{"id":2108,"date":"2018-05-07T10:58:03","date_gmt":"2018-05-07T10:58:03","guid":{"rendered":"https:\/\/www.tina.com\/resources\/?page_id=2108"},"modified":"2018-06-22T10:13:04","modified_gmt":"2018-06-22T10:13:04","slug":"9-fet-amplifier-analysis","status":"publish","type":"page","link":"https:\/\/www.tina.com\/resources\/home\/field-effect-transistor-amplifiers-2\/9-fet-amplifier-analysis\/","title":{"rendered":"9. FET Amplifier analysis"},"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; 9. FET Amplifier analysis<\/div>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/field-effect-transistor-amplifiers-2\/8-fet-amplifiers-canonical-configurations\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 8. FET Amplifiers &#8211; Canonical configurations<\/a><\/div>\n<div class=\"next-page\"><a style=\"font-size: 20px;\" href=\"https:\/\/www.tina.com\/resources\/home\/field-effect-transistor-amplifiers-2\/10-fet-amplifier-design\/\">NEXT- 10. FET Amplifier design<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<div><\/div>\n<p align=\"justify\"><strong><em><span style=\"font-size: 22px;\"> FET Amplifier analysis<\/span><\/em><\/strong><\/p>\n<div class=\"clear\">In the previous section, we defined four basic configurations for FET amplifiers. This section examines each of these configurations, and we derive expressions for the gain (current and voltage), the input resistance and the output resistance.<\/div>\n<div><\/div>\n<p>&nbsp;<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">9.1 The CS (and Source Resistor) Amplifier<\/span><\/b><\/span><\/em><\/h6>\n<div>\n<div id=\"attachment_2116\" style=\"width: 518px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2116\" class=\"wp-image-2116 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-33.png\" alt=\"The CS amplifier with source resistor\" width=\"508\" height=\"203\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-33.png 508w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-33-300x120.png 300w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><p id=\"caption-attachment-2116\" class=\"wp-caption-text\">Figure 33 &#8211; The CS amplifier with source resistor<\/p><\/div>\n<\/div>\n<div>\n<p>Figure 33(a) shows the CS amplifier with source resistor. The <em>ac<\/em> equivalent circuit is in Figure 33(b). We assume <em>r<sub>o<\/sub><\/em> is large compared to , so it can be neglected. If a capacitor is present between source and ground (i.e., the CS amplifier), we need simply set <em>R<sub>S<\/sub><\/em> equal to zero in the following <em>ac<\/em> equations. We do this at the conclusion of this derivation.<\/p>\n<p>In part (b) of Figure 33, <em>R<sub>G<\/sub><\/em> is the parallel combination of <em>R<sub>1<\/sub><\/em> and <em>R<sub>2<\/sub><\/em> and <em>V<sub>GG<\/sub><\/em> is the Thevenin equivalent voltage of the bias circuit:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2120\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-41.png\" alt=\"\" width=\"87\" height=\"50\" \/>\u00a0(41)<\/p>\n<p>To analyze the <em>ac <\/em>equivalent circuit, we write a KVL equation around the gate circuit.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2121\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-42.png\" alt=\"\" width=\"174\" height=\"89\" \/>\u00a0(42)<\/p>\n<p>The output voltage, <em>v<sub>out<\/sub><\/em>, is given by<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2123\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-43.png\" alt=\"\" width=\"234\" height=\"50\" \/><\/p>\n<p>The voltage gain, <em>A<sub>v<\/sub><\/em>, is now found.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2124\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-43V.png\" alt=\"\" width=\"138\" height=\"50\" \/>\u00a0(43)<\/p>\n<p>If the source resistance, <em>R<sub>S<\/sub><\/em>, is bypassed by a capacitor, we let <em>R<sub>S <\/sub><\/em>= 0, and the voltage gain increases to<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2126\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-44.png\" alt=\"\" width=\"126\" height=\"30\" \/>\u00a0(44)<\/p>\n<p>This is typically a large negative number.<\/p>\n<p>The input resistance and current gain are given by<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2131\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-45.png\" alt=\"\" width=\"272\" height=\"100\" \/>\u00a0(45)<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">9.2 The CG Amplifier<\/span><\/b><\/span><\/em><\/h6>\n<p>Figure 37(a) shows the single-stage common-gate amplifier and Figure 6.37(b) shows its <em>ac<\/em> equivalent. We have once again neglected <em>r<sub>o<\/sub><\/em> under the assumption that it is large compared to the parallel combination of <em>R<sub>D<\/sub><\/em> with <em>R<sub>load<\/sub><\/em>.<\/p>\n<div id=\"attachment_2137\" style=\"width: 537px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2137\" class=\"wp-image-2137 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-37.png\" alt=\" CG amplifier\" width=\"527\" height=\"240\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-37.png 527w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-37-300x137.png 300w\" sizes=\"auto, (max-width: 527px) 100vw, 527px\" \/><p id=\"caption-attachment-2137\" class=\"wp-caption-text\">Figure 37 \u2013 CG amplifier<\/p><\/div>\n<\/div>\n<p>From Figure 37(b) leftmost loop, the gate-to-source voltage is given by<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2139\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-46.png\" alt=\"\" width=\"74\" height=\"25\" \/>\u00a0(46)<\/p>\n<p>The current through <em>R<sub>S<\/sub><\/em> is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2140\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-47.png\" alt=\"\" width=\"159\" height=\"97\" \/>\u00a0(47)<\/p>\n<p>so the (input) resistance seen by the source is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2142\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-48.png\" alt=\"\" width=\"267\" height=\"49\" \/>\u00a0(48)<\/p>\n<p>This should be compared to Equation (45) for the CS amplifier. We see that if the gate resistance is high, the input resistance of the common-source amplifier can be much larger than that of the common-gate amplifier. In fact, the number of applications of the CG amplifier is limited due to the low input impedance.<\/p>\n<p>The voltage gain is given by<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2143 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-49.png\" alt=\"\" width=\"398\" height=\"70\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-49.png 398w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-49-300x53.png 300w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/>\u00a0(49)<\/p>\n<p>Comparing this with Equation (44) , we see that the voltage gain for the CS amplifier with an unbypassed resistance in the source circuit is the same as that of the CG amplifier except the CG amplifier does not shift the phase.<\/p>\n<p>The output resistance is simply given by <em>R<sub>D<\/sub><\/em> (put in a test current and measure the voltage while setting <em>v<sub>in<\/sub><\/em> to zero).<\/p>\n<p>The current gain of the CG amplifier is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2144\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-50-300x91.png\" alt=\"\" width=\"300\" height=\"91\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-50-300x91.png 300w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-50.png 301w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\u00a0(50)<\/p>\n<h6><em><span style=\"color: #000000; font-family: Bodoni MT,serif;\"><b><span lang=\"en-US\">9.3 The CD (SF) Amplifier<\/span><\/b><\/span><\/em><\/h6>\n<p>Figure 39(a) shows the single-stage common-drain source follower (SF) amplifier and Figure 39(b) shows its <em>ac<\/em> equivalent. As with each configuration we have analyzed, we omit the large resistance, <em>r<sub>o<\/sub><\/em> under the assumption it is much larger than the parallel combination of <em>R<sub>S<\/sub><\/em> with <em>R<sub>load<\/sub><\/em>.<\/p>\n<div id=\"attachment_2148\" style=\"width: 528px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2148\" class=\"wp-image-2148 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-39.png\" alt=\"The CD amplifier\" width=\"518\" height=\"215\" srcset=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-39.png 518w, https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersFigure6-39-300x125.png 300w\" sizes=\"auto, (max-width: 518px) 100vw, 518px\" \/><p id=\"caption-attachment-2148\" class=\"wp-caption-text\">Figure 39 \u2013 The CD amplifier<\/p><\/div>\n<p>The input resistance is simply <em>R<sub>in<\/sub><\/em> = <em>R<sub>G<\/sub><\/em>. Writing a KVL equation around the gate-to-source loop, we have<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2150\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-51.png\" alt=\"\" width=\"172\" height=\"35\" \/>\u00a0(51)<\/p>\n<p>from which we obtain<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2152 size-full\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-52.png\" alt=\"\" width=\"164\" height=\"35\" \/>\u00a0(52)<\/p>\n<p>The output voltage is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2153\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-53.png\" alt=\"\" width=\"147\" height=\"32\" \/>\u00a0(53)<\/p>\n<p>The voltage gain is the ratio of output to input voltage.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2154\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-54.png\" alt=\"\" width=\"166\" height=\"47\" \/>\u00a0(54)<\/p>\n<p>Note that this voltage gain is less than unity, and it approaches one as the parallel combination of <em>R<sub>S<\/sub><\/em> with <em>R<sub>load<\/sub><\/em> increases.<\/p>\n<p>We now find the current gain. The output current is the ratio of the output voltage to the load resistance. The input current is the input voltage divided by <em>R<sub>G<\/sub><\/em>. The gain is therefore given by<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2155\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-55.png\" alt=\"\" width=\"299\" height=\"118\" \/>\u00a0(55)<\/p>\n<p>The output resistance can be found by replacing the load resistor with a test voltage, v<sub>test<\/sub>, and then finding the resulting current, <em>i<sub>test<\/sub><\/em>. The current driven by this test source is found from a node equation at the source.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2156\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-56.png\" alt=\"\" width=\"115\" height=\"47\" \/>\u00a0(56)<\/p>\n<p>The gate-to-source voltage is simply <em>-v<sub>test<\/sub><\/em> since we assume the input voltage is zero. Therefore, the output resistance is<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2157\" src=\"https:\/\/www.tina.com\/resources\/wp-content\/uploads\/2018\/05\/Field-effectTransistorAmplifiersEq6-57.png\" alt=\"\" width=\"165\" height=\"53\" \/>\u00a0(57)<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"previous-page\"><a href=\"https:\/\/www.tina.com\/resources\/home\/field-effect-transistor-amplifiers-2\/8-fet-amplifiers-canonical-configurations\/\"><img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/leftarrow5.png\" \/>PREVIOUS- 8. FET Amplifiers &#8211; Canonical configurations<\/a><\/div>\n<div class=\"next-page\"><a style=\"font-size: 20px;\" href=\"https:\/\/www.tina.com\/resources\/home\/field-effect-transistor-amplifiers-2\/10-fet-amplifier-design\/\">NEXT- 10. FET Amplifier design<img decoding=\"async\" src=\"https:\/\/www.tina.com\/images\/resource\/rightarrow5.png\" \/><\/a><\/div>\n<div class=\"clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>CURRENT &#8211; 9. FET Amplifier analysis PREVIOUS- 8. FET Amplifiers &#8211; Canonical configurations NEXT- 10. FET Amplifier design FET Amplifier analysis In the previous section, we defined four basic configurations for FET amplifiers. This section examines each of these configurations, and we derive expressions for the gain (current and voltage), the input resistance and the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1764,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"yst_prominent_words":[188,180,183,186,190,189,179,167,141,168,176,178,182,181,185,177,184,187,32,170],"class_list":["post-2108","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/2108","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=2108"}],"version-history":[{"count":34,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/2108\/revisions"}],"predecessor-version":[{"id":3466,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/2108\/revisions\/3466"}],"up":[{"embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/pages\/1764"}],"wp:attachment":[{"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/media?parent=2108"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.tina.com\/resources\/wp-json\/wp\/v2\/yst_prominent_words?post=2108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}