{"id":1362,"date":"2018-04-20T08:23:57","date_gmt":"2018-04-20T08:23:57","guid":{"rendered":"https:\/\/www.tina.com\/resources\/?page_id=1362"},"modified":"2018-06-21T11:03:51","modified_gmt":"2018-06-21T11:03:51","slug":"7-non-inverting-amplifier","status":"publish","type":"page","link":"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/","title":{"rendered":"7. Non-inverting Amplifier"},"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; 7. Non-inverting Amplifier<\/div>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/6-computer-simulation-of-op-amp-circuits\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 6. Computer Simulation of Op-amp circuits<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/8-inverting-amplifier\/\">NEXT- 8. Inverting amplifier<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n<div class=\"clear\"><\/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<h6><em>Non-inverting Amplifier<\/em><\/h6>\n<div id=\"attachment_1365\" style=\"width: 522px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1365\" class=\"wp-image-1365 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-29.png\" alt=\"Non-inverting Amplifier, operational amplifiers\" width=\"512\" height=\"233\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-29.png 512w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-29-300x137.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><p id=\"caption-attachment-1365\" class=\"wp-caption-text\">Figure 29 &#8211; The non-inverting amplifier<\/p><\/div>\n<p>Figure 29(a) illustrates the <em>non-inverting amplifier<\/em>, and Figure 29(b) shows the equivalent circuit.<\/p>\n<p>The input voltage is applied through <em>R<sub>1<\/sub><\/em> into the non-inverting terminal.<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">7.1 Input and Output Resistances<\/span><\/b><\/span><\/em><\/h6>\n<p>The <em>input resistance <\/em>of this amplifier is found by determining the Thevenin equivalent of the input circuit. The load resistance is normally such that <em>R<sub>load<\/sub><\/em> &gt;&gt; <em>R<sub>o<\/sub><\/em>. If this were not true, the effective gain would be reduced and the effective value of <em>R<sub>o<\/sub><\/em> would be the parallel combination of <em>R<sub>o<\/sub><\/em> with <em>R<sub>load<\/sub><\/em>. Let us again define \u00a0and <em>R&#8217;<sub>F<\/sub><\/em> = <em>R<sub>F<\/sub><\/em> + <em>R<sub>o<\/sub><\/em>. We shall neglect <em>R<sub>1<\/sub><\/em>, since it is so much less than <em>R<sub>in<\/sub><\/em>. Now since <em>R<sub>load<\/sub><\/em> &gt;&gt; <em>R<sub>o<\/sub><\/em>, we can reduce Figure 29(a) to the simplified form of Figure 30(a).<\/p>\n<div id=\"attachment_1373\" style=\"width: 535px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1373\" class=\"wp-image-1373 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-30.png\" alt=\"operational amplifiers, op-amp, practical op-amp\" width=\"525\" height=\"272\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-30.png 525w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-30-300x155.png 300w\" sizes=\"auto, (max-width: 525px) 100vw, 525px\" \/><p id=\"caption-attachment-1373\" class=\"wp-caption-text\">Figure 30 &#8211; Reduced circuits for input resistance<\/p><\/div>\n<p>We find the Thevenin equivalent of the circuit surrounded by the elliptical curve, resulting in Figure 30(b). In Figure 30(c), the resistance to the right of 2<em>R<sub>cm<\/sub><\/em> is given by <em>v<\/em>\/<em>i&#8217;<\/em>. In order to evaluate this, we write a loop equation to obtain<\/p>\n<div id=\"attachment_1376\" style=\"width: 228px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1376\" class=\"wp-image-1376 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-31-53.png\" alt=\"\" width=\"218\" height=\"51\" \/><p id=\"caption-attachment-1376\" class=\"wp-caption-text\">(53)<\/p><\/div>\n<p>Therefore,<\/p>\n<div id=\"attachment_1378\" style=\"width: 215px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1378\" class=\"wp-image-1378 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-54.png\" alt=\"\" width=\"205\" height=\"51\" \/><p id=\"caption-attachment-1378\" class=\"wp-caption-text\">(54)<\/p><\/div>\n<p>The input resistance is the parallel combination of this quantity with 2<em>R<sub>cm<\/sub><\/em>.<\/p>\n<div id=\"attachment_1380\" style=\"width: 266px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1380\" class=\"wp-image-1380 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-55.png\" alt=\"\" width=\"256\" height=\"54\" \/><p id=\"caption-attachment-1380\" class=\"wp-caption-text\">(55)<\/p><\/div>\n<p>Recall that , <em>R&#8217;<sub>F<\/sub><\/em> = <em>R<sub>F<\/sub><\/em> + <em>R<sub>o<\/sub><\/em>, and <em>R<sub>load<\/sub><\/em> &gt;&gt; <em>R<sub>o<\/sub><\/em>. If we retain only the most significant terms and note that <em>R<sub>cm<\/sub><\/em> is large, Equation (55) reduces to<\/p>\n<div id=\"attachment_1383\" style=\"width: 143px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1383\" class=\"wp-image-1383 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-56.png\" alt=\"\" width=\"133\" height=\"85\" \/><p id=\"caption-attachment-1383\" class=\"wp-caption-text\">(56)<\/p><\/div>\n<p>where we again use the zero-frequency voltage gain, <em>G<sub>o<\/sub><\/em>.<\/p>\n<p>Equation (56) can be used to find the input resistance of the 741 op-amp. If we substitute the parameter values as given in Table 1, Equation (56) becomes<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1384\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-56Reduced.png\" alt=\"\" width=\"97\" height=\"21\" \/><\/p>\n<p>We again use the assumptions that <em>R<sub>cm<\/sub><\/em> is large, that is <em>R&#8217;<sub>F<\/sub><\/em> \u00bb <em>R<sub>F<\/sub><\/em> and <em>R&#8217;<sub>A<\/sub><\/em> \u00bb <em>R<sub>A<\/sub><\/em>. Then the output resistance of a 741 op-amp is given by<\/p>\n<div id=\"attachment_1385\" style=\"width: 146px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1385\" class=\"wp-image-1385 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-57.png\" alt=\"\" width=\"136\" height=\"42\" \/><p id=\"caption-attachment-1385\" class=\"wp-caption-text\">(57)<\/p><\/div>\n<h6><u>EXAMPLE<\/u><\/h6>\n<p>Calculate the input resistance for the unity-gain follower shown in Figure 31(a).<\/p>\n<div id=\"attachment_3204\" style=\"width: 501px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practical-op-amp9-figure31\/#main\" rel=\"attachment wp-att-3204\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3204\" class=\"wp-image-3204 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure31.png\" alt=\"Unity-gain follower\" width=\"491\" height=\"164\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure31.png 491w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure31-300x100.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/a><p id=\"caption-attachment-3204\" class=\"wp-caption-text\">Figure 31 &#8211; Unity-gain follower<\/p><\/div>\n<p><em>Solution:<\/em> \u00a0The equivalent circuit is shown in Figure 31(b). Since we assume the zero-frequency gain, <em>G<sub>o<\/sub><\/em>, and the common-mode resistance, <em>R<sub>cm<\/sub><\/em>, are high, we can neglect the term \u00a0<a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practical-op-amp9-example7a\/#main\" rel=\"attachment wp-att-3206\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3206 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example7a.png\" alt=\"\" width=\"72\" height=\"29\" \/><\/a>compared to (1+<em>G<sub>o<\/sub><\/em>)<em>R<sub>i<\/sub><\/em>. Equation (57) cannot be used since <em>R<sub>A<\/sub><\/em> = 0. The input resistance is then given by<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practical-op-amp9-example7b\/#main\" rel=\"attachment wp-att-3208\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3208 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example7b.png\" alt=\"\" width=\"206\" height=\"33\" \/><\/a><\/p>\n<p>This is typically equal to 400 M\u03a9 or more, so we can neglect <em>R<sub>1<\/sub><\/em> (i.e., set <em>R<sub>1 <\/sub><\/em>= 0).<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">7.2 Voltage Gain<\/span><\/b><\/span><\/em><\/h6>\n<p>We wish to determine the voltage gain, <em>A<sub>+<\/sub><\/em> for the non-inverting amplifier of Figure 32(a).<\/p>\n<div id=\"attachment_1391\" style=\"width: 563px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1391\" class=\"wp-image-1391 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-32.png\" alt=\"Non-inverting amplifier\" width=\"553\" height=\"395\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-32.png 553w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-32-300x214.png 300w\" sizes=\"auto, (max-width: 553px) 100vw, 553px\" \/><p id=\"caption-attachment-1391\" class=\"wp-caption-text\">Figure 32 \u2013 Non-inverting amplifier<\/p><\/div>\n<p>This gain is defined by<\/p>\n<div id=\"attachment_1393\" style=\"width: 108px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1393\" class=\"wp-image-1393 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-58.png\" alt=\"\" width=\"98\" height=\"47\" \/><p id=\"caption-attachment-1393\" class=\"wp-caption-text\">(58)<\/p><\/div>\n<p>The equivalent circuit is shown in Figure 32(b). If we assume <em>R<sub>F<\/sub><\/em>&gt;&gt;<em>R<sub>o<\/sub><\/em>, <em>R<sub>load<\/sub><\/em>&gt;&gt;<em>R<sub>o<\/sub><\/em> and , the circuit can be reduced to that shown in Figure 32(c). If we further define , then Figure 32(d) results.<\/p>\n<p>The assumed conditions are desirable in order to prevent reduction of the effective gain. The operation of taking Thevenin equivalents modifies the dependent voltage source and the driving voltage source as in Figure 32(d). Note that<\/p>\n<div id=\"attachment_1394\" style=\"width: 108px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1394\" class=\"wp-image-1394 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-59.png\" alt=\"\" width=\"98\" height=\"47\" \/><p id=\"caption-attachment-1394\" class=\"wp-caption-text\">(59)<\/p><\/div>\n<p>The output voltage is given by<\/p>\n<div id=\"attachment_1396\" style=\"width: 131px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1396\" class=\"wp-image-1396 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-60.png\" alt=\"\" width=\"121\" height=\"28\" \/><p id=\"caption-attachment-1396\" class=\"wp-caption-text\">(60)<\/p><\/div>\n<p>We can find <em>i<\/em> by applying KVL to the circuit of Figure 32(d) to obtain<\/p>\n<div id=\"attachment_1399\" style=\"width: 264px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1399\" class=\"wp-image-1399 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-61.png\" alt=\"\" width=\"254\" height=\"44\" \/><p id=\"caption-attachment-1399\" class=\"wp-caption-text\">(61)<\/p><\/div>\n<div id=\"attachment_1401\" style=\"width: 80px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1401\" class=\"wp-image-1401 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-62.png\" alt=\"\" width=\"70\" height=\"24\" \/><p id=\"caption-attachment-1401\" class=\"wp-caption-text\">(62)<\/p><\/div>\n<p>where<\/p>\n<p>and\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1402\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-61A.png\" alt=\"\" width=\"70\" height=\"24\" \/> \u00a0implying\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1403\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-61B.png\" alt=\"\" width=\"70\" height=\"24\" \/> .<\/p>\n<p>Solving for the current,<em> i<\/em>, we obtain<\/p>\n<div id=\"attachment_1405\" style=\"width: 287px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1405\" class=\"wp-image-1405 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-63.png\" alt=\"\" width=\"277\" height=\"46\" \/><p id=\"caption-attachment-1405\" class=\"wp-caption-text\">(63)<\/p><\/div>\n<p>The voltage gain is given by the ratio of output to input voltage.<\/p>\n<div id=\"attachment_1407\" style=\"width: 310px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1407\" class=\"wp-image-1407 size-medium\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-64-300x46.png\" alt=\"\" width=\"300\" height=\"46\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-64-300x46.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-64.png 312w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-1407\" class=\"wp-caption-text\">(64)<\/p><\/div>\n<p>As a check of this result, we can reduce the model to that of the ideal op-amp. We use the zero-frequency gain, <em>G<sub>o<\/sub><\/em>, in place of <em>G<\/em> in Equation (64) and also the following equalities.<\/p>\n<div id=\"attachment_1411\" style=\"width: 94px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1411\" class=\"wp-image-1411 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-65.png\" alt=\"\" width=\"84\" height=\"109\" \/><p id=\"caption-attachment-1411\" class=\"wp-caption-text\">(65)<\/p><\/div>\n<p>When we let <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1416\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-64A.png\" alt=\"\" width=\"58\" height=\"24\" \/>, Equation (64) becomes<\/p>\n<div id=\"attachment_1413\" style=\"width: 95px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1413\" class=\"wp-image-1413 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-66.png\" alt=\"\" width=\"85\" height=\"42\" \/><p id=\"caption-attachment-1413\" class=\"wp-caption-text\">(66)<\/p><\/div>\n<p>which agrees with the result for the idealized model.<\/p>\n<h6><strong><u>Example<\/u><\/strong><\/h6>\n<p>Find the gain of the unity-gain follower shown in Figure 33.<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practicalamplifier-figure9-33-2\/#main\" rel=\"attachment wp-att-3214\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3214 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Figure9-33-1.png\" alt=\"Unity gain, practical op-amps, operational amplifiers\" width=\"335\" height=\"148\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Figure9-33-1.png 335w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Figure9-33-1-300x133.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/a><\/p>\n<p>Figure 33 \u2013 Unity gain follower<em>Solution:<\/em>\u00a0 In this circuit, <a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practicalamplifier-example9-8a\/#main\" rel=\"attachment wp-att-3215\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3215 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-8a.png\" alt=\"\" width=\"50\" height=\"28\" \/><\/a>, <em>R&#8217;<sub>A<\/sub><\/em> = 2<em>R<sub>cm<\/sub><\/em>, and <em>R<sub>F<\/sub><\/em> &lt;&lt; <em>R&#8217;<sub>A<\/sub><\/em>. We assume that <em>G<sub>o<\/sub><\/em> is large, <a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practicalamplifier-example9-8b\/#main\" rel=\"attachment wp-att-3216\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3216 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-8b.png\" alt=\"\" width=\"57\" height=\"22\" \/><\/a>, and we set <em>R<sub>1<\/sub><\/em> = <em>R<sub>F<\/sub><\/em>. Equation\u00a0 (64) then reduces to<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/7-non-inverting-amplifier\/practicalamplifier-example9-8equation67\/#main\" rel=\"attachment wp-att-3218\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3218 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/PracticalAmplifier-Example9-8Equation67.png\" alt=\"\" width=\"200\" height=\"47\" \/><\/a><\/p>\n<p>(67)<\/p>\n<p>so <em>v<sub>out<\/sub><\/em> = <em>v<sub>in<\/sub><\/em> as expected.<\/p>\n<p>&nbsp;<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">7.3 Multiple-Input Amplifiers<\/span><\/b><\/span><\/em><\/h6>\n<p>We extend the previous results to the case of the non-inverting amplifier with multiple voltage inputs. Figure 34 shows a multiple-input non-inverting amplifier.<\/p>\n<div id=\"attachment_1422\" style=\"width: 455px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1422\" class=\"wp-image-1422 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-34M.png\" alt=\"Multiple-input non-inverting amplifier\" width=\"445\" height=\"231\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-34M.png 445w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-34M-300x156.png 300w\" sizes=\"auto, (max-width: 445px) 100vw, 445px\" \/><p id=\"caption-attachment-1422\" class=\"wp-caption-text\">Figure 34 \u2013 Multiple-input non-inverting amplifier<\/p><\/div>\n<p class=\"MTDisplayEquation7\" style=\"text-indent: 13.5pt; line-height: normal; tab-stops: center 2.75in right 405.0pt;\">If inputs <i>v<sub>1<\/sub><\/i>, <i>v<sub>2<\/sub><\/i>, <i>v<sub>3<\/sub><\/i>, &#8230;, <i>v<sub>n<\/sub><\/i> are applied through input resistances <i>R<sub>1<\/sub><\/i>, <i>R<sub>2<\/sub><\/i>, <i>R<sub>3<\/sub><\/i>, &#8230;, <i>R<sub>n<\/sub><\/i>, we obtain a special case of the general result derived in Chapter &#8220;Ideal Operational Amplifiers&#8221;, as follows:<\/p>\n<div id=\"attachment_1427\" style=\"width: 239px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1427\" class=\"wp-image-1427 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-68.png\" alt=\"\" width=\"229\" height=\"56\" \/><p id=\"caption-attachment-1427\" class=\"wp-caption-text\">(68)<\/p><\/div>\n<p>We choose<\/p>\n<div id=\"attachment_1429\" style=\"width: 160px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1429\" class=\"wp-image-1429 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-69.png\" alt=\"\" width=\"150\" height=\"31\" \/><p id=\"caption-attachment-1429\" class=\"wp-caption-text\">(69)<\/p><\/div>\n<p>to achieve bias balance. The output resistance is found from Equation (52).<\/p>\n<p>As a specific example, let us determine the output voltage of the two-input summer of Figure 35.<\/p>\n<div id=\"attachment_1431\" style=\"width: 194px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1431\" class=\"wp-image-1431 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-35.png\" alt=\"\" width=\"184\" height=\"133\" \/><p id=\"caption-attachment-1431\" class=\"wp-caption-text\">(35)<\/p><\/div>\n<p>The output voltage is found from Equation (68) , as follows:<\/p>\n<div id=\"attachment_1432\" style=\"width: 222px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1432\" class=\"wp-image-1432 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-70.png\" alt=\"\" width=\"212\" height=\"45\" \/><p id=\"caption-attachment-1432\" class=\"wp-caption-text\">(70)<\/p><\/div>\n<p>We choose\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1433\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-70A.png\" alt=\"\" width=\"94\" height=\"25\" \/> \u00a0to achieve bias balance. If we assume <em>R<sub>F<\/sub><\/em> = <em>R<sub>1<\/sub><\/em> = <em>R<sub>2<\/sub><\/em> = <em>R<sub>A<\/sub><\/em>, then Equation (70) reduces to <em>v<sub>out<\/sub><\/em> = <em>v<sub>1<\/sub><\/em> + <em>v<sub>2<\/sub><\/em>, which is a unity-gain two-input summer.<\/p>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/6-computer-simulation-of-op-amp-circuits\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 6. Computer simulation of op-amp circuits<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/8-inverting-amplifier\/\">NEXT- 8. Inverting amplifier<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>CURRENT &#8211; 7. Non-inverting Amplifier PREVIOUS- 6. Computer Simulation of Op-amp circuits NEXT- 8. Inverting amplifier Non-inverting Amplifier Figure 29(a) illustrates the non-inverting amplifier, and Figure 29(b) shows the equivalent circuit. The input voltage is applied through R1 into the non-inverting terminal. 7.1 Input and Output Resistances The input resistance of this amplifier is found [&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":[465,450,474,466,268,469,470,462,463,464,467,468,449,473,475],"class_list":["post-1362","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1362","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=1362"}],"version-history":[{"count":71,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1362\/revisions"}],"predecessor-version":[{"id":3415,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1362\/revisions\/3415"}],"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=1362"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/yst_prominent_words?post=1362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}