{"id":983,"date":"2024-10-10T16:04:16","date_gmt":"2024-10-10T08:04:16","guid":{"rendered":"https:\/\/dt9025a.top\/?p=983"},"modified":"2025-08-27T19:44:43","modified_gmt":"2025-08-27T11:44:43","slug":"widlar-%e7%94%b5%e6%b5%81%e6%ba%90-constant-gm-%e5%81%8f%e7%bd%ae","status":"publish","type":"post","link":"https:\/\/dt9025a.top\/?p=983","title":{"rendered":"Widlar \u7535\u6d41\u6e90 \/ Constant Gm \u504f\u7f6e"},"content":{"rendered":"\n<p><a href=\"https:\/\/blog.csdn.net\/weixin_42221495\/article\/details\/130483487\" target=\"_blank\" rel=\"noreferrer noopener\">Reference \u6587\u7ae0\u94fe\u63a5<\/a><\/p>\n\n\n\n\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u524d\u7f6e\u77e5\u8bc6<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1\u3001\u8de8\u5bfc gm \u7684\u8868\u8fbe<\/h3>\n\n\n\n$$\n\\begin{align*}\ng_m&amp;=\\mu C_{ox}\\frac{W}{L}(V_{GS}- V_{TH}) \\\\\n&amp;=\\sqrt[]{2\\mu C_{ox}\\frac{W}{L}I_D} \\\\\n&amp;=\\frac{2I_D}{(V_{GS}- V_{TH})}  \n\\end{align*}\n$$\n\n\n\n<h3 class=\"wp-block-heading\">2\u3001\u653e\u5927\u5668\u7684\u5c0f\u4fe1\u53f7\u7535\u538b\u589e\u76ca<\/h3>\n\n\n\n$$ A_V=G_m\\times R_{out} $$\n\n\n\n<p>\u5176\u4e2d\uff0c<code>Gm<\/code> \u4e3a\u8f93\u51fa\u77ed\u8def\u5230\u5730\u8ba1\u7b97\u7684\u8de8\u5bfc\u3001<code>Rout<\/code> \u4e3a\u8f93\u5165\u77ed\u8def\u5230\u5730\u8ba1\u7b97\u7684\u8f93\u51fa\u963b\u6297\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3\u3001\u4e8c\u6781\u7ba1\u578b\u8fde\u63a5\u5668\u4ef6\u7684\u963b\u6297<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"698\" height=\"271\" src=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-2.png\" alt=\"\" class=\"wp-image-988\" srcset=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-2.png 698w, https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-2-300x116.png 300w\" sizes=\"auto, (max-width: 698px) 100vw, 698px\" \/><\/figure>\n<\/div>\n\n\n<p>\u4e8c\u6781\u7ba1\u578b\u8fde\u63a5\u5668\u4ef6\u4ece\u6f0f\u7aef\u770b\u53bb\u7684\u5c0f\u4fe1\u53f7\u963b\u6297\u4e3a\uff1a<\/p>\n\n\n\n$$ r=\\frac{1}{g_m} $$\n\n\n\n<h3 class=\"wp-block-heading\">4\u3001\u5e26\u6e90\u6781\u8d1f\u53cd\u9988\u7684\u5171\u6e90\u6781<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"323\" src=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image.png\" alt=\"\" class=\"wp-image-986\" srcset=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image.png 319w, https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-296x300.png 296w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/figure>\n<\/div>\n\n\n<p>\u5bf9\u4e8e\u5e26\u6e90\u6781\u8d1f\u53cd\u9988\u7684\u5171\u6e90\u6781\uff0c\u5176\u8de8\u5bfc\u4e3a\uff1a<\/p>\n\n\n\n$$ G_m=\\frac{g_{m1}}{1+g_{m1}R_s} $$\n\n\n\n<p>\u8be5\u7535\u8def\u5177\u6709\u53cd\u76f8\u4f5c\u7528\uff0c\u56e0\u6b64\u5176\u5c0f\u4fe1\u53f7\u7535\u538b\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nA_V&amp;=-G_mR_D\\\\\n&amp;=-\\frac{g_{m1}R_D}{1+g_{m1}R_s}\n\\end{align*} $$\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u73af\u8def\u5206\u6790<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"375\" src=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-1.png\" alt=\"\" class=\"wp-image-987\" srcset=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-1.png 634w, https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-1-300x177.png 300w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/figure>\n<\/div>\n\n\n<p>\u7531\u4e8e M2 \u7684 Vgs &lt; M1 \u7684 Vgs\uff0c\u56e0\u6b64\u901a\u5e38\u6709\uff1a<\/p>\n\n\n\n$$ (W\/L)_{M2}:(W\/L)_{M1}=K:1 $$\n\n\n\n<p>\u901a\u5e38\uff0c\u6211\u4eec\u8ba4\u4e3a\u5de6\u8fb9\u7684\u73af\u8def\u8fde\u63a5\u65b9\u5f0f\u7a33\u5b9a\uff0c\u4e3a\u4ec0\u4e48\u5462\uff1f\u8fd9\u5c31\u9700\u8981\u5bf9\u73af\u8def\u8fdb\u884c\u5206\u6790\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1\u3001\u5b9a\u6027\u5206\u6790<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u5de6\u8fb9\u7684\u73af\u8def\u8fde\u63a5\u65b9\u5f0f\uff0c\u4ece M3 \u7684\u6805\u6781\u65ad\u5f00\u73af\u8def\uff0c\u4ee4 M3 \u6805\u538b\u4e0a\u5347\u65f6\uff0cM3 \u4e3a\u7ef4\u6301\u7535\u6d41\u6052\u5b9a\u800c\u5206\u538b\u589e\u52a0\uff0c\u5bfc\u81f4 M1\u3001M2 \u6805\u538b\u4e0b\u964d\uff0cM2 \u4e3a\u7ef4\u6301\u7535\u6d41\u6052\u5b9a\u5206\u538b\u589e\u52a0\uff0c\u5bfc\u81f4 \uff08M3\u3001\uff09M4 \u6805\u538b\u4e0a\u5347\uff0c\u6b63\u53cd\u9988\uff1b<\/p>\n\n\n\n<p>\u7c7b\u4f3c\u5730\uff0c\u5bf9\u4e8e\u53f3\u8fb9\u7684\u73af\u8def\u8fde\u63a5\u65b9\u5f0f\uff0c\u4ece M4 \u6805\u6781\u65ad\u5f00\u73af\u8def\uff0c\u4ee4 M4 \u6805\u538b\u4e0a\u5347\u65f6\uff0cM4 \u4e3a\u7ef4\u6301\u7535\u6d41\u6052\u5b9a\u800c\u5403\u6389\u66f4\u591a\u7535\u538b\uff0cM1\u3001M2 \u6805\u538b\u964d\u4f4e\uff0cM1 \u4e3a\u7ef4\u6301\u7535\u6d41\u6052\u5b9a\u5403\u6389\u66f4\u591a\u7535\u538b\uff0c\u4ece\u800c\u5bfc\u81f4 M3\uff08\u3001M4\uff09 \u6805\u538b\u4e0a\u5347\uff0c\u6b63\u53cd\u9988\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2\u3001\u5b9a\u91cf\u5206\u6790<\/h3>\n\n\n\n<p>\u63a5\u4e0b\u6765\uff0c\u5206\u522b\u8ba1\u7b97\u4e24\u79cd\u73af\u8def\u7684\u73af\u8def\u589e\u76ca\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.1 \u5de6\u8fb9\u7684\u73af\u8def\u8fde\u63a5\u65b9\u5f0f<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"374\" src=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-3.png\" alt=\"\" class=\"wp-image-989\" srcset=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-3.png 284w, https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-3-228x300.png 228w\" sizes=\"auto, (max-width: 284px) 100vw, 284px\" \/><\/figure>\n<\/div>\n\n\n<p>\u5728 M3 \u7684\u6805\u6781\u65ad\u5f00\u73af\u8def\uff0c\u65bd\u52a0\u5c0f\u4fe1\u53f7\u7535\u538b Vx\uff0cM3 \u4e0e M1 \u5f62\u6210\u4e86\u4e00\u4e2a\u4ee5\u4e8c\u6781\u7ba1\u8fde\u63a5\u5f62\u5f0f\u7684 M1 \u4e3a\u8d1f\u8f7d\u7684\u5171\u6e90\u6781\u653e\u5927\u5668\uff0c\u5219\u8be5\u90e8\u5206\u7684\u5c0f\u4fe1\u53f7\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nA_{V1}&amp;=-G_mR_{out}\\\\\n&amp;=-g_{m3}\\times\\frac{1}{g_{m1}}\n\\end{align*} $$\n\n\n\n<p>M2 \u4e0e M4 \u6784\u6210\u4e86\u5e26\u6709\u6e90\u6781\u8d1f\u53cd\u9988\u7684\u5171\u6e90\u6781\uff0c\u5c0f\u4fe1\u53f7\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nA_{V2}&amp;=-G_mR_{out}\\\\\n&amp;=-\\frac{g_{m2}\\times \\frac{1}{g_{m4}}}{1+g_{m2}R_S}\n\\end{align*} $$\n\n\n\n<p>\u6574\u4e2a\u73af\u8def\u7684\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nLG&amp;=A_{V1}A_{V2}\\\\\n&amp;=\\frac{g_{m3}}{g_{m1}}\\frac{g_{m2}\\times \\frac{1}{g_{m4}}}{1+g_{m2}R_S}\\mid_{g_{m3}=g_{m4}}\\\\\n&amp;=\\frac{1}{\\frac{g_{m1}}{g_{m2}}(1+g_{m2}R_S)}\n\\end{align*} $$\n\n\n\n<p>\u7531 gm \u7684\u8868\u8fbe\u5f0f\u53ef\u5f97\uff1a<\/p>\n\n\n\n$$ \\left\\{\\begin{matrix} \ng_{m1}=\\sqrt[]{2\\mu C_{ox}(\\frac{W}{L})_1I_D}\\\\\ng_{m2}=\\sqrt[]{2\\mu C_{ox}K(\\frac{W}{L})_1I_D}\n\\end{matrix}\n\\right. \\Rightarrow \\frac{g_{m1}}{g_{m2}}=\\frac{1}{\\sqrt{K}} $$\n\n\n\n<p>\u901a\u5e38\uff0c\u6211\u4eec\u53d6 K=4\uff0cg<sub>m2<\/sub>\u00d7Rs&gt;1\uff0c\u5219\u5206\u6bcd\u5927\u4e8e 1\uff0c\u73af\u8def\u589e\u76ca\u5c0f\u4e8e 1\uff0c\u73af\u8def\u7a33\u5b9a\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.2 \u53f3\u8fb9\u7684\u73af\u8def\u8fde\u63a5\u65b9\u5f0f<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"374\" src=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-5.png\" alt=\"\" class=\"wp-image-992\" srcset=\"https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-5.png 284w, https:\/\/dt9025a.top\/wp-content\/uploads\/2024\/10\/image-5-228x300.png 228w\" sizes=\"auto, (max-width: 284px) 100vw, 284px\" \/><\/figure>\n<\/div>\n\n\n<p>\u4e0e\u4e4b\u524d\u7684\u5206\u6790\u7c7b\u4f3c\uff0cM4 \u4e0e M2 \u5f62\u6210\u5171\u6e90\u6781\uff0c\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nA_{V1}&amp;=-G_mR_{out}\\\\\n&amp;=-g_{m4}\\times(\\frac{1}{g_{m2}}+R_S)\n\\end{align*} $$\n\n\n\n<p>M1 \u4e0e M3 \u5f62\u6210\u5171\u6e90\u6781\uff0c\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nA_{V2}&amp;=-G_mR_{out}\\\\\n&amp;=-g_{m1}\\times(\\frac{1}{g_{m3}})\n\\end{align*} $$\n\n\n\n<p>\u73af\u8def\u589e\u76ca\u4e3a\uff1a<\/p>\n\n\n\n$$ \\begin{align*}\nLG&amp;=A_{V1}A_{V2}\\\\\n&amp;=g_{m1}g_{m4}\\frac{1}{g_{m3}}(\\frac{1}{g_{m2}}+R_S)\\mid_{g_{m3}=g_{m4}}\\\\\n&amp;=(\\frac{1}{\\frac{g_{m1}}{g_{m2}}(1+g_{m2}R_S)})^{-1}\n\\end{align*} $$\n\n\n\n<p>\u6b64\u73af\u8def\u7684\u589e\u76ca\u4e3a\u4e4b\u524d\u8ba1\u7b97\u73af\u8def\u589e\u76ca\u7684\u5012\u6570\uff0c\u7531\u4e8e\u4e4b\u524d\u8ba1\u7b97\u7684\u73af\u8def\u589e\u76ca &lt; 1\uff1b\u56e0\u6b64\u8be5\u73af\u8def\u589e\u76ca &gt; 1\uff1b\u73af\u8def\u4e0d\u7a33\u5b9a\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u5bf9\u4e8e\u6b63\u786e\u73af\u8def\u7684\u8fde\u63a5\u65b9\u5f0f\uff0c\u8f93\u51fa\u7684\u7535\u6d41\u53ef\u4ee5\u88ab\u5982\u4e0b\u7684\u65b9\u5f0f\u8ba1\u7b97\u51fa\u6765\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nI_D &#038; = \\frac{1}{2}\\mu_nC_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\\\\nI_D &#038; = \\frac{1}{2}\\mu_nC_{ox}K\\frac{W}{L}(V_{GS}-I_DR_S-V_{TH})^2 \\\\\nI_DR_S &#038;= \\sqrt[]{\\frac{2I_D}{\\mu_nC_{ox}\\frac{W}{L}} } (1-\\frac{1}{\\sqrt[]{K} } ) \\\\\nI_D &#038;= \\frac{2}{\\mu_nC_{ox}\\frac{W}{L}} \\frac{1}{R_S^2} (1-\\frac{1}{\\sqrt[]{K} } )^2\n\\end{align}\n$$\n","protected":false},"excerpt":{"rendered":"<p>Reference \u6587\u7ae0\u94fe\u63a5 \u524d\u7f6e\u77e5\u8bc6 1\u3001\u8de8\u5bfc gm \u7684\u8868\u8fbe $$ \\begin{align*} g_m&#038;a&#8230; <\/p>\n<div class=\"read-more navbutton\"><a href=\"https:\/\/dt9025a.top\/?p=983\">\u9605\u8bfb\u66f4\u591a<i class=\"fa fa-angle-double-right\"><\/i><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":["post-983","post","type-post","status-publish","format-standard","hentry","category-ic-design"],"_links":{"self":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=983"}],"version-history":[{"count":1,"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/983\/revisions"}],"predecessor-version":[{"id":1178,"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/983\/revisions\/1178"}],"wp:attachment":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}