{"id":2587,"date":"2024-08-05T16:55:34","date_gmt":"2024-08-05T11:25:34","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=2587"},"modified":"2025-07-16T15:24:38","modified_gmt":"2025-07-16T09:54:38","slug":"amplifier-frequency-response","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ec\/analog-circuits\/amplifier-frequency-response","title":{"rendered":"Amplifier Frequency Response"},"content":{"rendered":"<h3 style=\"text-align: justify;\"><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2377 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/amplifier-gain.jpg\" alt=\"Amplifier Gain\" width=\"418\" height=\"231\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/amplifier-gain.jpg 418w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/amplifier-gain-300x166.jpg 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/p>\n<p style=\"text-align: justify;\">In general, an amplifier gain factor versus frequency will resemble as shown in Figure (a). Both gain factor and frequency are plotted on logarithmic scales (the gain factor in terms of decibels). Three frequency ranges, low, midband and high are indicated. . In low-frequency range, f &lt; f<sub>L<\/sub> , the gain decreases with decrease in frequency due to the effect of coupling and bypass capacitor. . In high frequency range, f &gt; f<sub>H<\/sub>, stray capacitance and transistor capacitance effect causes the gain to decrease as the frequency increases. The mid-band range is the region where coupling and bypass capacitors act as short-circuit, and stray and transistor is the region where coupling and bypass capacitors act as short-circuit, and stray and transistor capacitances act as open circuit. capacitances act as open circuit. In capacitances act as open circuit. this region, the gain is almost constant. The gain at f = f<sub>L<\/sub> and at f = f<sub>H<\/sub> is 3-dB less than the maximum midband gain. The bandwidth of the amplifier (in Hz) is defined as<\/p>\n<p style=\"text-align: justify;\">f<sub>BW<\/sub> = f<sub>H<\/sub> &#8211; f<sub>L<\/sub><\/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\/amplifier-frequency-response\/#The-Differential-Amplifier\" >The Differential Amplifier<\/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\/amplifier-frequency-response\/#Feedback-Amplifiers\" >Feedback Amplifiers<\/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\/amplifier-frequency-response\/#Operational-Amplifier\" >Operational 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\/amplifier-frequency-response\/#Summing-Amplifier\" >Summing Amplifier<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"The-Differential-Amplifier\"><\/span>The Differential Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The block diagram of differential is shown above. There are two input terminals and one output terminal. Ideally, the output signal is proportional to the difference between two input signals.<\/p>\n<p style=\"text-align: justify;\">The ideal output voltage can be written as<br \/>\nV0 = A<sub>vol<\/sub>(V<sub>1<\/sub> \u2013 V<sub>2<\/sub>)<br \/>\nwhere A<sub>vol<\/sub> is open-loop voltage gain. In ideal case, if V<sub>1<\/sub> = V<sub>2<\/sub>, the output voltage is zero. We only obtain a non-zero output voltage if V<sub>1<\/sub> and V<sub>2<\/sub> are not equal.<\/p>\n<p style=\"text-align: justify;\">We define the differential-mode input voltage as<br \/>\nV<sub>d<\/sub> = V<sub>1<\/sub> \u2013 V<sub>2<\/sub><br \/>\nand the common-mode input voltage as common-mode input voltage<br \/>\nV<sub>cm<\/sub> = V<sub>1<\/sub> + V<sub>2<\/sub>\/2<\/p>\n<p style=\"text-align: justify;\">The differential mode voltage for two inputs tells how different they are. The common mode voltage is the part of the voltage that is the same for both i.e. the part they have in common.<\/p>\n<p style=\"text-align: justify;\">The equations show that if V1 = V2, the differential-mode input signal is zero and the common-mode input signal is V<sub>cm<\/sub> = V<sub>1<\/sub> = V<sub>2<\/sub>.<\/p>\n<p style=\"text-align: justify;\">If for example, V<sub>1<\/sub> = +10 \u00b5V and V2 = \u201310 \u00b5V, then the differential-mode voltage is Vd = 20 \u00b5V and the common- mode voltage is Vcm = 0. However, if V1 = 110 \u00b5V and V2 = 90 \u00b5V, then the differential-mode input signals is 20 \u00b5V and Vcm = 100 \u00b5V. If each pair of input voltages were applied to ideal differential amplifier, the output voltage in each case would be exactly the same. However, amplifiers are not ideal, and the common-mode input signal does affect the output. The goal of designing differential amplifiers is to minimize the effect of common-mode input signal.<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Feedback-Amplifiers\"><\/span>Feedback Amplifiers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">An ideal linear amplifier in the mid frequency region provides an output signal that is an exact replica of the applied input signal. But, the practical amplifiers depart from the ideal one for several reasons like non-linearity of transistor characteristics, parameter variation, temperature effects etc. As a matter of fact, some of these factors can be minimized by improving the involved basic device. The best approach is to use the principle of feedback to achieved a desired degree of improvement. The feedback may be defined as a process of injecting some energy from the output and then return it back to the input. Thus, the process of combining a fraction of the output energy (i.e. voltage or current) back to the input is called the feedback. The amplifiers, which use the feedback principle, are known as feedback amplifiers.<\/p>\n<p style=\"text-align: justify;\">Feedback can either be negative or positive. In negative feedback, a portion of output signal is subtracted , from input signal; in positive feedback, a portion of output signal is added to input signal. Negative feedback, for example, tends to maintain a constant value of amplifier voltage gain against variations in transistor parameters, supply voltages, and temperature. Positive feedback is used in the design of oscillators and in number of other applications. In this chapter, we will concentrate on negative feedback.<\/p>\n<h4 style=\"text-align: justify;\">Types of feedback<\/h4>\n<p style=\"text-align: justify;\">Table summarizes the ideal relationships, including the transfer functions, input and output resistances, obtained in the analysis of the four types of feedback amplifier.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2389 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/feedback-amplifier.jpg\" alt=\"Feedback Amplifier\" width=\"636\" height=\"218\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/feedback-amplifier.jpg 636w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/feedback-amplifier-300x103.jpg 300w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/p>\n<h4 style=\"text-align: justify;\">Procedure to identify the type of feedback:<\/h4>\n<ul style=\"text-align: justify;\">\n<li>Step-1: Identify the element responsible for the feedback.<\/li>\n<li>Step-2: If feedback element is directly connected to the output node, it indicates voltage sampling otherwise it indicates current sampling.<\/li>\n<li>Step-3: If feedback element is directly connected to the input node, it indicates shunt mixing otherwise it indicates series mixing.<\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Operational-Amplifier\"><\/span>Operational Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Linear integrated circuits are being used in a number of electronic applications such as in fields like audio and radio communication, medical electronics, instrumentation control, etc. An important linear IC is operational amplifier which will be discussed in this chapter.<\/p>\n<p style=\"text-align: justify;\">An operational amplifier is a direct-coupled high-gain amplifier usually consisting of one or more differential amplifiers and usually followed by a level translator and an output stage. <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2390 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/operational-amplifier.jpg\" alt=\"Operational Amplifier\" width=\"298\" height=\"207\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/operational-amplifier.jpg 298w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/operational-amplifier-130x90.jpg 130w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/p>\n<p style=\"text-align: justify;\">The op-amp can be represented as<\/p>\n<p style=\"text-align: justify;\">Here, V<sub>1<\/sub> is non-inverting terminal voltage<br \/>\nV<sub>2<\/sub> is inverting terminal voltage<br \/>\nZ<sub>i<\/sub> is input impedance<br \/>\nZ<sub>0<\/sub> is output impedance<br \/>\nV<sub>0<\/sub> is output voltage<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Summing-Amplifier\"><\/span>Summing Amplifier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Figure shows the inverting weighted-summer circuit. From our previous discussion, the ideal op-amp will have a virtual ground appearing at its negative input terminal. Ohm\u2019s law tells us that currents i<sub>1<\/sub>, i<sub>2<\/sub>,&#8230;.., i<sub>n<\/sub>\u00a0are given by<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2391 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/weighted-summer-circuit.jpg\" alt=\"Weighted Summer Circuit\" width=\"226\" height=\"54\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2392 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/summing-amplifier.jpg\" alt=\"Summing Amplifier\" width=\"707\" height=\"360\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/summing-amplifier.jpg 707w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/summing-amplifier-300x153.jpg 300w\" sizes=\"auto, (max-width: 707px) 100vw, 707px\" \/><\/p>\n<p style=\"text-align: justify;\">That is, the output voltage is weighted sum of input voltages V<sub>1<\/sub>, V<sub>2<\/sub>,&#8230;&#8230;&#8230;., V<sub>n<\/sub>. This circuit is therefore called weighted summer weighted summer. Note that each summing coefficient may be independently adjusted by adjusting the corresponding \u201cfeed-in\u201d resistor (R<sub>1<\/sub> to R<sub>n<\/sub>).<\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/analog-circuits\/small-signal-model\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/analog-circuits\/voltage-follower\/\" 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>In general, an amplifier gain factor versus frequency will resemble as shown in Figure (a). Both gain factor and frequency<\/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":[703,705,675,706],"class_list":["post-2587","post","type-post","status-publish","format-standard","hentry","category-analog-circuits","category-ec","tag-differential-amplifier","tag-feedback-amplifiers","tag-operational-amplifier","tag-types-of-feedback"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2587","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=2587"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/2587\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=2587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=2587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=2587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}