{"id":1134,"date":"2025-09-04T14:10:53","date_gmt":"2025-09-04T06:10:53","guid":{"rendered":"https:\/\/dt9025a.top\/?p=1134"},"modified":"2025-09-04T14:10:53","modified_gmt":"2025-09-04T06:10:53","slug":"%e5%ae%9a%e9%87%8f%e8%ae%a1%e7%ae%97%e8%bf%90%e7%ae%97%e6%94%be%e5%a4%a7%e5%99%a8%e4%b8%ad%e7%9a%84-vos","status":"publish","type":"post","link":"https:\/\/dt9025a.top\/?p=1134","title":{"rendered":"\u5b9a\u91cf\u8ba1\u7b97\u8fd0\u7b97\u653e\u5927\u5668\u4e2d\u7684 Vos"},"content":{"rendered":"
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ANALOG DESIGN ESSENTIALS\uff0cWilly M. C. Sansen<\/figcaption><\/figure>\n<\/div>\n\n\n\n\n\n\n
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\u5f15\u5165<\/h2>\n\n\n\n

\u5728\u5b9e\u9645\u7535\u8def\u4e2d\uff0c\u7531\u4e8e\u975e\u7406\u60f3\u56e0\u7d20\u7684\u5b58\u5728\u4f1a\u5bfc\u81f4\u5668\u4ef6\u4e4b\u95f4\u4ea7\u751f\u7269\u7406\u4e0a\u7684 Mismatch\uff0c\u8fdb\u800c\u5bfc\u81f4\u4e86\u7535\u8def Offset \u7684\u5b58\u5728\u3002\u901a\u5e38\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7 Monte Carlo \u4eff\u771f\u6765\u5bf9\u8fd9\u4e00\u60c5\u51b5\u8fdb\u884c\u8bc4\u4f30\u4eff\u771f\u3002<\/p>\n\n\n\n

\u5ffd\u7565\u6c9f\u9053\u957f\u5ea6\u8c03\u5236\u6548\u5e94\uff0c\u6676\u4f53\u7ba1\u5728\u9971\u548c\u533a\u7684\u7535\u6d41\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nI_D & = \\frac{1}{2} \\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH}) ^2\\\\\n & = \\frac{1}{2} \\beta (V_{GS}-V_{TH}) ^2\uff0c\u5176\u4e2d \\beta =\\mu C_{ox}\\frac{W}{L}\n\\end{align}\n$$\n\n\n\n

\u901a\u8fc7\u4e0a\u5f0f\uff0c\u5728 VGS<\/sub> \u6052\u5b9a\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5931\u914d\u5927\u4f53\u5206\u4e3a \u03b2 \u5931\u914d\u4e0e VTH<\/sub> \u5931\u914d\u3002<\/p>\n\n\n\n

\u5728\u4e0a\u56fe\u6240\u793a\u7684\u6298\u53e0\u5f0f\u5171\u6e90\u5171\u6805\u8fd0\u7b97\u653e\u5927\u5668\u4e2d\uff0cM1-2\u3001M5-6 \u4ee5\u53ca M10-11 \u4ea7\u751f\u7684\u5931\u914d\u5bf9 Offset \u7684\u8d21\u732e\u5ea6\u6700\u663e\u8457\uff0c\u800c M3-4\u3001M7-8 \u4ea7\u751f\u7684\u5931\u914d\u5bf9 Offset \u7684\u8d21\u732e\u5ea6\u8f83\u4e0d\u660e\u663e\uff08\u7c7b\u6bd4\u566a\u58f0\u7684\u8d21\u732e\u5ea6\uff09\u3002\u56e0\u6b64\uff0c\u5728\u8ba1\u7b97\u4e2d\u6211\u4eec\u4e0d\u8003\u8651 M3-4\u3001M7-8 \u4ea7\u751f\u7684\u5931\u914d\u3002<\/p>\n\n\n\n

\u4e0b\u6587\u8ba1\u7b97\u4ee5 M5-6 \u4e3a\u4f8b\uff0c\u5047\u5b9a Cox<\/sub> \u4e3a\u6052\u5b9a\u503c\uff0c\u5931\u914d\u91cf \u0394 \u6781\u5c0f\uff0c\u4e14\u8ba1\u7b97\u4e00\u4e2a\u9879\u76ee\u7684\u5931\u914d\u65f6\u5047\u5b9a\u5176\u4ed6\u9879\u76ee\u4e0d\u5b58\u5728\u5931\u914d\u3002ID5,6<\/sub>=ID1,2<\/sub>=ID<\/sub>=1\/2ID10,11<\/sub>\u3002<\/p>\n\n\n\n

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\u5931\u914d\u7535\u6d41\u7684\u63a8\u5bfc<\/h2>\n\n\n\n

\u03b2 \u5931\u914d\u5bfc\u81f4\u7684 \u0394I (\u03b2)<\/h3>\n\n\n\n

$$\u7531\u4e8e \\beta =\\mu C_{ox}\\frac{W}{L}\uff0c\u6211\u4eec\u5206\u522b\u63a8\u5bfc \\mu\uff0cW\uff0cL \u5931\u914d\u7684\u8868\u8fbe\u5f0f\uff0c\u8fdb\u800c\u5f97\u5230 \\beta \u5931\u914d\u7684\u8868\u8fbe\u3002$$<\/p>\n\n\n\n

\u5bf9\u4e8e \u03bc \u5931\u914d\uff0c\u6709\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nI_{D5}&=\\frac{1}{2}\\mu _5C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\\\\nI_{D6}&=\\frac{1}{2}\\mu _6C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\\\ \n\\newline \n\\Delta I_D (\\mu)&=I_{D5}-I_{D6} \\\\\n&=\\frac{1}{2}(\\mu _5-\\mu _6)C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2\\\\\n&=\\frac{1}{2}\\Delta \\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\\\\n&=\\frac{1}{2}\\Delta \\mu \\frac{\\mu }{\\mu } C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\\\\n&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})^2 \\frac{\\Delta \\mu }{\\mu }\\\\\n&=I_D \\frac{\\Delta \\mu }{\\mu }\\\\\n\\end{align}\n$$\n\n\n\n

\u540c\u7406\uff0c\u5bf9\u4e8e W \u5931\u914d\uff0c\u6709\uff1a<\/p>\n\n\n\n$$\n\\Delta I_D(W)=I_D \\frac{\\Delta W }{W }\n$$\n\n\n\n

\u5bf9\u4e8e L \u5931\u914d\uff0c\u6709\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nI_{D5}&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L_5}(V_{GS}-V_{TH})^2 \\\\\nI_{D6}&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L_6}(V_{GS}-V_{TH})^2 \\\\ \nL_6 &= L_5+\\Delta L\\\\\n\\newline \n\\Delta I_D(L)&=I_{D5}-I_{D6} \\\\\n&=\\frac{1}{2}\\mu C_{ox}(\\frac{W}{L_5}-\\frac{W}{L_6})(V_{GS}-V_{TH})^2\\\\\n&=\\frac{1}{2}\\mu C_{ox}(\\frac{W}{L_5}-\\frac{W}{L_5+\\Delta L})(V_{GS}-V_{TH})^2\\\\\n&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}(\\frac{\\Delta L}{L+\\Delta L})(V_{GS}-V_{TH})^2\\\\\n&=I_D\\frac{\\Delta L}{L+\\Delta L}\\\\\n\\newline \n\u53c8\u56e0\u4e3a \\Delta L &\\rightarrow 0\uff0c\u6709\uff1a\\\\\n\\Delta I_D(L)&=I_D\\frac{\\Delta L}{L+\\Delta L} \\\\\n & \\approx I_D\\frac{\\Delta L}{L}\n\\end{align}\n$$\n\n\n\n

\u5bf9\u4e0a\u8ff0\u7ed3\u679c\u8fdb\u884c\u5f52\u7eb3\u603b\u7ed3\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230 \u03b2 \u5931\u914d\u5bfc\u81f4\u7684 \u0394I (\u03b2) \u7684\u8868\u8fbe\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n$$\n\\Delta I(\\beta )=I_D\\frac{\\Delta \\beta }{\\beta } \n$$\n\n\n\n

VTH<\/sub> \u5931\u914d\u5bfc\u81f4\u7684 \u0394I (VTH<\/sub>)<\/h3>\n\n\n\n\\begin{align}\nI_{D5}&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH5})^2 \\\\\nI_{D6}&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH6})^2 \\\\ \nV_{TH6} &= V_{TH5}+\\Delta V_{TH}\\\\\n\\newline \n\\Delta I_D(V_{TH})&=I_{D5}-I_{D6} \\\\\n&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}[(V_{GS}-V_{TH5})^2-(V_{GS}-V_{TH6})^2 ]\\\\\n&=\\frac{1}{2}\\mu C_{ox}\\frac{W}{L}[2\\Delta V_{TH}(V_{GS}-V_{TH})-\\Delta V_{TH}^2]\\\\\n\\newline \n\u53c8\u56e0\u4e3a \\Delta V_{TH} &\\rightarrow 0\uff0cg_m=\\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})\uff1a\\\\\n\\Delta I_D(V_{TH})&\\approx\\mu C_{ox}\\frac{W}{L}(V_{GS}-V_{TH})\\Delta V_{TH}\\\\\n&=g_m\\Delta V_{TH}\n\\end{align}\n\n\n\n
\n\n\n\n

\u8f93\u5165\u7aef\u7b49\u6548 VOS<\/sub> \u7684\u8ba1\u7b97<\/h2>\n\n\n\n

\u4e0a\u6587\u6211\u4eec\u5df2\u7ecf\u8ba1\u7b97\u5f97\u5230\u4e86\u5931\u914d\u6240\u5bfc\u81f4\u7684 \u0394I\uff0c\u4f46\u901a\u5e38\u6211\u4eec\u6240\u9700\u7684\u662f\u5931\u914d\u4ea7\u751f\u7684 VOS<\/sub> \u800c\u4e0d\u662f \u0394I\u3002\u4e3a\u4e86\u5c06 \u0394I \u8f6c\u6362\u4e3a\u8f93\u51fa\u7aef VOS<\/sub>\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5c06\u5176\u4e58\u4ee5 Rout<\/sub> \u5373\u53ef\uff1a<\/p>\n\n\n\n$$\nV_{OS}=\\Delta I\\times R_{out}\n$$\n\n\n\n

\u5c06\u8f93\u51fa\u7aef VOS<\/sub> \u8f6c\u6362\u4e3a\u8f93\u5165\u7aef VOS<\/sub>\uff0c\u9700\u8981\u5c06 VOS<\/sub> \/ Av\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nV_{OS,in}&=\\frac{V_{OS,out}}{A_V} \\\\\n&= \\frac{\\Delta I\\times R_{out}}{G_{m}\\times R_{out}} \\\\\n&= \\frac{\\Delta I}{G_{m}} \\\\\n\\end{align}\n$$\n\n\n\n

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\u6574\u4f53\u5931\u8c03\u7684\u8ba1\u7b97<\/h2>\n\n\n\n

\u5c06\u4e0a\u6587\u6240\u8ff0\u7684 \u0394I (\u03b2) \u4e0e \u0394I (VTH<\/sub>) \u6574\u5408\uff0c\u5e76\u7b49\u6548\u4e3a\u8f93\u5165\u7aef VOS<\/sub>\uff0c\u53ef\u5f97\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nV_{OS} &= \\frac{(\\Delta I(\\beta _{5-6,10-11})+\\Delta I(V_{TH_{5-6,10-11}}))R_{Out}}{A_V} +\\Delta V_{TH_{1,2}} \\\\\n&=\\frac{g_{m_{5,6}}}{g_{m_{1,2}}} \\Delta V_{TH_{5,6}}+\\frac{g_{m_{10,11}}}{g_{m_{1,2}}} \\Delta V_{TH_{10,11}} +\n\\frac{I_D(\\frac{\\Delta \\beta _{1,2}}{\\beta _{1,2}} +\\frac{\\Delta \\beta _{5,6}}{\\beta _{5,6}})R_{Out}}{g_{m_{1,2}}R_{Out}} +\\frac{2I_D\\frac{\\Delta \\beta _{10,11}}{\\beta _{10,11}}R_{Out}}{g_{m_{1,2}}R_{Out}} +\n\\Delta V_{TH_{1,2}} \\\\\n&=\\frac{g_{m_{5,6}}}{g_{m_{1,2}}} \\Delta V_{TH_{5,6}}+\\frac{g_{m_{10,11}}}{g_{m_{1,2}}} \\Delta V_{TH_{10,11}} +\n\\frac{V_{GS_1}-V_{TH_1}}{2} (\\frac{\\Delta \\beta _{1,2}}{\\beta _{1,2}} +\\frac{\\Delta \\beta _{5,6}}{\\beta _{5,6}}+2\\frac{\\Delta \\beta _{10,11}}{\\beta _{10,11}}) +\n\\Delta V_{TH_{1,2}} \n\\end{align}\n$$\n\n\n\n

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\u8865\u5145 – \u5171\u6e90\u5171\u6805\u7ea7\u4e2d\u5171\u6805\u7ba1\u7684\u5931\u8c03<\/h2>\n\n\n\n

\u5bf9\u4e8e\u5171\u6805\u7ba1\uff0c\u5728 gmRs >> 1 \u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\nG_{m7} = \\frac{g_{m7}}{1+g_{m7}R_s} &\\approx \\frac{1}{R_s} \\\\\n\u5176\u4e2d\uff0cR_s &=r_{o5} \\\\\n\u5219\u6709 G_{m7}&\\approx \\frac{1}{r_{o5}} \n\\end{align}\n$$\n\n\n\n

\u5047\u8bbe \u0394VTH7,8<\/sub>\uff0c\u6709\uff1a<\/p>\n\n\n\n$$\n\\begin{align}\n\\Delta V_{in}&=\\frac{G_{m7}\\Delta V_{TH}}{g_{m_{in}}} \\\\\n&=\\frac{\\Delta V_{TH}}{g_{m_{in}}r_{o5}}=(\\frac{1}{g_{m7}r_{o5}} )\\frac{\\Delta V_{TH}g_{m7}}{g_{m_{in}}}\n\\end{align}\n$$\n\n\n\n

\u56e0\u6b64\uff0c\u4ece\u4e0a\u8ff0\u63a8\u5bfc\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\uff0c\u76f8\u8f83\u4e8e\u5171\u6e90\u7ba1\uff0c\u5171\u6805\u7ba1\u7684\u7b49\u6548\u8f93\u5165 VOS<\/sub> \u88ab\u7f29\u5c0f\u4e86 gm7<\/sub>ro5<\/sub> \u500d\uff0c\u56e0\u6b64\u5728\u901a\u5e38\u7684\u8ba1\u7b97\u4e2d\u4e0d\u4e88\u8003\u8651\u3002<\/p>\n\n\n\n

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\u53c2\u8003\u9605\u8bfb<\/h2>\n\n\n\n

\u5dee\u5206\u8fd0\u653e\u5931\u8c03\u7535\u538b\u7684\u624b\u5de5\u8ba1\u7b97<\/a><\/p>\n\n\n\n

[\u539f\u521b] \u5dee\u5206\u8fd0\u653e\u8f93\u5165\u5931\u8c03\u5206\u6790<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

ANALOG DESIGN ESSENTIALS\uff0cWilly M. C. Sansen \u5f15\u5165 \u5728\u5b9e\u9645\u7535\u8def\u4e2d\uff0c\u7531… <\/p>\n

\u9605\u8bfb\u66f4\u591a<\/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":[15,9],"tags":[],"class_list":["post-1134","post","type-post","status-publish","format-standard","hentry","category-ic-design","category-9"],"_links":{"self":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/1134","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=1134"}],"version-history":[{"count":2,"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/1134\/revisions"}],"predecessor-version":[{"id":1179,"href":"https:\/\/dt9025a.top\/index.php?rest_route=\/wp\/v2\/posts\/1134\/revisions\/1179"}],"wp:attachment":[{"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dt9025a.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}