{"id":1220,"date":"2018-04-19T09:07:41","date_gmt":"2018-04-19T09:07:41","guid":{"rendered":"https:\/\/www.tina.com\/resources\/?page_id=1220"},"modified":"2018-07-12T11:27:20","modified_gmt":"2018-07-12T11:27:20","slug":"5-practical-op-amps","status":"publish","type":"page","link":"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/","title":{"rendered":"5. Practical Op-amps"},"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; 5. Practical Op-amps<\/div>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/4-manufacturers-specifications\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 4. Manufacturers&#8217; specifications<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/6-computer-simulation-of-op-amp-circuits\/\">NEXT- 6. Computer simulation op-amp circuits<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>Practical Op-amps<\/em><\/h6>\n<p>Practical Op-amps approximate their <em>ideal<\/em> counterparts but differ in some important respects. It is important for the circuit designer to understand the differences between actual op-amps and ideal op-amps, since these differences can adversely affect circuit performance.<\/p>\n<p>Our goal is to develop a detailed model of the practical op-amp &#8211; a model that takes into account the most significant characteristics of the non-ideal device. We begin by defining the parameters used to describe practical op-amps. These parameters are specified in listings on data sheets supplied by the op-amp manufacturer.<\/p>\n<p>Table 1 lists the parameter values for three particular op-amps, one of the three being the \u03bcA741. We use \u03bcA741 operational amplifiers in many of the examples and end-of-chapter problems for the following reasons: (1) they have been fabricated by many IC manufacturers, (2) they are found in great quantities throughout the electronics industry, and (3) they are general-purpose internally-compensated op-amps, and their properties can be used as a reference for comparison purposes when dealing with other op-amp types. As the various parameters are defined in the following sections, reference should be made to Table 9.1 in order to find typical values.<\/p>\n<div id=\"attachment_1223\" style=\"width: 592px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1223\" class=\"wp-image-1223 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Table9-1.png\" alt=\"Practical Op-amps, operational amplifiers\" width=\"582\" height=\"238\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Table9-1.png 582w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Table9-1-300x123.png 300w\" sizes=\"auto, (max-width: 582px) 100vw, 582px\" \/><p id=\"caption-attachment-1223\" class=\"wp-caption-text\">Table 1 &#8211; Parameter values for op-amps<\/p><\/div>\n<p>The most significant difference between ideal and actual op-amps is in the voltage gain. The ideal op-amp has a voltage gain that approaches infinity. The actual op-amp has a finite voltage gain that decreases as the frequency increases (we explore this in detail in the next chapter).<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.1 Open-Loop Voltage Gain (G)<\/span><\/b><\/span><\/em><\/h6>\n<p>The open-loop voltage gain of an op-amp is the ratio of the change in output voltage to a change in the input voltage without feedback. Voltage gain is a dimensionless quantity. The symbol G is used to indicate the open-loop voltage gain. Op-amps have high voltage gain for low-frequency inputs. The op-amp specification lists the voltage gain in volts per millivolt or in decibels (dB) [defined as 20log<sub>10<\/sub>(<em>v<sub>out<\/sub><\/em>\/<em>v<sub>in<\/sub><\/em>)].<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.2 Modified Op-amp Model\u00a0<\/span><\/b><\/span><\/em><\/h6>\n<p>Figure 14 shows a modified version of the idealized op-amp model. We have altered the idealized model by adding input resistance (<em>R<sub>i<\/sub><\/em>), output resistance (<em>R<sub>o<\/sub><\/em>), and common-mode resistance (<em>R<sub>cm<\/sub><\/em>).<\/p>\n<div id=\"attachment_1237\" style=\"width: 318px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1237\" class=\"wp-image-1237 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-14.png\" alt=\"op-amp, practical op-amps\" width=\"308\" height=\"164\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-14.png 308w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-14-300x160.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><p id=\"caption-attachment-1237\" class=\"wp-caption-text\">Figure 14 \u2013 Modified op-amp model<\/p><\/div>\n<p>Typical values of these parameters (for the 741 op-amp) are<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1240\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Value-of-741Opamp.png\" alt=\"\" width=\"162\" height=\"91\" \/><\/p>\n<p>We now consider the circuit of Figure 15 in order to examine op-amp performance. The inverting and non-inverting inputs of the op-amp are driven by sources that have series resistance. The output of the op-amp is fed back to the input through a resistor, <em>R<sub>F<\/sub><\/em>.<\/p>\n<p>The sources driving the two inputs are denoted <em>v<sub>A<\/sub><\/em> and <em>v<sub>1<\/sub><\/em>, and the associated series resistances are <em>R<sub>A<\/sub><\/em> and <em>R<sub>1<\/sub><\/em>. If the input circuitry is more complex, these resistances can be considered as Thevenin equivalents of that circuitry.<\/p>\n<div id=\"attachment_1243\" style=\"width: 310px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1243\" class=\"wp-image-1243 size-medium\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-15-300x171.png\" alt=\"Practical Op-amps, operational amplifiers\" width=\"300\" height=\"171\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-15-300x171.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-15.png 385w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-1243\" class=\"wp-caption-text\">Figure 15 \u2013 Op-amp circuit<\/p><\/div>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.3\u00a0<strong>Input Offset Voltage (V<sub>io<\/sub>)<\/strong><\/span><\/b><\/span><\/em><\/h6>\n<p>When the input voltage to an ideal op-amp is zero, the output voltage is also zero. This is not true for an actual op-amp. The <em>input offset voltage<\/em>, <em>V<sub>io<\/sub><\/em>, is defined as the differential input voltage required to make the output voltage equal to zero. <em>V<sub>io<\/sub><\/em> is zero for the ideal op-amp. A typical value of <em>V<sub>io<\/sub><\/em> for the 741 op-amp is 2 mV. A non-zero value of <em>V<sub>io<\/sub><\/em> is undesirable because the op-amp amplifies any input offset, thus causing a larger output <em>dc<\/em> error.<\/p>\n<p>The following technique can be used to measure the input offset voltage. Rather than vary the input voltage in order to force the output to zero, the input is set equal to zero, as shown in Figure 16, and the output voltage is measured.<\/p>\n<div id=\"attachment_1322\" style=\"width: 372px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1322\" class=\"wp-image-1322 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-16MM.png\" alt=\"op-amps, operational amplifiers\" width=\"362\" height=\"113\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-16MM.png 362w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-16MM-300x94.png 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><p id=\"caption-attachment-1322\" class=\"wp-caption-text\">Figure 16 \u2013 Technique for measuring Vio<\/p><\/div>\n<p>The output voltage resulting from a zero input voltage is known as the <em>output dc offset voltage.<\/em> The input offset voltage is obtained by dividing this quantity by the open-loop gain of the op-amp.<\/p>\n<p>The effects of input offset voltage can be incorporated into the op-amp model as shown in Figure 17.<\/p>\n<p>In addition to including input offset voltage, the ideal op-amp model has been further modified with the addition of four resistances. <em>R<sub>o<\/sub><\/em> is the <em>output resistance<\/em>. The <em>input resistance <\/em>of the op-amp, <em>R<sub>i<\/sub><\/em>, is measured between the inverting and non-inverting terminals. The model also contains a resistor connecting each of the two inputs to ground.<\/p>\n<p>These are the <em>common-mode resistances<\/em>, and each is equal to 2<em>R<sub>cm<\/sub><\/em>. If the inputs are connected together as in Figure 16, these two resistors are in parallel, and the combined Thevenin resistance to ground is <em>R<sub>cm<\/sub><\/em>. If the op-amp is ideal, <em>R<sub>i<\/sub><\/em> and <em>R<sub>cm<\/sub><\/em> approach infinity (i.e., open circuit) and <em>R<sub>o<\/sub><\/em> is zero (i.e., short circuit).<\/p>\n<div id=\"attachment_1250\" style=\"width: 347px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1250\" class=\"wp-image-1250 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-17.png\" alt=\"\" width=\"337\" height=\"155\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-17.png 337w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-17-300x138.png 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><p id=\"caption-attachment-1250\" class=\"wp-caption-text\">Figure 17 \u2013 Input offset voltage<\/p><\/div>\n<p>The external configuration shown in Figure 18(a) can be used to negate the effects of offset voltage. A variable voltage is applied to the inverting input terminal. Proper choice of this voltage cancels the input offset. Similarly, Figure 18(b) illustrates this balancing circuit applied to the non-inverting input.<\/p>\n<div id=\"attachment_1253\" style=\"width: 519px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1253\" class=\"wp-image-1253 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-18.png\" alt=\"practical op-amps, op-amps\" width=\"509\" height=\"227\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-18.png 509w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-18-300x134.png 300w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><p id=\"caption-attachment-1253\" class=\"wp-caption-text\">Figure 18 &#8211; Offset voltage balancing<\/p><\/div>\n<p><em><strong><u>APPLICATION<\/u><\/strong><\/em><\/p>\n<div>\n<p>You can test the Input Offset Voltage Balancing of the 18 (a) circuit by simulation online with the TINACloud Circuit Simulator by clicking the link below.<\/p>\n<div id=\"attachment_3639\" style=\"width: 1137px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3639\" class=\"wp-image-3639 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationA.png\" alt=\"Input Offset Voltage Balancing Circuit Simulation (a) with TINACloud \" width=\"1127\" height=\"501\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationA.png 1127w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationA-300x133.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationA-768x341.png 768w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationA-1024x455.png 1024w\" sizes=\"auto, (max-width: 1127px) 100vw, 1127px\" \/><p id=\"caption-attachment-3639\" class=\"wp-caption-text\">Input Offset Voltage Balancing Circuit Simulation (a) with TINACloud<\/p><\/div>\n<p><a href=\"https:\/\/www.tinacloud.com\/tinademo\/tina.php?c=5b3df99866a30:89749&amp;amp;act;act=&amp;amp;noad&amp;amp;inframe=https%3A%2F%2Fwww.tina.com\" target=\"_blank\" rel=\"noopener\"><em><strong><span style=\"color: #466ce0;\"><em><strong>Input Offset Voltage Balancing Circuit Simulation (a) with TINACloud <\/strong><\/em><\/span><\/strong><\/em><\/a><\/p>\n<p><em><strong><u>APPLICATION<\/u><\/strong><\/em><\/p>\n<p>You can test the Input Offset Balancing of the 18 (b) circuit by simulation online with the TINACloud Circuit Simulator by clicking the link below:<\/p>\n<div id=\"attachment_3641\" style=\"width: 1137px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3641\" class=\"wp-image-3641 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationB.png\" alt=\"Input Offset Voltage Balancing Circuit Simulation (b) with TINACloud \" width=\"1127\" height=\"531\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationB.png 1127w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationB-300x141.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationB-768x362.png 768w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputOffsetVoltageBalancingSimulationB-1024x482.png 1024w\" sizes=\"auto, (max-width: 1127px) 100vw, 1127px\" \/><p id=\"caption-attachment-3641\" class=\"wp-caption-text\">Input Offset Voltage Balancing Circuit Simulation (b) with TINACloud<\/p><\/div>\n<p><a href=\"https:\/\/www.tinacloud.com\/tinademo\/tina.php?c=5b433b739ce2f:548371&amp;amp;act;act=&amp;amp;noad&amp;amp;inframe=https%3A%2F%2Fwww.tina.com\" target=\"_blank\" rel=\"noopener\"><em><strong><span style=\"color: #466ce0;\"><em><strong>Input Offset Balancing Circuit Simulation (b) with TINACloud <\/strong><\/em><\/span><\/strong><\/em><\/a><\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.4\u00a0<strong>Input Bias Current (I<sub>Bias<\/sub>)<\/strong><\/span><\/b><\/span><\/em><\/h6>\n<p>Although ideal op-amp inputs draw no current, actual op-amps allow some bias current to enter each input terminal. <em>I<sub>Bias<\/sub><\/em> is the <em>dc<\/em> current into the input transistor, and a typical value is 2 \u03bcA. When the source impedance is low, <em>I<sub>Bias<\/sub><\/em> has little effect, since it causes a relatively small change in input voltage. However, with high-impedance driving circuits, a small current can lead to a large voltage.<\/p>\n<p>The bias current can be modeled as two current sinks, as shown in Figure 19.<\/p>\n<div id=\"attachment_1325\" style=\"width: 361px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1325\" class=\"wp-image-1325 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-19M.png\" alt=\"op-amps, operational amplifiers\" width=\"351\" height=\"189\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-19M.png 351w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-19M-300x162.png 300w\" sizes=\"auto, (max-width: 351px) 100vw, 351px\" \/><p id=\"caption-attachment-1325\" class=\"wp-caption-text\">Figure 19 \u2013 Offset voltage balancing<\/p><\/div>\n<p>The values of these sinks are independent of the source impedance. The <em>bias current<\/em> is defined as the average value of the two current sinks. Thus<\/p>\n<div id=\"attachment_1257\" style=\"width: 119px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1257\" class=\"wp-image-1257 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-40.png\" alt=\"\" width=\"109\" height=\"48\" \/><p id=\"caption-attachment-1257\" class=\"wp-caption-text\">(40)<\/p><\/div>\n<p>The difference between the two sink values is known as the <em>input offset current<\/em>, <em>I<sub>io<\/sub><\/em>, and is given by<\/p>\n<div id=\"attachment_1258\" style=\"width: 107px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1258\" class=\"wp-image-1258 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-41.png\" alt=\"\" width=\"97\" height=\"27\" \/><p id=\"caption-attachment-1258\" class=\"wp-caption-text\">(41)<\/p><\/div>\n<p>Both the input-bias current and the input offset current are temperature dependent. The <em>input bias current temperature coefficient<\/em> is defined as the ratio of change in bias current to change in temperature. A typical value is 10 nA\/<sup>o<\/sup>C. The <em>input offset current temperature coefficient<\/em> is defined as the ratio of the change in magnitude of the offset current to the change in temperature. A typical value is -2nA\/<sup>o<\/sup>C.<\/p>\n<div id=\"attachment_1261\" style=\"width: 357px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1261\" class=\"wp-image-1261 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-20.png\" alt=\"op-amp, operational amplifier\" width=\"347\" height=\"182\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-20.png 347w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-20-300x157.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><p id=\"caption-attachment-1261\" class=\"wp-caption-text\">Figure 20 \u2013 Input bias current model<\/p><\/div>\n<p style=\"text-align: left;\">The input bias currents are incorporated into the op-amp model of Figure 20, where we assume that the input offset current is negligible.<\/p>\n<p>That is,<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1263\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-42-1.png\" alt=\"\" width=\"97\" height=\"27\" \/><\/p>\n<div id=\"attachment_1269\" style=\"width: 214px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1269\" class=\"wp-image-1269 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21A.png\" alt=\"op-amp, operational amplifier\" width=\"204\" height=\"160\" \/><p id=\"caption-attachment-1269\" class=\"wp-caption-text\">Figure 21(a) \u2013 The circuit<\/p><\/div>\n<p>We analyze this model in order to find the output voltage caused by the input bias currents.<\/p>\n<p>Figure 21(a) shows an op-amp circuit where the inverting and non-inverting inputs are connected to ground through resistances.<\/p>\n<p>The circuit is replaced by its equivalent in Figure 21(b), where we have neglected <em>V<sub>io<\/sub><\/em>. We further simplify the circuit in Figure 21(c) by neglecting <em>R<sub>o<\/sub><\/em> and <em>R<sub>load<\/sub><\/em>. That is, we assume <em>R<sub>F<\/sub><\/em> &gt;&gt; <em>R<sub>o<\/sub><\/em> and <em>R<sub>load<\/sub><\/em> &gt;&gt; <em>R<sub>o<\/sub><\/em>. Output loading requirements usually ensure that these inequalities are met.<\/p>\n<p>The circuit is further simplified in Figure 21(d) where the series combination of the dependent voltage source and resistor is replaced by a parallel combination of a dependent current source and resistor.<\/p>\n<p>Finally, we combine resistances and change both current sources back to voltage sources to obtain the simplified equivalent of Figure 21(e).<\/p>\n<div id=\"attachment_1267\" style=\"width: 310px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1267\" class=\"wp-image-1267 size-medium\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21BC-300x151.png\" alt=\"op-amp, operational amplifier\" width=\"300\" height=\"151\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21BC-300x151.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21BC.png 557w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><p id=\"caption-attachment-1267\" class=\"wp-caption-text\">Figure 21(b) and (c) \u2013 Input bias effects<\/p><\/div>\n<p>We use a loop equation to find the output voltage.<\/p>\n<div id=\"attachment_1271\" style=\"width: 355px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1271\" class=\"wp-image-1271 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-43.png\" alt=\"\" width=\"345\" height=\"52\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-43.png 345w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-43-300x45.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><p id=\"caption-attachment-1271\" class=\"wp-caption-text\">(43)<\/p><\/div>\n<p>where<\/p>\n<div id=\"attachment_1273\" style=\"width: 107px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1273\" class=\"wp-image-1273 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-44.png\" alt=\"\" width=\"97\" height=\"178\" \/><p id=\"caption-attachment-1273\" class=\"wp-caption-text\">(44)<\/p><\/div>\n<p>The common-mode resistance, <em>R<sub>cm<\/sub><\/em>, is in the range of several hundred megohms for most op-amps. Therefore<\/p>\n<div id=\"attachment_1275\" style=\"width: 107px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1275\" class=\"wp-image-1275 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-45.png\" alt=\"\" width=\"97\" height=\"41\" \/><p id=\"caption-attachment-1275\" class=\"wp-caption-text\">(45)<\/p><\/div>\n<p>If we further assume that <em>G<sub>o<\/sub><\/em> is large, Equation (43) becomes Equation .<\/p>\n<div id=\"attachment_1278\" style=\"width: 198px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1278\" class=\"wp-image-1278 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-46.png\" alt=\"\" width=\"188\" height=\"45\" \/><p id=\"caption-attachment-1278\" class=\"wp-caption-text\">(46)<\/p><\/div>\n<div id=\"attachment_1279\" style=\"width: 515px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1279\" class=\"wp-image-1279 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21DE.png\" alt=\"op-amp, operational amplifier\" width=\"505\" height=\"234\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21DE.png 505w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-21DE-300x139.png 300w\" sizes=\"auto, (max-width: 505px) 100vw, 505px\" \/><p id=\"caption-attachment-1279\" class=\"wp-caption-text\">Figure 21(d) and (e) \u2013 Input bias effects<\/p><\/div>\n<p>Note that if the value of <em>R<sub>1<\/sub><\/em> is selected to be equal to , then the output voltage is zero. We conclude from this analysis that the <em>dc<\/em> resistance from <em>V<sub>+<\/sub><\/em> to ground should equal the <em>dc<\/em> resistance from <em>V<sub>&#8211;<\/sub><\/em> to ground. We use this <em>bias balance <\/em>constraint many times in our designs. It is important that both the inverting and non-inverting terminals have a <em>dc<\/em> path to ground to reduce the effects of input bias current.<\/p>\n<div id=\"attachment_3183\" style=\"width: 443px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-figure22\/#main\" rel=\"attachment wp-att-3183\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3183\" class=\"wp-image-3183 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/practical-op-amp9-Figure22.png\" alt=\"Input Bias Current, practical op-amp, operational amplifiers\" width=\"433\" height=\"185\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/practical-op-amp9-Figure22.png 433w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/practical-op-amp9-Figure22-300x128.png 300w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><\/a><p id=\"caption-attachment-3183\" class=\"wp-caption-text\">Figure 22 &#8211; Configurations for Example 1<\/p><\/div>\n<h6><u>Example 1<\/u><\/h6>\n<p>Find the output voltage for the configurations of Figure 22 where <em>I<sub>B<\/sub><\/em> = 80 nA = 8 \u00a010<sup>-8<\/sup> A.<br \/>\n<em>Solution:<\/em> We use the simplified form of Equation (46) to find the output voltages for the circuit of Figure 22(a).<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example5a\/#main\" rel=\"attachment wp-att-3186\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3186 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5a.png\" alt=\"\" width=\"313\" height=\"47\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5a.png 313w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5a-300x45.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/a><\/p>\n<p>For the circuit of Figure 22(b), we obtain<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example5b\/#main\" rel=\"attachment wp-att-3188\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3188 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5b.png\" alt=\"\" width=\"318\" height=\"50\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5b.png 318w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example5b-300x47.png 300w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/><\/a><\/p>\n<p><em><strong><u>APPLICATION<\/u><\/strong><\/em><\/p>\n<div>\n<p>Also, you can carry out these calculations with TINACloud circuit simulator, using its Interpreter tool by clicking the link below.<\/p>\n<div id=\"attachment_3624\" style=\"width: 1154px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3624\" class=\"wp-image-3624 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputBiasModelingCircuitResources.png\" alt=\"Input Bias Current Modeling Circuit Simulation\" width=\"1144\" height=\"532\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputBiasModelingCircuitResources.png 1144w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputBiasModelingCircuitResources-300x140.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputBiasModelingCircuitResources-768x357.png 768w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/InputBiasModelingCircuitResources-1024x476.png 1024w\" sizes=\"auto, (max-width: 1144px) 100vw, 1144px\" \/><p id=\"caption-attachment-3624\" class=\"wp-caption-text\">Input Bias Current Modeling Circuit Simulation with TINACloud<\/p><\/div>\n<p><a href=\"https:\/\/www.tinacloud.com\/tinademo\/tina.php?c=5b35f73c1abbd:47471&amp;amp;act;act=&amp;amp;noad&amp;amp;inframe=https%3A%2F%2Fwww.tina.com\" target=\"_blank\" rel=\"noopener\"><em><strong><span style=\"color: #466ce0;\"><em><strong>Input Bias Current Modeling Circuit Simulation with TINACloud <\/strong><\/em><\/span><\/strong><\/em><\/a><\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.5\u00a0<strong>Common-Mode Rejection<\/strong><\/span><\/b><\/span><\/em><\/h6>\n<p>The op-amp is normally used to amplify the difference between two input voltages. It therefore operates in the <em>differential mode<\/em>. A constant voltage added to each of these two inputs\u00a0should not affect the difference and should therefore not be transferred to the output. In the practical case, this constant, or average value of the inputs <em>does <\/em>affect the output voltage. If we consider only the equal parts of the two inputs, we are considering what is known as the <em>common mode<\/em>.<\/p>\n<div id=\"attachment_1287\" style=\"width: 208px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1287\" class=\"wp-image-1287 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-23.png\" alt=\"op-amp, operational amplifier\" width=\"198\" height=\"113\" \/><p id=\"caption-attachment-1287\" class=\"wp-caption-text\">Figure 23 \u2013 Common mode<\/p><\/div>\n<p>Let us assume that the two input terminals of an actual op-amp are connected together and then to a common source voltage. This is illustrated in Figure 23. The output voltage would be zero in the ideal case. In the practical case, this output is non-zero. The ratio of the non-zero output voltage to the applied input voltage is the <em>common-mode voltage gain<\/em>, <em>G<sub>cm<\/sub><\/em>. The <em>common-mode rejection ratio<\/em> (CMRR) is defined as the ratio of the <em>dc<\/em> open-loop gain, <em>G<sub>o<\/sub><\/em>, to the common mode gain. Thus,<\/p>\n<div id=\"attachment_1289\" style=\"width: 204px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1289\" class=\"wp-image-1289 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-47.png\" alt=\"\" width=\"194\" height=\"46\" \/><p id=\"caption-attachment-1289\" class=\"wp-caption-text\">(47)<\/p><\/div>\n<p>Typical values of the CMRR range from 80 to 100 dB. It is desirable to have the CMRR as high as possible.<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.6\u00a0<strong>Power Supply Rejection Ratio<\/strong><\/span><\/b><\/span><\/em><\/h6>\n<p>Power supply rejection ratio is a measure of the ability of the op-amp to ignore changes in the power supply voltage. If the output stage of a system draws a variable amount of current, the supply voltage could vary. This load-induced change in supply voltage could then cause changes in the operation of other amplifiers sharing the same supply. This is known as <em>cross-talk<\/em>, and it can lead to instability.<\/p>\n<p>The <em>power supply rejection ratio<\/em> (<em>PSRR<\/em>) is the ratio of the change in <em>v<sub>out<\/sub><\/em> to the total change in power supply voltage. For example, if the positive and negative supplies vary from \u00b15 V to \u00b15.5 V, the total change is 11 &#8211; 10 = 1 V. The PSRR is usually specified in microvolts per volt or sometimes in decibels. Typical op-amps have a PSRR of about 30 \u03bcV\/V.<\/p>\n<p>To decrease changes in supply voltage, the power supply for each group of op-amps should be <em>decoupled <\/em>(i.e., isolated) from those of other groups. This confines the interaction to a single group of op-amps. In practice, each printed circuit card should have the supply lines bypassed to ground via a 0.1-\u03bcF ceramic or 1-\u03bcF tantalum capacitor. This ensures that load variations will not feed significantly through the supply to other cards.<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">5.7\u00a0<strong>Output Resistance<\/strong><\/span><\/b><\/span><\/em><\/h6>\n<p>As a first step in determining the output resistance, <em>R<sub>out<\/sub><\/em>, we find the Thevenin equivalent for the portion of the op-amp circuit shown in the box enclosed in dashed lines in Figure 24. Note that we are ignoring the offset current and voltage in this analysis.<\/p>\n<div id=\"attachment_1294\" style=\"width: 279px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1294\" class=\"wp-image-1294 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-24.png\" alt=\"\" width=\"269\" height=\"138\" \/><p id=\"caption-attachment-1294\" class=\"wp-caption-text\">(24)<\/p><\/div>\n<p>Since the circuit contains no independent sources, the Thevenin equivalent voltage is zero, so the circuit is equivalent to a single resistor. The value of the resistor cannot be found using resistor combinations. To find the equivalent resistance, assume that a voltage source, v, is\u00a0 applied to the output leads. We then calculate the resulting current, <em>i<\/em>, and take the ratio <em>v<\/em>\/<em>i<\/em>. This yields the Thevenin resistance.<\/p>\n<div id=\"attachment_1317\" style=\"width: 465px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1317\" class=\"wp-image-1317 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25A.png\" alt=\"op-amp, operational amplifier\" width=\"455\" height=\"218\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25A.png 455w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25A-300x144.png 300w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><p id=\"caption-attachment-1317\" class=\"wp-caption-text\">Figure 25 (part a) &#8211; Thevenin equivalent circuits<\/p><\/div>\n<div id=\"attachment_1299\" style=\"width: 387px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1299\" class=\"wp-image-1299 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25BM.png\" alt=\"op-amp, operational amplifier\" width=\"377\" height=\"218\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25BM.png 377w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25BM-300x173.png 300w\" sizes=\"auto, (max-width: 377px) 100vw, 377px\" \/><p id=\"caption-attachment-1299\" class=\"wp-caption-text\">Figure 25 (part b)<\/p><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left;\">Figure 25(a) illustrates the applied voltage source. The circuit is simplified to that shown in Figure 25(b).<\/p>\n<p>The circuit can be further reduced to that shown in Figure 25(c), where we define two new resistances as follows:<\/p>\n<div id=\"attachment_1301\" style=\"width: 114px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1301\" class=\"wp-image-1301 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-48.png\" alt=\"\" width=\"104\" height=\"51\" \/><p id=\"caption-attachment-1301\" class=\"wp-caption-text\">(48)<\/p><\/div>\n<p>We make the assumption that<em> R&#8217;<sub>A<\/sub> <\/em>&lt;&lt; (<em>R&#8217;<sub>1<\/sub><\/em> + <em>R<sub>i<\/sub><\/em>) and <em>R<sub>i<\/sub><\/em> &gt;&gt; <em>R&#8217;<sub>1<\/sub><\/em>. The simplified circuit of Figure 25(d) results.<\/p>\n<p>The input differential voltage, <em>v<sub>d<\/sub><\/em>, is found from this simplified circuit using a voltage divider ratio.<\/p>\n<div id=\"attachment_1303\" style=\"width: 114px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1303\" class=\"wp-image-1303 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-49.png\" alt=\"\" width=\"104\" height=\"51\" \/><p id=\"caption-attachment-1303\" class=\"wp-caption-text\">(49)<\/p><\/div>\n<p>To find the output resistance, we begin by writing the output loop equation.<\/p>\n<div id=\"attachment_1305\" style=\"width: 211px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1305\" class=\"wp-image-1305 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-50.png\" alt=\"\" width=\"201\" height=\"51\" \/><p id=\"caption-attachment-1305\" class=\"wp-caption-text\">(50)<\/p><\/div>\n<div id=\"attachment_1307\" style=\"width: 547px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1307\" class=\"wp-image-1307 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25CD.png\" alt=\"op-amp, operational amplifier\" width=\"537\" height=\"184\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25CD.png 537w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-ampFigure9-25CD-300x103.png 300w\" sizes=\"auto, (max-width: 537px) 100vw, 537px\" \/><p id=\"caption-attachment-1307\" class=\"wp-caption-text\">Figure 25 (parts c and d) &#8211; Reduced Thevenin equivalent circuits<\/p><\/div>\n<p>The output resistance is then given by Equation (51).<\/p>\n<div id=\"attachment_1311\" style=\"width: 162px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1311\" class=\"wp-image-1311 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-51.png\" alt=\"\" width=\"152\" height=\"62\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-51.png 152w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-51-150x62.png 150w\" sizes=\"auto, (max-width: 152px) 100vw, 152px\" \/><p id=\"caption-attachment-1311\" class=\"wp-caption-text\">(51)<\/p><\/div>\n<p>In most cases, <em>R<sub>cm<\/sub><\/em> is so large that <em>R&#8217;<sub>A<\/sub><\/em>\u00bb<em>R<sub>A<\/sub><\/em> and <em>R<sub>1<\/sub>&#8216;<\/em>\u00bb<em>R<sub>1<\/sub><\/em>. Equation (51) can be simplified using the zero-frequency voltage gain, <em>G<sub>o<\/sub><\/em>. The result is Equation (52).<\/p>\n<div id=\"attachment_1314\" style=\"width: 126px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1314\" class=\"wp-image-1314 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/04\/Practical-op-amp9-52.png\" alt=\"\" width=\"116\" height=\"51\" \/><p id=\"caption-attachment-1314\" class=\"wp-caption-text\">(52)<\/p><\/div>\n<p><em><strong><u>APPLICATION<\/u><\/strong><\/em><\/p>\n<div>\n<p>You can calculate the Output Impedance of the circuit 25 (a)\u00a0 with circuit simulation using the TINACloud Circuit Simulator by clicking the link below.<\/p>\n<div id=\"attachment_3652\" style=\"width: 1137px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3652\" class=\"wp-image-3652 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/OutputImpedanceofanopams.png\" alt=\"Output Impedance of an Opamp Circuit Simulation with TINACloud\" width=\"1127\" height=\"512\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/OutputImpedanceofanopams.png 1127w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/OutputImpedanceofanopams-300x136.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/OutputImpedanceofanopams-768x349.png 768w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/07\/OutputImpedanceofanopams-1024x465.png 1024w\" sizes=\"auto, (max-width: 1127px) 100vw, 1127px\" \/><p id=\"caption-attachment-3652\" class=\"wp-caption-text\">Output Impedance of an Opamp Circuit Simulation with TINACloud<\/p><\/div>\n<p><a href=\"https:\/\/www.tinacloud.com\/tinademo\/tina.php?c=5b4736487b081:467932&amp;amp;act;act=&amp;amp;noad&amp;amp;inframe=https%3A%2F%2Fwww.tina.com\" target=\"_blank\" rel=\"noopener\"><em><strong><span style=\"color: #466ce0;\"><em><strong>Output Impedance of an Opamp Circuit Simulation with TINACloud <\/strong><\/em><\/span><\/strong><\/em><\/a><\/p>\n<p>&nbsp;<\/p>\n<h6><u>Example 2<\/u><\/h6>\n<p>Find the output impedance of a unity-gain buffer as shown in Figure 26.<\/p>\n<div id=\"attachment_3191\" style=\"width: 330px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-figure26\/#main\" rel=\"attachment wp-att-3191\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3191\" class=\"wp-image-3191 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure26.png\" alt=\" practical op-amp, operational amplifiers\" width=\"320\" height=\"89\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure26.png 320w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Figure26-300x83.png 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><p id=\"caption-attachment-3191\" class=\"wp-caption-text\">Figure 26 \u2013 Unity gain buffer<\/p><\/div>\n<p>&nbsp;<\/p>\n<p><em>Solution:<\/em>\u00a0 When the circuit of Figure 26 is compared to the feedback circuit of Figure 24, we find that<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example6a\/#main\" rel=\"attachment wp-att-3192\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3192 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6a.png\" alt=\"\" width=\"72\" height=\"29\" \/><\/a><\/p>\n<p>Therefore,<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example6b\/#main\" rel=\"attachment wp-att-3193\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3193 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6b.png\" alt=\"\" width=\"156\" height=\"32\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6b.png 156w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6b-150x32.png 150w\" sizes=\"auto, (max-width: 156px) 100vw, 156px\" \/><\/a><\/p>\n<p>Equation (51) cannot be used, since we are not sure that the inequalities leading to the simplification of Figure 25(c) apply in this case. That is, the simplification requires that<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example6-d\/#main\" rel=\"attachment wp-att-3195\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3195 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6-d.png\" alt=\"\" width=\"154\" height=\"29\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6-d.png 154w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6-d-150x29.png 150w\" sizes=\"auto, (max-width: 154px) 100vw, 154px\" \/><\/a><\/p>\n<p>Without this simplification, the circuit takes the form shown in Figure 27.<\/p>\n<div id=\"attachment_3196\" style=\"width: 292px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-figure27\/#main\" rel=\"attachment wp-att-3196\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3196\" class=\"wp-image-3196 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/practical-op-amp9-Figure27.png\" alt=\"Unity gain buffer, practical op-amps, operational amplifiers,\" width=\"282\" height=\"168\" \/><\/a><p id=\"caption-attachment-3196\" class=\"wp-caption-text\">Figure 27 \u2013 Equivalent circuit for Unity gain buffer<\/p><\/div>\n<p>This circuit is analyzed to find the following relations:<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example6-e\/#main\" rel=\"attachment wp-att-3198\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3198 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6-e.png\" alt=\"\" width=\"237\" height=\"120\" \/><\/a><\/p>\n<p>In the first of these equations, we have assumed that <em>R<sub>o<\/sub><\/em>&lt;&lt;(<em>R&#8217;<sub>1<\/sub><\/em>+<em>R<sub>i<\/sub><\/em>)&lt;&lt;2<em>R<sub>cm<\/sub><\/em>. The output resistance is then given by<\/p>\n<p><a href=\"https:\/\/www.tina.com\/resources\/home\/practical-operational-amplifiers\/5-practical-op-amps\/practical-op-amp9-example6-f\/#main\" rel=\"attachment wp-att-3200\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3200 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Practical-op-amp9-Example6-f.png\" alt=\"\" width=\"202\" height=\"48\" \/><\/a><\/p>\n<p>Where we again use the zero-frequency voltage gain, <em>G<sub>o<\/sub><\/em>.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/4-manufacturers-specifications\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 4. Manufacturers&#8217; specifications<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/practical-operational-amplifiers\/6-computer-simulation-of-op-amp-circuits\/\">NEXT- 6. Computer simulation op-amp circuits<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>CURRENT &#8211; 5. Practical Op-amps PREVIOUS- 4. Manufacturers&#8217; specifications NEXT- 6. Computer simulation op-amp circuits Practical Op-amps Practical Op-amps approximate their ideal counterparts but differ in some important respects. It is important for the circuit designer to understand the differences between actual op-amps and ideal op-amps, since these differences can adversely affect circuit performance. 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