure 42(b). However, for this implementation, the bias and input resistances are not equal in the two switch positions.<\/p>\n<h6><u>Example<\/u><\/h6>\n<p>Determine the output resistance and the input resistance at each of the inputs of a multiple input 741 amplifier which has an output of<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-10equation1\/#main\" rel=\"attachment wp-att-3231\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3231 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation1.png\" alt=\"\" width=\"205\" height=\"23\" \/><\/a><\/p>\n<p>Assume that the value of the resistance at the + and &#8211; terminals is 10 k\u03a9.<\/p>\n<p><em>Solution:<\/em> Using the larger of <em>X<\/em> and (<em>Y<\/em>+1) yields the multiplying factor for determining <em>R<sub>F<\/sub><\/em>.<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-10equation2\/#main\" rel=\"attachment wp-att-3234\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3234 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation2.png\" alt=\"\" width=\"107\" height=\"47\" \/><\/a>, then<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-10equation3\/#main\" rel=\"attachment wp-att-3235\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3235 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation3.png\" alt=\"\" width=\"112\" height=\"26\" \/><\/a><\/p>\n<p>The circuit is shown in Figure 43.<\/p>\n<div id=\"attachment_3237\" style=\"width: 230px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-figure43\/#main\" rel=\"attachment wp-att-3237\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3237\" class=\"wp-image-3237 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-Figure43.png\" alt=\"\" width=\"220\" height=\"204\" \/><\/a><p id=\"caption-attachment-3237\" class=\"wp-caption-text\">Figure 43-Circuit for Example<\/p><\/div>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-10equation4-10\/#main\" rel=\"attachment wp-att-3238\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3238 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation4-10.png\" alt=\"\" width=\"185\" height=\"266\" \/><\/a><br \/>\n<a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/9-differential-summing\/practicalamplifier-example9-10equation11-16\/#main\" rel=\"attachment wp-att-3240\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3240 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation11-16.png\" alt=\"\" width=\"352\" height=\"180\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation11-16.png 352w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-10Equation11-16-300x153.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/a><\/p>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/8-inverting-amplifier\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 8. Inverting Amplifier<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/10-amplifiers-with-balanced-inputs-or-outputs\/\">NEXT- 10. Amplifiers with balanced inputs or outputs<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>CURRENT &#8211; 9. Differential Summing PREVIOUS- 8. Inverting Amplifier NEXT- 10. Amplifiers with balanced inputs or outputs We have seen that an op-amp can be configured to produce an output that is a weighted sum of multiple inputs. If the sum includes both positive and negative signs, Differential Summing results. The op-amp configuration of Figure [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":917,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"yst_prominent_words":[480,493,254,491,494,477,351,350,496,168,487,469,492,470,462,495,368,490,489,488],"class_list":["post-1508","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1508","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/comments?post=1508"}],"version-history":[{"count":47,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1508\/revisions"}],"predecessor-version":[{"id":3417,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1508\/revisions\/3417"}],"up":[{"embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/917"}],"wp:attachment":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/media?parent=1508"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/yst_prominent_words?post=1508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}