{"id":2585,"date":"2024-08-05T14:51:36","date_gmt":"2024-08-05T09:21:36","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=2585"},"modified":"2025-07-16T15:24:27","modified_gmt":"2025-07-16T09:54:27","slug":"voltage-follower","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower","title":{"rendered":"Voltage Follower &#8211; Analog Circuits"},"content":{"rendered":"<ul style=\"text-align: justify;\">\n<li>An interesting property of non-inverting op-amp occurs when R<sub>1<\/sub> = \u221e, an open circuit. The closed loop gain is independent of resistor R<sub>2<\/sub> (except when R<sub>2<\/sub> = \u221e), so we can set R<sub>2<\/sub> = 0 to create a short-circuit.<\/li>\n<li>Since, the output voltage follows the input, this op-amp circuit is called a voltage follower voltage follower.<\/li>\n<li>The voltage-follower op-amp circuit is shown in the figure. The property of high input impedance is a desirable feature of non-inverting configuration; which enables this circuit to behave as a buffer amplifier to connect a source with high impedance to low-impedance load. The gain of buffer amplifier is<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2393 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/voltage-follower.jpg\" alt=\"Voltage Follower\" width=\"590\" height=\"230\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/voltage-follower.jpg 590w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/voltage-follower-300x117.jpg 300w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Current-to-Voltage-Converter\" >Current-to-Voltage Converter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Voltage-to-Current-Converter\" >Voltage-to-Current Converter<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Differential-Amplifier\" >Differential Amplifier<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Integrator-and-Differentiator\" >Integrator and Differentiator<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Instrumentation-Amplifier\" >Instrumentation Amplifier<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/voltage-follower\/#Antilog-or-Exponential-Amplifier\" >Antilog or Exponential Amplifier<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Current-to-Voltage-Converter\"><\/span>Current-to-Voltage Converter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2394 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/current-to-voltage-converter.jpg\" alt=\"Current-to-Voltage Converter\" width=\"683\" height=\"218\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/current-to-voltage-converter.jpg 683w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/current-to-voltage-converter-300x96.jpg 300w\" sizes=\"auto, (max-width: 683px) 100vw, 683px\" \/><\/p>\n<p style=\"text-align: justify;\">The output voltage is directly proportional to signal current, and the feedback resistance R<sub>F<\/sub> is equal to the magnitude of the ratio of output voltage to signal current.<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Voltage-to-Current-Converter\"><\/span>Voltage-to-Current Converter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Consider the circuit given in the figure. The inverting terminal (1) is not at virtual ground. From the virtual<br \/>\nshort concept, V<sub>1<\/sub> = V<sub>2<\/sub> and we also note that V<sub>1<\/sub> = V<sub>2<\/sub> = V<sub>L<\/sub> = i<sub>L<\/sub> Z<sub>L<\/sub>. Equating the current i<sub>1<\/sub> and i<sub>2<\/sub>, we have<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2396 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/current-converter.jpg\" alt=\"Current Converter\" width=\"668\" height=\"415\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/current-converter.jpg 668w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/current-converter-300x186.jpg 300w\" sizes=\"auto, (max-width: 668px) 100vw, 668px\" \/><\/p>\n<p style=\"text-align: justify;\">which means that the load current is proportional to input voltage and is independent of the load impedance Z<sub>L<\/sub> , as long as the output voltage remains between allowed limits.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2397 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/current-converter-1.jpg\" alt=\"Current Converter\" width=\"295\" height=\"259\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Differential-Amplifier\"><\/span>Differential Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">An ideal difference amplifier amplifies only the difference between two signals; rejects any common signal to two input terminals. Consider the circuit shown in Figure<\/p>\n<p style=\"text-align: justify;\">(a), with inputs V<sub>i1<\/sub> and . V<sub>i2<\/sub> To analyze the circuit, we will use the concept of superposition and virtual short.<\/p>\n<p style=\"text-align: justify;\">(b) shows the circuit with input V<sub>i2<\/sub> = 0. No current will flow in R<sub>3<\/sub> and R<sub>4<\/sub>; therefore, V<sub>2a<\/sub> = 0. The resulting circuit will behave as an inverting amplifier so<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2398 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differential-amplifier.jpg\" alt=\"Differential Amplifier\" width=\"664\" height=\"437\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier.jpg 664w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier-300x197.jpg 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/p>\n<p style=\"text-align: justify;\">Fig. (c) shows the circuit with V<sub>i1<\/sub> = 0. Since the current into the op-amp is zero, R<sub>3<\/sub> and R<sub>4<\/sub> form a voltage divider. Therefore,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2409 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differential-amplifier-1-e1721990343893.jpg\" alt=\" Differential Amplifier\" width=\"707\" height=\"481\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier-1-e1721990343893.jpg 707w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier-1-e1721990343893-300x204.jpg 300w\" sizes=\"auto, (max-width: 707px) 100vw, 707px\" \/><\/p>\n<p style=\"text-align: justify;\">The differential input resistance of a differential amplifier can be determined by using the circuit shown in the figure. In the figure, we have imposed the condition given in equation (10.50) and have set R<sub>1<\/sub> = R<sub>3<\/sub> and R<sub>2<\/sub> = R<sub>4<\/sub>. The input resistance is then defined as<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2412 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/circuit-3.jpg\" alt=\"Circuit\" width=\"578\" height=\"245\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/circuit-3.jpg 578w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/circuit-3-300x127.jpg 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/p>\n<p style=\"text-align: justify;\">Taking into account the virtual short concept, we can write the following loop equation,<\/p>\n<p style=\"text-align: justify;\">V<sub>i<\/sub> = i R<sub>1<\/sub> + i R<sub>1<\/sub> = i(2 R<sub>1<\/sub>)<\/p>\n<p style=\"text-align: justify;\">Therefore, the input resistance is<\/p>\n<p style=\"text-align: justify;\">R<sub>1<\/sub> = 2 R<sub>1<\/sub><\/p>\n<p style=\"text-align: justify;\">In the ideal difference amplifier, the output v<sub>0<\/sub> is zero when V<sub>i1<\/sub> = V<sub>i2<\/sub> However, an inspection of equation (10.49) shows that, this condition is not satisfied if R<sub>4<\/sub>\/R<sub>3<\/sub> \u2260 R<sub>2<\/sub>\/R<sub>1<\/sub>. When V<sub>i1<\/sub> = V<sub>i2 <\/sub>the input is called common-mode input signal. The common-mode input voltage is defined as .<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2414 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/common-mode-rejection.jpg\" alt=\"Common Mode Rejection\" width=\"686\" height=\"265\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/common-mode-rejection.jpg 686w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/common-mode-rejection-300x116.jpg 300w\" sizes=\"auto, (max-width: 686px) 100vw, 686px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Integrator-and-Differentiator\"><\/span>Integrator and Differentiator<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure shows a generalized inverting amplifier for which the voltage transfer function has similar general form as calculated earlier, that is V<sub>0<\/sub>\/V<sub>1<\/sub> = -Z<sub>2<\/sub>\/Z<sub>1<\/sub><\/p>\n<p style=\"text-align: justify;\">where Z<sub>1<\/sub> and Z<sub>2<\/sub> are generalized impedances. Two special circuits can be developed from this generalized inverting amplifier.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2415 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differentiator.jpg\" alt=\"Differentiator\" width=\"664\" height=\"172\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator.jpg 664w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-300x78.jpg 300w\" sizes=\"auto, (max-width: 664px) 100vw, 664px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2416 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differentiator-1.jpg\" alt=\"Differentiator\" width=\"348\" height=\"158\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-1.jpg 348w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-1-300x136.jpg 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/p>\n<p style=\"text-align: justify;\">In Figure (b), Z<sub>1<\/sub> corresponds to a resistor and Z<sub>2<\/sub> to a capacitor. The impedance are then Z<sub>1<\/sub> = R<sub>1<\/sub> and Z<sub>2<\/sub> = 1\/sC<sub>2<\/sub>, where s is the complex frequency. The output voltage is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2417 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differentiator-2.jpg\" alt=\"Differentiator\" width=\"466\" height=\"45\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-2.jpg 466w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-2-300x29.jpg 300w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/p>\n<p style=\"text-align: justify;\">Equation (10.59) represents integration in time domain. If V<sub>c<\/sub> is the voltage across the capacitor at t = 0, the output voltage is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2419 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differentiator-3.jpg\" alt=\"Differentiator\" width=\"450\" height=\"53\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-3.jpg 450w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-3-300x35.jpg 300w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/p>\n<p style=\"text-align: justify;\">where t\u2032 is the variable of integration. Figure (b) summarizes these results.<\/p>\n<p style=\"text-align: justify;\">The second generalized inverting op-amp uses a capacitor for Z<sub>1<\/sub> and a resistor for Z<sub>2<\/sub>, as shown in Figure (c). The impedances are Z<sub>1<\/sub> = 1\/sC<sub>1<\/sub> and Z<sub>2<\/sub> = R<sub>2<\/sub>, and the voltage transfer function is<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2421 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differentiator-4.jpg\" alt=\"Differentiator\" width=\"655\" height=\"160\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-4.jpg 655w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differentiator-4-300x73.jpg 300w\" sizes=\"auto, (max-width: 655px) 100vw, 655px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Instrumentation-Amplifier\"><\/span>Instrumentation Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">In a number of industrial and consumer applications, one is required to measure and control physical quantities. Some typical examples are measurement and control of temperature, humidity, light intensity, water flow etc. These physical quantities are usually measured with the help of transducers. The output of transducer has to be amplified so that it can drive the indicator or display system. This function is performed by an instrumentation amplifier. The important features of an instrumentation amplifier are:<\/p>\n<ul style=\"text-align: justify;\">\n<li>high gain accuracy<\/li>\n<li>high CMRR<\/li>\n<li>high gain stability with low temperature coefficient.<\/li>\n<li>low DC offset<\/li>\n<li>low output impedance<\/li>\n<li>high input impedance<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">The instrumentation amplifier has high common mode rejection capability that means it can reject a signal that is common to both terminal but amplify a differential signal and this feature is useful for receiving small signals buried in large common-mode offsets or noise.<\/p>\n<p style=\"text-align: justify;\">[There are specially designed op-amps such as \u00b5A 725 to meet above stated requirements of a good instrumentation amplifier. Monolithic (single chip) instrumentation amplifiers are also available commercially such as AD521, AD524, AD620, AD624 by Analog Devices, LM-363.XX (XX \u2192 10,100,500) by National Semiconductor and INA101,104, 3636, 3629 by Burr-Brown.]<\/p>\n<p style=\"text-align: justify;\">Consider the basic differential amplifier as shown in Figure (a). It can be easily seen that the output voltage V<sub>0<\/sub> is given by,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2423 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier.jpg\" alt=\"Instrumentation Amplifier\" width=\"660\" height=\"236\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier.jpg 660w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier-300x107.jpg 300w\" sizes=\"auto, (max-width: 660px) 100vw, 660px\" \/><\/p>\n<p style=\"text-align: justify;\">In Figure (a), source V1 sees an input impedance = R3 + R4 (= 101 k\u2126) and the impedance seen by source V2 is only R1 (1 k\u2126). This low impedance may load the signal source heavily. Therefore, high resistance buffer is used proceeding each input to avoid this loading effect as shown in Figure (b).<\/p>\n<p style=\"text-align: justify;\">The op-amps A1 and A2 have differential input voltage as zero. For V1 = V2, that is, under common mode condition, the voltage across R will be zero. As no current flows through R and R\u2032 the non-inverting amplifier A1 acts as voltage follower, so its output V&#8217;2 = V2. However, if <em>V<\/em>1 \u00b9 <em>V<\/em>2, current flows in R and R&#8217;2 , and (<em>V<\/em><sub>2&#8242;<\/sub>\u00a0&#8211; <em>V<\/em><sub>1&#8242;<\/sub>) &gt; (<em>V<\/em><sub>2<\/sub> &#8211; <em>V<\/em><sub>1<\/sub>). Therefore, this circuit has differential gain and CMRR more as compared to the single op-amp circuit of Fig. 10.23 (a). The output voltage Vo can be calculated as follows:<\/p>\n<p style=\"text-align: justify;\">The voltage at the (+) input terminal of op-amp A3 is R2V&#8217;1\/R1+R2 Using superposition theorem,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2427 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier-1.jpg\" alt=\"Instrumentation Amplifier\" width=\"641\" height=\"522\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier-1.jpg 641w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/instrumentation-amplifier-1-300x244.jpg 300w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2428 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/differential-amplifier-2.jpg\" alt=\"Differential Amplifier\" width=\"673\" height=\"331\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier-2.jpg 673w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/differential-amplifier-2-300x148.jpg 300w\" sizes=\"auto, (max-width: 673px) 100vw, 673px\" \/><\/p>\n<p style=\"text-align: justify;\">Consider the circuit given in the figure. The diode is to be forward biased, so the input voltage is limited to positive values. The diode current is<\/p>\n<p style=\"text-align: justify;\"><em>i<sub>D<\/sub> <\/em>=\u00a0<em>I<sub>s <\/sub>(e<sup>VD\/hVT<\/sup> &#8211; 1)<\/em><\/p>\n<p style=\"text-align: justify;\">If the diode is sufficiently forward biased, the (\u20131) term is neglected and diode current can be rewritten as<\/p>\n<p style=\"text-align: justify;\"><em>i<sub>D<\/sub> <\/em>=\u00a0<em>I<sub>s <\/sub><sup>eVD\/hVT<\/sup>\u00a0<\/em><\/p>\n<p style=\"text-align: justify;\">The input current can be written as,<\/p>\n<p style=\"text-align: justify;\">i<sub>1<\/sub> = V<sub>i<\/sub>\/R<sub>1<\/sub><\/p>\n<p style=\"text-align: justify;\">and the output voltage, since voltage at inverting terminal of op-amp is at virtual ground, is given by<\/p>\n<p style=\"text-align: justify;\">V<sub>0<\/sub> = \u2013V<sub>D<\/sub><\/p>\n<p style=\"text-align: justify;\">Noting that i<sub>1<\/sub> = i<sub>D<\/sub>, we can write<\/p>\n<p style=\"text-align: justify;\">i<sub>1<\/sub> = V<sub>i<\/sub>\/R<sub>1<\/sub> = <em>i<sub>D<\/sub><\/em> = <em>I<sub>s <\/sub><sup>eVD\/hVT<\/sup><\/em><sub>1<\/sub><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2430 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/log-amplifier.jpg\" alt=\"Log Amplifier\" width=\"688\" height=\"406\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/log-amplifier.jpg 688w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/log-amplifier-300x177.jpg 300w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Antilog-or-Exponential-Amplifier\"><\/span>Antilog or Exponential Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The complement or inverse function of a log amplifier is antilog, or exponential amplifier. A simple example using a diode is shown in the figure. Since V<sub>1<\/sub> is at virtual ground, we can write for V<sub>1<\/sub> &gt; 0<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2431 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/antilog.jpg\" alt=\"Antilog\" width=\"629\" height=\"248\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/antilog.jpg 629w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/antilog-300x118.jpg 300w\" sizes=\"auto, (max-width: 629px) 100vw, 629px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/analog-circuits\/amplifier-frequency-response\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/analog-circuits\/bipolar-junction-transistors\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-are-analog-circuits\/\" target=\"_blank\" rel=\"noopener\"><strong>What are Analog Circuits?<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An interesting property of non-inverting op-amp occurs when R1 = \u221e, an open circuit. The closed loop gain is independent<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[650,6],"tags":[701,703,704,702],"class_list":["post-2585","post","type-post","status-publish","format-standard","hentry","category-analog-circuits","category-ec","tag-current-converter","tag-differential-amplifier","tag-integrator","tag-voltage-converter"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=2585"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2585\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=2585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=2585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=2585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}