{"id":383,"date":"2018-04-06T10:26:21","date_gmt":"2018-04-06T10:26:21","guid":{"rendered":"https:\/\/www.tina.com\/resources\/?page_id=383"},"modified":"2018-06-22T07:28:50","modified_gmt":"2018-06-22T07:28:50","slug":"1-ideal-op-amps","status":"publish","type":"page","link":"https:\/\/www.tina.com\/resources\/home\/ideal-operational-amplifiers-2\/1-ideal-op-amps\/","title":{"rendered":"1. Ideal 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; 1. Ideal op-amps<\/div>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/ideal-operational-amplifiers\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- Ideal Operational Amplifiers Introduction<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/2-the-inverting-amplifier\/\">NEXT-2. The 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<p align=\"justify\"><strong><em><span style=\"font-size: 22px;\">Ideal op-amps<\/span><\/em><\/strong><\/p>\n<p>This section uses a <i>systems<\/i> approach to present the fundamentals of Ideal Operational Amplifiers. As such, we consider the op-amp as a block with input and output terminals. We are not currently concerned with the individual electronic devices within the op-amp.<\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">An op-amp is an amplifier that is often powered by both positive and negative supply voltages. This allows the output voltage to swing both above and below ground potential. The op-amp finds wide application in many linear electronic systems.<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">The name <i>operational amplifier<\/i> is derived from one of the original uses of op-amp circuits; to perform mathematical <i>operations<\/i> in analog computers. This traditional application is discussed later in this chapter. Early op-amps used a single inverting input. A positive voltage change at the input caused a negative change at the output.<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">Hence, to understand the operation of the op-amp, it is necessary to first become familiar with the concept of controlled (dependent) sources since they form the basis of the op-amp model.<\/span><\/span><\/p>\n<h6><span style=\"color: #000000;\"><em><span style=\"font-family: Bodoni MT,serif;\"><b>1.1 Dependent Sources<\/b><\/span><\/em><\/span><\/h6>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">Dependent (or controlled) sources produce a voltage or current whose value is determined by a voltage or current existing in another location in the circuit. In contrast, passive devices produce a voltage or current whose value is determined by a voltage or current existing at the same location in the circuit. Both independent and dependent voltage and current sources are active elements. That is, they are capable of delivering power to some external device. Passive elements are not capable of generating power, although they can store energy for delivery at a later time, as is the case with capacitors and inductors.<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">The figure below illustrates an equivalent circuit configuration of an amplifying device often used in circuit analysis. The rightmost<a href=\"https:\/\/www.tina.com\/resources\/home\/ideal-operational-amplifiers-2\/1-ideal-op-amps\/idealopamps-20kw\/#main\" rel=\"attachment wp-att-3383\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-3383 alignnone\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/06\/Idealopamps-20kW.png\" alt=\"\" width=\"42\" height=\"19\" \/><\/a>resistor is the load. We will find the voltage and current gain of this system. Voltage gain, Av is defined as the ratio of output voltage to input voltage. Similarly, current gain, Ai is the ratio of output current to input current.<\/span><\/span><\/p>\n<div id=\"attachment_10\" style=\"width: 470px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-10\" class=\"wp-image-10 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/Equivalent-circuit-of-a-solid-state-amplifying-device.png\" alt=\"Ideal op-amps\" width=\"460\" height=\"137\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/Equivalent-circuit-of-a-solid-state-amplifying-device.png 460w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/Equivalent-circuit-of-a-solid-state-amplifying-device-300x89.png 300w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><p id=\"caption-attachment-10\" class=\"wp-caption-text\">Figure 1- Equivalent circuit of a solid-state amplifying device<\/p><\/div>\n<h6 align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span lang=\"en-US\">The input current is:<\/span><\/span><\/h6>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-12 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/InputCurrent.png\" alt=\"\" width=\"273\" height=\"59\" \/><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">The current in the second resistor, <\/span><span lang=\"en-US\"><i>i<\/i><\/span><sub><span lang=\"en-US\"><i>1<\/i><\/span><\/sub><span lang=\"en-US\">, is found directly from Ohm&#8217;s law:<\/span><\/span><\/span><\/p>\n<div id=\"attachment_14\" style=\"width: 179px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-14\" class=\"wp-image-14 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/CurrentinthesecondResistor.png\" alt=\"\" width=\"169\" height=\"59\" \/><p id=\"caption-attachment-14\" class=\"wp-caption-text\">(2)<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">The output voltage is then given by:<\/span><\/span><\/span><\/p>\n<div id=\"attachment_17\" style=\"width: 275px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-17\" class=\"wp-image-17 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OutputVoltage.png\" alt=\"\" width=\"265\" height=\"28\" \/><p id=\"caption-attachment-17\" class=\"wp-caption-text\">(3)<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">In Equation (3), <\/span><\/span><span style=\"color: #000000; font-family: Times New Roman;\">\u2016<\/span><span style=\"color: #000000;\"><span style=\"margin: 0px; font-family: 'Bodoni MT',serif; font-size: 14pt;\"><span style=\"font-family: Bodoni MT;\"> indicates a parallel combination of resistors. The output current is found directly from Ohm&#8217;s law.<\/span><\/span><\/span><\/p>\n<div id=\"attachment_315\" style=\"width: 206px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-315\" class=\"wp-image-315 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/Opamp2-4.png\" alt=\"\" width=\"196\" height=\"42\" \/><p id=\"caption-attachment-315\" class=\"wp-caption-text\">(4)<\/p><\/div>\n<p align=\"justify\"><span style=\"margin: 0px; font-family: 'Bodoni MT',serif; font-size: 14pt;\"><span style=\"color: #000000;\">The voltage and current gains are then found by forming the ratios:<\/span><\/span><\/p>\n<div id=\"attachment_20\" style=\"width: 90px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-20\" class=\"wp-image-20 size-full\" src=\"http:\/\/www.designsoftware.com\/wordpress_rc\/wp-content\/uploads\/2018\/03\/VoltageandCurrentGains.png\" alt=\"\" width=\"80\" height=\"45\" \/><p id=\"caption-attachment-20\" class=\"wp-caption-text\">(5)<\/p><\/div>\n<div id=\"attachment_21\" style=\"width: 90px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-21\" class=\"wp-image-21 size-full\" src=\"http:\/\/www.designsoftware.com\/wordpress_rc\/wp-content\/uploads\/2018\/03\/VoltageandCurrentGains2.png\" alt=\"\" width=\"80\" height=\"45\" \/><p id=\"caption-attachment-21\" class=\"wp-caption-text\">(6)<\/p><\/div>\n<h6><em><span style=\"margin: 0px; font-family: 'Bodoni MT',serif;\"><span style=\"color: #000000;\">\u00a0<strong>1.2\u00a0<\/strong><\/span><\/span><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">Operational Amplifier Equivalent Circuit<\/span><\/b><\/span><\/em><\/h6>\n<div id=\"attachment_53\" style=\"width: 522px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-53\" class=\"wp-image-53 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit.png\" alt=\"Ideal op-amps\" width=\"512\" height=\"292\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit.png 512w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-300x171.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><p id=\"caption-attachment-53\" class=\"wp-caption-text\">Figure 2- Operational amplifier and equivalent circuit<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: 'Bodoni MT', serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">F<\/span><span lang=\"en-US\">igure 2 <\/span><span lang=\"en-US\">(a) <\/span><span lang=\"en-US\">presents the symbol for the operational amplifier, and Figure 2 (b) shows its equivalent circuit. The input terminals are <\/span><span lang=\"en-US\"><i>v<\/i><\/span><sub><span lang=\"en-US\"><i>+<\/i><\/span><\/sub><span lang=\"en-US\"> and <\/span><span lang=\"en-US\"><i>v<\/i><\/span><sub><span lang=\"en-US\"><i>&#8211;<\/i><\/span><\/sub><span lang=\"en-US\"><i>.<\/i><\/span><span lang=\"en-US\"> The output terminal is <\/span><span lang=\"en-US\"><i>v<\/i><\/span><sub><span lang=\"en-US\"><i>out<\/i><\/span><\/sub><span lang=\"en-US\">. The power supply connections are at the <\/span><span lang=\"en-US\"><i>+V<\/i><\/span><span lang=\"en-US\">, <\/span><span lang=\"en-US\"><i>-V <\/i><\/span><span lang=\"en-US\">and ground terminals. The power supply connections are often\u00a0<\/span><\/span><\/span><span style=\"font-family: 'Bodoni MT', serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">omitted from schematic drawings. The value of the output voltage is bounded by <\/span><span lang=\"en-US\"><i>+V<\/i><\/span><span lang=\"en-US\"> and <\/span><span lang=\"en-US\"><i>-V<\/i><\/span><span lang=\"en-US\"> since these are the most positive and negative voltages in the circuit.<\/span><\/span><\/span><\/p>\n<p class=\"western\" align=\"justify\"><span style=\"font-family: 'Bodoni MT', serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">The model contains a dependent voltage source whose voltage depends on the input voltage difference between <\/span><span lang=\"en-US\"><i>v<\/i><\/span><sub><span lang=\"en-US\"><i>+<\/i><\/span><\/sub><span lang=\"en-US\"> and <\/span><span lang=\"en-US\"><i>v<\/i><\/span><sub><span lang=\"en-US\"><i>&#8211;<\/i><\/span><\/sub><span lang=\"en-US\">. The two input terminals are known as the <\/span><span lang=\"en-US\"><i>non-inverting <\/i><\/span><span lang=\"en-US\">and <\/span><span lang=\"en-US\"><i>inverting <\/i><\/span><span lang=\"en-US\">inputs respectively. Ideally, the output of the amplifier does not depend on the magnitudes of the two input voltages, but only on the difference between them. We define the <\/span><span lang=\"en-US\"><i>differential input voltage, v<\/i><\/span><sub><span lang=\"en-US\"><i>d<\/i><\/span><\/sub><span lang=\"en-US\">, as the difference,<\/span><\/span><\/span><\/p>\n<div id=\"attachment_60\" style=\"width: 106px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-60\" class=\"wp-image-60 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd.png\" alt=\"\" width=\"96\" height=\"26\" \/><p id=\"caption-attachment-60\" class=\"wp-caption-text\">(7)<\/p><\/div>\n<p class=\"western\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\"><span lang=\"en-US\">The output voltage is proportional to the differential input voltage, and we designate the ratio as the open-loop gain, G. Thus, the output voltage is<\/span><\/span><\/span><\/p>\n<div id=\"attachment_61\" style=\"width: 163px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-61\" class=\"wp-image-61 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output.png\" alt=\"\" width=\"153\" height=\"26\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output.png 153w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output-150x26.png 150w\" sizes=\"auto, (max-width: 153px) 100vw, 153px\" \/><p id=\"caption-attachment-61\" class=\"wp-caption-text\">(8)<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">As an example, an input of\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-63\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-Esin.png\" alt=\"\" width=\"80\" height=\"22\" \/>(<em>E<\/em> is usually a small amplitude) applied to the non-inverting input with the inverting terminal grounded, produces\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-65\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-EsinG.png\" alt=\"\" width=\"84\" height=\"25\" \/> at the output.\u00a0<\/span><\/span><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">When the same source signal is applied to the inverting input with the non-inverting terminal grounded, the output is <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-66\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-EsinG-.png\" alt=\"\" width=\"84\" height=\"25\" \/>.<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">The input impedance of the op-amp is shown as a resistance in Figure 2(b).<br \/>\nThe output impedance is represented in the figure as a resistance, Ro.<\/span><\/span><\/p>\n<h6 align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\">An ideal operational amplifier is characterized as follows:<\/span><\/h6>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-166\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-IdealOpamp3.png\" alt=\"\" width=\"263\" height=\"65\" \/><\/p>\n<p><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">These are usually good approximations to the parameters of real op-amps. Typical parameters of real op-amps are:<\/span><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-163 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-RealOpampModified.png\" alt=\"\" width=\"438\" height=\"65\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-RealOpampModified.png 438w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-RealOpampModified-300x45.png 300w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Using ideal op-amps to approximate real op-amps is therefore a valuable simplification for circuit analysis.<br \/>\nLet us explore the implication of the open-loop gain being infinite. If we rewrite Equation (8) <\/span><\/span><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-61 size-thumbnail\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output-150x26.png\" alt=\"\" width=\"150\" height=\"26\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output-150x26.png 150w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OpampandEquivalentcircuit-vd-output.png 153w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/> as follows:\u00a0<\/span><\/span><\/p>\n<div id=\"attachment_87\" style=\"width: 98px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-87\" class=\"wp-image-87 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-rewriteEQ.png\" alt=\"\" width=\"88\" height=\"42\" \/><p id=\"caption-attachment-87\" class=\"wp-caption-text\">(9)<\/p><\/div>\n<p><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">and let <em>G<\/em> approach infinity, we see that<\/span><\/span><\/p>\n<div id=\"attachment_89\" style=\"width: 81px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-89\" class=\"wp-image-89 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuit-EQ-2-10.png\" alt=\"\" width=\"71\" height=\"23\" \/><p id=\"caption-attachment-89\" class=\"wp-caption-text\">(10)<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Equation (10) results by observing that the output voltage cannot be infinite. The value of the output voltage is bounded by the positive and negative power supply values. Equation (10) indicates that the voltages at the two terminals are the same: <\/span><\/span><\/p>\n<div id=\"attachment_90\" style=\"width: 64px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-90\" class=\"wp-image-90 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMPandequivalantCircuitEquivalentvoltages.png\" alt=\"\" width=\"54\" height=\"25\" \/><p id=\"caption-attachment-90\" class=\"wp-caption-text\">(11)<\/p><\/div>\n<h6 align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Therefore, the equality of Equation (11) leads us to say there is a virtual short circuit between the input terminals.<\/span><\/span><\/h6>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Since the input resistance of the ideal op-amp is infinite, the current into each input, inverting terminal and non-inverting terminal, is zero.<br \/>\nWhen real op-amps are used in a linear amplification mode, the gain is very large, and Equation (11) is a good approximation. However, several applications for real op-amps use the device in a nonlinear mode. The approximation of Equation (11) is not valid for these circuits.\u00a0<\/span><\/span><br \/>\n<span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Although practical op-amps have high voltage gain, this gain varies with frequency. For this reason, an op-amp is not normally used in the form shown in Figure 2 (a). This configuration is known as open loop because there is no feedback from output to input. We see later that, while the open-loop configuration is useful for comparator applications, the more common configuration for linear applications is the closed-loop circuit with feedback.<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">External elements are used to &#8220;feedback&#8221; a portion of the output signal to the input. If the feedback elements are placed between the output and the inverting input, the closed-loop gain is decreased since a portion of the output subtracts from the input. We will see later that feedback not only decreases the overall gain, but it also makes that gain less sensitive to the value of G. With feedback, the closed-loop gain depends more on the feedback circuit elements, and less on the basic op-amp voltage gain, G. In fact, the closed-loop gain is essentially independent of the value of G-it depends only on values of the external circuit elements.\u00a0<\/span><\/span><\/p>\n<h6 align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Figure (3) illustrates a single stage negative feedback op-amp circuit.<\/span><\/span><\/h6>\n<div id=\"attachment_96\" style=\"width: 554px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-96\" class=\"wp-image-96 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMP-InvertingOpamp.png\" alt=\"Ideal op-amps\" width=\"544\" height=\"226\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMP-InvertingOpamp.png 544w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/03\/OPAMP-InvertingOpamp-300x125.png 300w\" sizes=\"auto, (max-width: 544px) 100vw, 544px\" \/><p id=\"caption-attachment-96\" class=\"wp-caption-text\">Figure 3- The inverting op-amp<\/p><\/div>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Therefore, we will analyze this circuit in the next section. For now, note that a single resistor, <em>R<sub>F<\/sub><\/em>, is used to connect the output voltage, <em>v<sub>out<\/sub><\/em> to the inverting input, <em>v<sub>&#8211;<\/sub><\/em>. \u00a0<\/span><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Another resistor, <em>R<sub>a<\/sub><\/em> is connected from the inverting input, <em>v<sub>&#8211;<\/sub><\/em>, to the input voltage, <em>v<sub>a<\/sub><\/em>. A third resistor, <em>R<\/em> is placed between the non-inverting input and ground.<br \/>\nCircuits using op-amps, resistors and capacitors can be configured to perform many useful operations such as summing, subtracting, integrating, differentiating, filtering, comparing, and amplifying.<\/span><\/span><\/p>\n<h6><em><strong><span style=\"margin: 0px; font-family: 'Bodoni MT',serif;\"><span style=\"color: #000000;\">1.3\u00a0<\/span><\/span><\/strong><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">Analysis Method<\/span><\/b><\/span><\/em><\/h6>\n<p><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">We analyze circuits using the two important ideal op-amp properties:<\/span><\/span><\/p>\n<ul>\n<li><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">The voltage between <em>v<sub>+<\/sub><\/em> and <em>v<sub>&#8211;<\/sub><\/em> is zero, or <em>v<sub>+<\/sub> = v<sub>&#8211;<\/sub><\/em>.<\/span><\/span><\/li>\n<li><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">The current into both the <em>v<sub>+<\/sub><\/em> and <em>v<sub>&#8211;<\/sub><\/em> terminal is zero.<\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">These simple observations lead to a procedure for analyzing any ideal op-amp circuit as follows:<\/span><\/span><\/p>\n<ul>\n<li><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Write the Kirchhoff current law node equation at the non-inverting terminal, <em>v<sub>+<\/sub><\/em>.<\/span><\/span><\/li>\n<li><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\">Write the Kirchhoff current law node equation at the inverting terminal, <em>v<sub>&#8211;<\/sub><\/em>.<\/span><\/span><\/li>\n<li><span style=\"font-family: Bodoni MT, serif;\"><span style=\"font-size: large;\"> Set <em>v<sub>+<\/sub> = v<sub>&#8211;<\/sub><\/em> and solve for the desired closed-loop gains.<\/span><\/span><\/li>\n<\/ul>\n<p align=\"justify\"><span style=\"font-family: Bodoni MT,serif;\"><span style=\"font-size: large;\">When applying Kirchhoff&#8217;s laws, remember that the current into both the <em>v<sub>+<\/sub><\/em> and <em>v<sub>&#8211;<\/sub><\/em> terminal is zero.<\/span><\/span><\/p>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/ideal-operational-amplifiers\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- Ideal Operational Amplifiers Introduction<\/a><\/div>\n<div class=\"next-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/2-the-inverting-amplifier\/\">NEXT-2. The inverting amplifier <img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>CURRENT &#8211; 1. Ideal op-amps PREVIOUS- Ideal Operational Amplifiers Introduction NEXT-2. The inverting amplifier Ideal op-amps This section uses a systems approach to present the fundamentals of Ideal Operational Amplifiers. As such, we consider the op-amp as a block with input and output terminals. We are not currently concerned with the individual electronic devices within [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1357,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"yst_prominent_words":[216,247,242,223,241,172,249,248,251,228,306,244,238,250,245,240,239,246,243,32],"class_list":["post-383","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/383","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=383"}],"version-history":[{"count":93,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/383\/revisions"}],"predecessor-version":[{"id":3889,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/383\/revisions\/3889"}],"up":[{"embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1357"}],"wp:attachment":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/media?parent=383"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/yst_prominent_words?post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}