{"id":28603,"date":"2026-01-10T09:02:54","date_gmt":"2026-01-10T01:02:54","guid":{"rendered":"https:\/\/techclass.wfjydl.com\/?p=28603"},"modified":"2026-01-12T12:03:07","modified_gmt":"2026-01-12T04:03:07","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e8%8a%82%e7%82%b9%e5%88%86%e6%9e%90%e6%b3%95%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/techclass.wfjydl.com\/knowledge\/circuit-design\/circuit-design-basic\/26747","title":{"rendered":"\u4ec0\u4e48\u662f\u8282\u70b9\u5206\u6790\u6cd5\uff1f"},"content":{"rendered":"\\(\\)\n<h1 class=\"c-ttl-5\">\u4ec0\u4e48\u662f\u8282\u70b9\u5206\u6790\u6cd5\uff1f<\/h1>\n<p>\u8282\u70b9\u5206\u6790\u6cd5\uff08\u8282\u70b9\u7535\u538b\u6cd5\u3001\u8282\u70b9\u7535\u4f4d\u6cd5\uff09\u662f\u4e00\u79cd\u7535\u8def\u5206\u6790\u6280\u672f\uff0c\u4ee5\u7535\u8def\u4e2d\u5404\u8282\u70b9\uff08\u8fde\u63a5\u70b9\uff09\u7684\u7535\u4f4d\u4f5c\u4e3a\u672a\u77e5\u91cf\uff0c\u8fd0\u7528\u57fa\u5c14\u970d\u592b\u7535\u6d41\u5b9a\u5f8b\uff08KCL\uff09\u5efa\u7acb\u8054\u7acb\u65b9\u7a0b\u8fdb\u884c\u6c42\u89e3\u3002\u4f5c\u4e3a\u4e0e\u7f51\u5b54\u5206\u6790\u6cd5\u540c\u6837\u91cd\u8981\u7684\u7ecf\u5178\u7535\u8def\u5206\u6790\u65b9\u6cd5\uff0c\u5373\u4f7f\u662f\u5305\u542b\u4f17\u591a\u7535\u963b\u548c\u7535\u6e90\u7684\u590d\u6742\u7535\u8def\uff0c\u5229\u7528\u8be5\u65b9\u6cd5\u4e5f\u80fd\u51c6\u786e\u6c42\u51fa\u5404\u8282\u70b9\u7684\u7535\u538b\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u9610\u8ff0\u8282\u70b9\u5206\u6790\u6cd5\u7684\u5177\u4f53\u8ba1\u7b97\u6b65\u9aa4\u3002<\/p>\n<h2 id=\"toc1\">\u8282\u70b9\u5206\u6790\u6cd5\u6982\u8ff0<\/h2>\n<p>\u8282\u70b9\u5206\u6790\u6cd5\u662f\u5c06\u7535\u8def\u4e2d\u5404\u8282\u70b9\u7684\u7535\u4f4d\u4f5c\u4e3a\u672a\u77e5\u91cf\u8fdb\u884c\u5b9a\u4e49\uff0c\u5e76\u8fd0\u7528\u57fa\u5c14\u970d\u592b\u7535\u6d41\u5b9a\u5f8b\uff08KCL\uff09\u6765\u8868\u793a\u6d41\u5165\u548c\u6d41\u51fa\u8be5\u8282\u70b9\u7684\u7535\u6d41\u603b\u548c\u7684\u5206\u6790\u65b9\u6cd5\u3002\u968f\u7740\u7535\u8def\u590d\u6742\u7a0b\u5ea6\u7684\u589e\u52a0\uff0c\u9010\u4e2a\u8ffd\u8e2a\u5404\u4e2a\u7535\u6d41\u548c\u7535\u538b\u7684\u96be\u5ea6\u4e5f\u8d8a\u6765\u8d8a\u5927\u3002\u901a\u8fc7\u805a\u7126\u4e8e\u8282\u70b9\u95f4\u7684\u7535\u4f4d\u5dee\uff0c\u53ef\u5c06\u95ee\u9898\u4ee5\u8054\u7acb\u65b9\u7a0b\u7684\u5f62\u5f0f\u8fdb\u884c\u7b80\u6d01\u660e\u4e86\u7684\u5904\u7406\u3002\u5728\u4e0b\u56fe\u793a\u4f8b\u4e2d\uff0c\u672a\u77e5\u8282\u70b9\u88ab\u8bbe\u4e3a\u201c\u8282\u70b9V\u201d\uff0c\u5e76\u5c06\u5176\u7535\u4f4d\u4f5c\u4e3a\u672a\u77e5\u91cf\u5904\u7406\u3002<\/p>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/01-overview-of-nodal-analysis.jpg\" alt=\"\u8282\u70b9\u5206\u6790\u6cd5\u7684\u6982\u5ff5\" width=\"700\" height=\"394\" \/><\/p>\n<h3 id=\"toc2\">\u8282\u70b9\u4e0e\u53c2\u8003\u8282\u70b9\uff08\u57fa\u51c6\u8282\u70b9\uff09<\/h3>\n<p>\u901a\u5e38\u4f1a\u9009\u62e9\u7535\u8def\u4e2d\u7684\u4efb\u610f\u4e00\u70b9\u4f5c\u4e3a\u53c2\u8003\u8282\u70b9\uff08\u63a5\u5730\uff09\u3002\u4ee5\u8be5\u53c2\u8003\u8282\u70b9\u4e3a\u53c2\u8003\u70b9\uff0c\u5c06\u5176\u4ed6\u6240\u6709\u8282\u70b9\u7535\u538b\u5747\u5b9a\u4e49\u4e3a\u76f8\u5bf9\u4e8e\u8be5\u70b9\u7684\u76f8\u5bf9\u7535\u4f4d\u3002\u7531\u4e8e\u672a\u77e5\u91cf\u7684\u6570\u91cf\u7b49\u4e8e\u201c\u8282\u70b9\u6570\u51cf1\u201d\uff0c\u56e0\u6b64\u5373\u4f7f\u7535\u8def\u89c4\u6a21\u5e9e\u5927\uff0c\u4e5f\u53ef\u6709\u6548\u7f29\u51cf\u8054\u7acb\u65b9\u7a0b\u7684\u89c4\u6a21\u3002<\/p>\n<h2 id=\"toc3\">\u8282\u70b9\u5206\u6790\u6cd5\u7684\u7406\u8bba\u57fa\u7840<\/h2>\n<p>\u8282\u70b9\u5206\u6790\u6cd5\u4e3b\u8981\u7ed3\u5408\u57fa\u5c14\u970d\u592b\u7535\u6d41\u5b9a\u5f8b\uff08KCL\uff09\u548c\u6b27\u59c6\u5b9a\u5f8b\u8fdb\u884c\u5206\u6790\u3002KCL\u8868\u660e\u6d41\u5165\u8282\u70b9\u7684\u7535\u6d41\u603b\u548c\u7b49\u4e8e\u6d41\u51fa\u8282\u70b9\u7684\u7535\u6d41\u603b\u548c\uff0c\u800c\u6b27\u59c6\u5b9a\u5f8b\u5219\u63ed\u793a\u4e86\u7535\u538b\u4e0e\u7535\u6d41\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\u3002\u901a\u8fc7\u4e0e\u8fd9\u4e9b\u5b9a\u5f8b\u76f8\u7ed3\u5408\uff0c\u4e3a\u5404\u8282\u70b9\u5efa\u7acb\u65b9\u7a0b\u5e76\u6c42\u89e3\u8054\u7acb\u65b9\u7a0b\uff0c\u5373\u53ef\u5b8c\u6210\u6574\u4e2a\u7535\u8def\u7684\u5206\u6790\u3002<\/p>\n<h3 id=\"toc4\">\u57fa\u5c14\u970d\u592b\u7535\u6d41\u5b9a\u5f8b\uff08KCL\uff09\u7684\u5e94\u7528<\/h3>\n<p>\u5bf9\u4e8e\u5355\u4e00\u8282\u70b9\u800c\u8a00\uff0c\u6d41\u5165\u8be5\u8282\u70b9\u7684\u7535\u6d41\u603b\u548c\u4e0e\u6d41\u51fa\u8be5\u8282\u70b9\u7684\u7535\u6d41\u603b\u548c\u76f8\u7b49\uff1a<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(i_1+i_2+\u22ef+i_n=0\\)<\/span><\/p>\n<p>\u8fd9\u662f\u8282\u70b9\u5206\u6790\u7684\u57fa\u672c\u65b9\u7a0b\u3002<\/p>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/02-relationship-between-kcl-and-nodal-analysis.jpg\" alt=\"\u8282\u70b9\u5206\u6790\u4e0eKCL\u7684\u5173\u7cfb\" width=\"700\" height=\"394\" \/><\/p>\n<h3 id=\"toc5\">\u6b27\u59c6\u5b9a\u5f8b\u4e0e\u963b\u6297<\/h3>\n<p>\u5404\u652f\u8def\u7535\u6d41\u53ef\u7531\u5143\u5668\u4ef6\u4e24\u7aef\u7684\u7535\u4f4d\u5dee\u9664\u4ee5\u7535\u963b\u6216\u963b\u6297\u6765\u8868\u793a\u3002<\/p>\n<p>\u7535\u963bR\u65f6\uff1a<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(i=\\displaystyle\\frac{(V_1-V_2)}{R}\\)<\/span><\/p>\n<p>\u540c\u6837\u5730\uff0c\u7535\u5bb9\u548c\u7535\u611f\u5206\u522b\u4ee5\u9891\u57df\u4e2d\u7684\u963b\u6297\\({j\u03c9L}\\)\u548c1\/(\\({j\u03c9C}\\))\u6765\u8868\u793a\u3002<\/p>\n<h2 id=\"toc6\">\u8282\u70b9\u5206\u6790\u7684\u57fa\u672c\u6b65\u9aa4<\/h2>\n<p>\u4e0b\u9762\u662f\u5206\u9636\u6bb5\u5b9e\u65bd\u8282\u70b9\u5206\u6790\u7684\u6b65\u9aa4\u53ca\u6ce8\u610f\u4e8b\u9879\u3002\u5373\u4f7f\u662f\u5927\u89c4\u6a21\u7684\u590d\u6742\u7535\u8def\uff0c\u53ea\u8981\u6309\u6b65\u9aa4\u8fdb\u884c\uff0c\u4e5f\u53ef\u9ad8\u6548\u7387\u5730\u6c42\u89e3\u672a\u77e5\u8282\u70b9\u7535\u538b\u3002\u672c\u8282\u5c06\u8be6\u7ec6\u9610\u8ff0\u91c7\u7528\u77e9\u9635\u5f62\u5f0f\uff08\u77e9\u9635\u6cd5\uff09\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff08\u542b\u4e2d\u95f4\u6b65\u9aa4\uff09\u3002<\/p>\n<h3 id=\"toc7\">\u7b2c\u4e00\u6b65\uff1a\u9009\u62e9\u53c2\u8003\u8282\u70b9<\/h3>\n<p>\u5c06\u7535\u8def\u4e2d\u7684\u4e00\u4e2a\u8282\u70b9\u8bbe\u4e3a\u53c2\u8003\u8282\u70b9\uff08\u63a5\u5730\uff0c0V\uff09\u3002\u901a\u5e38\uff0c\u9009\u62e9\u8fde\u63a5\u5143\u5668\u4ef6\u6700\u591a\u7684\u8282\u70b9\u6216\u5b9e\u9645\u7535\u8def\u4e2d\u7528\u4f5c\u63a5\u5730\u7aef\u5b50\u7684\u8282\u70b9\uff0c\u53ef\u51cf\u5c11\u672a\u77e5\u91cf\uff0c\u4f7f\u8ba1\u7b97\u66f4\u7b80\u5355\u3002<\/p>\n<p><strong>\u53c2\u8003\u8282\u70b9\u9009\u62e9\u8981\u70b9<\/strong><\/p>\n<ul class=\"unordered-list\">\n<li>\u9009\u62e9\u8fde\u63a5\u591a\u4e2a\u5143\u5668\u4ef6\uff08\u7535\u963b\u3001\u7535\u6e90\u3001\u8d1f\u8f7d\u7b49\uff09\u7684\u8282\u70b9\u66f4\u5bb9\u6613\u5efa\u7acb\u65b9\u7a0b\u3002<\/li>\n<li>\u5728\u540c\u65f6\u5b58\u5728\u76f4\u6d41\u7535\uff08DC\uff09\u548c\u4ea4\u6d41\u7535\uff08AC\uff09\u7684\u591a\u7535\u6e90\u6df7\u5408\u7535\u8def\u4e2d\uff0c\u53ef\u80fd\u6709\u4e9b\u590d\u6742\uff0c\u4f46\u9009\u62e9\u80fd\u4f7f\u8ba1\u7b97\u540e\u7684\u5904\u7406\u66f4\u7b80\u5355\u7684\u8282\u70b9\u4f5c\u4e3a\u53c2\u8003\u70b9\u66f4\u4e3a\u6709\u5229\u3002<\/li>\n<\/ul>\n<h3 id=\"toc8\">\u7b2c\u4e8c\u6b65\uff1a\u5b9a\u4e49\u8282\u70b9\u7535\u538b<\/h3>\n<p>\u7ed9\u53c2\u8003\u8282\u70b9\u4ee5\u5916\u7684\u5404\u8282\u70b9\u5206\u914d\u7535\u538b\\(V_1\\),\u202f\\(V_2\\),\u202f\u2026,\u202f\\(V_n\\)\u8bbe\u603b\u8282\u70b9\u6570\u4e3a\\(N\\)\u65f6\uff0c\u672a\u77e5\u91cf\u4e3a\uff08\\(N\\)\u22121\uff09\u4e2a\u3002\u5373\u4f7f\u662f\u5927\u89c4\u6a21\u7535\u8def\uff0c\u4e5f\u53ef\u660e\u786e\u53d8\u91cf\u7684\u6570\u91cf\u3002<\/p>\n<h3 id=\"toc9\">\u7b2c\u4e09\u6b65\uff1a\u5efa\u7acb\u5404\u8282\u70b9\u7684KCL\u65b9\u7a0b<\/h3>\n<p>\u5173\u4e8e\u5404\u8282\u70b9<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\u03a3\\)<\/span><span class=\"fz-120\">(\u6d41\u5165\u7535\u6d41)<\/span><span class=\"mathjax-text\">\\(=0\\)<\/span><\/p>\n<p>\u5bf9\u4e8e\u7535\u963b\u548c\u963b\u6297\u800c\u8a00\uff0c\u5747\u53ef\u8fd0\u7528\u6b27\u59c6\u5b9a\u5f8b\u6765\u8868\u793a\u7535\u6d41\u3002<\/p>\n<ul class=\"unordered-list\">\n<li>\u4f8b\u5982\uff0c\u8282\u70b9\\(V\\)\u901a\u8fc7\u7535\u963b\\(R_1\\)\u8fde\u63a5\u81f3\u7535\u538b\u6e90\\(E_1\\)\uff08\u5de6\u4fa7\u8282\u70b9\uff09\uff0c\u5e76\u8fdb\u4e00\u6b65\u901a\u8fc7\u7535\u963b\\(R_2\\)\u548c\\(R_3\\)\u8fde\u63a5\u81f3\u53c2\u8003\u8282\u70b9\\(G\\)=0V\u65f6\uff0c\u9488\u5bf9\u8282\u70b9\\(V\\)\u7684KCL\u65b9\u7a0b\u4e3a\uff1a\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\\displaystyle\\frac{V-E_1}{R_1}+\\displaystyle\\frac{V}{R_2}+\\displaystyle\\frac{V}{R_3}=0\\)<\/span><\/li>\n<\/ul>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/03-write-kcl-equations-at-node-v.jpg\" alt=\"\u5bf9\u8282\u70b9\u5e94\u7528KCL\" width=\"700\" height=\"394\" \/><\/p>\n<p><strong>\u4e2d\u95f4\u8ba1\u7b97\u8be6\u7ec6\u793a\u4f8b<\/strong><\/p>\n<p>\u8bbe\\(R_1\\)=3\u03a9\u3001\\(R_2\\)=6\u03a9\u3001\\(R_3\\)=9\u03a9\u3001\u7535\u538b\u6e90\\(E_1\\)=12V\u3001\u672a\u77e5\u8282\u70b9\u7535\u538b\u4e3a\\(V\\)\u5219<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\\displaystyle\\frac{V-12}{3}+\\displaystyle\\frac{V}{6}+\\displaystyle\\frac{V}{9}=0\\)<\/span><\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\u27f9V\u22486.55V\\)<\/span><\/p>\n<p>\u5728\u8fd9\u91cc\u57fa\u4e8eKCL\u5f97\u51fa\u7684\u65b9\u7a0b\uff0c\u4e5f\u79f0\u4e3a\u201c\u8282\u70b9\u65b9\u7a0b\uff08\u8282\u70b9\u7535\u538b\u65b9\u7a0b\uff09\u201d\u3002\u5f53\u5b58\u5728\u5176\u4ed6\u8282\u70b9\u65f6\uff0c\u4e5f\u53ef\u4ee5\u540c\u6837\u5730\u5efa\u7acb\u76f8\u5e94\u7684\u65b9\u7a0b\uff0c\u901a\u8fc7\u8054\u7acb\u6c42\u89e3\u5f97\u51fa\u5404\u8282\u70b9\u7684\u7535\u4f4d\u3002<\/p>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/04-write-kcl-equations-at-node-v-example.jpg\" alt=\"\u5bf9\u8282\u70b9\u5e94\u7528KCL\u7684\u793a\u4f8b\" width=\"700\" height=\"394\" \/><\/p>\n<h3 id=\"toc10\">\u7b2c\u56db\u6b65\uff1a\u6574\u7406\u4e3a\u77e9\u9635\u5f62\u5f0f\u5e76\u6c42\u89e3<\/h3>\n<p>\u5c06\u8054\u7acb\u65b9\u7a0b\u6574\u7406\u4e3a\u5bfc\u7eb3\u77e9\u9635\\(G\\)\u4e0e\u672a\u77e5\u8282\u70b9\u7535\u538b\u5411\u91cf\\(V\\)\u7684\u4e58\u79ef\\({GV}\\) = \\(I\\)\u540e\uff0c\u4fbf\u53ef\u8fdb\u884c\u7cfb\u7edf\u6027\u5904\u7406\u3002\u5f53\u672a\u77e5\u91cf\u8f83\u591a\u65f6\uff0c\u53ef\u91c7\u7528\u8ba1\u7b97\u673a\u7684\u8054\u7acb\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3\u5668\uff08\u77e9\u9635\u6c42\u89e3\u5668\uff09\uff0c\u53ea\u8981\u6b63\u786e\u6784\u5efa\u77e9\u9635\\(G\\)\u5373\u53ef\u901a\u8fc7\\(V\\)=\\(G^{-1}\\)\\(I\\)\u6c42\u89e3\u3002<\/p>\n<p><strong>\u77e9\u9635\u6cd5\u793a\u4f8b<\/strong><\/p>\n<p>\u672a\u77e5\u91cf\u4e2d\u5305\u542b\u8282\u70b9\u7535\u538b\u548c\u90e8\u5206\u7535\u6d41\u65f6\u7684\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<ol class=\"ordered-list\">\n<li>\u5c06KCL\u3001\u7535\u538b\u6e90\u7684\u7ea6\u675f\u77e9\u9635\u5316<\/li>\n<li>\u901a\u8fc7\u9006\u77e9\u9635\u6216\u9ad8\u65af\u6d88\u5143\u6cd5\u7b49\u76f4\u63a5\u7684\u65b9\u6cd5\u6c42\u89e3\\({GV}\\) = \\(I\\)<\/li>\n<\/ol>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/05-nodal-analysis-using-matrix-form.jpg\" alt=\"\u57fa\u4e8e\u77e9\u9635\u5f62\u5f0f\u7684\u8282\u70b9\u5206\u6790\u6cd5\" width=\"700\" height=\"394\" \/><\/p>\n<p>\u8865\u5145\u8bf4\u660e\uff1a\u5bf9\u4e8e\u7535\u538b\u6e90\u8f83\u591a\u4e14\u56de\u8def\u6570\u8f83\u5c11\u7684\u5e73\u9762\u7535\u8def\uff0c\u91c7\u7528\u7f51\u5b54\u5206\u6790\u6cd5\u53ef\u80fd\u4f1a\u4f7f\u672a\u77e5\u91cf\u66f4\u5c11\u3002<\/p>\n<h2 id=\"toc11\">\u8d85\u8282\u70b9\u7684\u5904\u7406<\/h2>\n<p>\u5f53\u4e24\u4e2a\u975e\u53c2\u8003\u8282\u70b9\u4e4b\u95f4\u76f4\u63a5\u8fde\u63a5\u72ec\u7acb\u7535\u538b\u6e90\u65f6\uff0c\u4ec5\u9760\u5e38\u89c4\u7684KCL\u65b9\u5f0f\u662f\u4e0d\u591f\u7684\u3002\u8fd9\u79cd\u60c5\u51b5\u79f0\u4e3a\u201c\u8d85\u8282\u70b9\u201d\uff0c\u9700\u8981\u6dfb\u52a0\u7535\u538b\u7ea6\u675f\u65b9\u7a0b\u3002<\/p>\n<h3 id=\"toc12\">\u8d85\u8282\u70b9\u7684\u6982\u5ff5<\/h3>\n<p>\u5728\u5c06\u7535\u538b\u6e90\u8fde\u63a5\u7684\u4e24\u4e2a\u8282\u70b9\u89c6\u4e3a\u4e00\u4e2a\u201c\u5408\u6210\u8282\u70b9\u201d\u5e76\u5e94\u7528KCL\u65f6\uff0c\u9700\u540c\u65f6\u6dfb\u52a0\u7535\u538b\u6761\u4ef6\uff1a\\(V_1\\)\u2212\\(V_2\\)=\u7535\u538b\u6e90\u3002<\/p>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/06-concept-of-supernode.jpg\" alt=\"\u8d85\u8282\u70b9\u7684\u6982\u5ff5\" width=\"700\" height=\"394\" \/><\/p>\n<p><strong>\u6ce8\u610f\u7535\u538b\u6e90\u7684\u6781\u6027<\/strong><\/p>\n<ul class=\"unordered-list\">\n<li>\u5982\u679c\u5c06\\(V_1\\)\u2212\\(V_2\\)=\\(V_S\\)\u6216\\(V_2\\)\u2212\\(V_1\\)=\\(V_S\\)\u5904\u7406\u9519\u8bef\uff0c\u5c06\u4f1a\u5bfc\u81f4\u7b26\u53f7\u9519\u8bef\u3002<\/li>\n<\/ul>\n<h3 id=\"toc13\">\u8d85\u8282\u70b9\u65b9\u7a0b\u548c\u4e2d\u95f4\u8ba1\u7b97<\/h3>\n<p>\u4f8b\u5982\uff0c\u8282\u70b9A\u548c\u8282\u70b9B\u901a\u8fc7\u7535\u538b\u6e90\\(V_S\\)\u76f8\u8fde\uff0c\u4e14\u5404\u81ea\u5bf9\u53c2\u8003\u8282\u70b9\u5b58\u5728\u7535\u963b\u65f6\uff1a<\/p>\n<ol class=\"ordered-list\">\n<li><strong>KCL\uff08\u8d85\u8282\u70b9\u6574\u4f53\uff09<\/strong>\n<p>(\\(V_1\\)\u22120)\/\\(R_1\\)+(\\(V_2\\)\u22120)\/\\(R_2\\)+\u2026=0<\/li>\n<li><strong>\u7535\u538b\u7ea6\u675f<\/strong>\n<p>\\(V_1\\)\u2212\\(V_2\\)=\\(V_S\\)<\/li>\n<\/ol>\n<p>\u5c06\u4e24\u8005\u6574\u5408\u81f3\\({GV}\\) = \\(I\\)\u4e2d\u3002<\/p>\n<h2 id=\"toc14\">\u8282\u70b9\u5206\u6790\u6cd5\u7684\u5b9e\u8df5\u6848\u4f8b<\/h2>\n<p>\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528\u4ee3\u5165\u4e86\u5177\u4f53\u6570\u503c\u7684\u7535\u8def\u3001\u5206\u6b65\u9aa4\u8fdb\u884c\u8282\u70b9\u5206\u6790\u7684\u793a\u4f8b\u3002\u793a\u4f8b\u4e2d\u4e5f\u7ed9\u51fa\u4e86\u5728\u4e0d\u7701\u7565\u4e2d\u95f4\u8ba1\u7b97\u6b65\u9aa4\u7684\u60c5\u51b5\u4e0b\uff0c\u540c\u65f6\u5c06\u7535\u6d41\u548c\u8282\u70b9\u7535\u538b\u7eb3\u5165\u77e9\u9635\u89e3\u7684\u5206\u6790\u65b9\u6cd5\u3002<\/p>\n<h3 id=\"toc15\">\u95ee\u9898\u8bbe\u5b9a<\/h3>\n<p>\u6c42\u5305\u542b\u591a\u4e2a\u7535\u538b\u6e90\u548c\u7535\u963b\u7684\u7535\u8def\uff08\u5982\u4e0b\u56fe\u6240\u793a\uff09\u4e2d\u7684\u8282\u70b9\u7535\u538b\\(V_1\\), \\(V_2\\)\u4e0e\u652f\u8def\u7535\u6d41\\(I_1\\), \\(I_3\\)\u3002<\/p>\n<ul class=\"unordered-list\">\n<li>\u7535\u538b\u6e90\uff08\u76f8\u5bf9\u4e8e0V\u53c2\u8003\u8282\u70b9\uff09\n<p>\\(E_1\\)=12V<\/li>\n<li>\u7535\u963b\n<p>\\(R_1\\)=3\u03a9, \\(R_2\\)=6\u03a9, \\(R_3\\)=9\u03a9, \\(R_4\\)=12\u03a9, \\(R_5\\)=15\u03a9<\/li>\n<\/ul>\n<p><strong>\u5177\u4f53\u793a\u4f8b\uff08\u672a\u77e5\u91cf\u7684\u9009\u5b9a\uff09<\/strong><\/p>\n<ul class=\"unordered-list\">\n<li>\u8282\u70b9\u7535\u538b\\(V_1\\),\u202f\\(V_2\\)<\/li>\n<li>\u652f\u8def\u7535\u6d41\\(I_1\\),\u202f\\(I_3\\)<\/li>\n<\/ul>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/07-example-of-nodal-analysis-using-matrix-form-in-practice.jpg\" alt=\"\u91c7\u7528\u77e9\u9635\u5f62\u5f0f\u7684\u8282\u70b9\u5206\u6790\u6cd5\u5b9e\u4f8b\u8bbe\u7f6e\" width=\"700\" height=\"394\" \/><\/p>\n<h3 id=\"toc16\">\u8054\u7acb\u65b9\u7a0b\u7684\u6784\u5efa<\/h3>\n<ol class=\"ordered-list\">\n<li>KCL\uff08\u8282\u70b9\\(V_1\\)\uff09\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\\displaystyle\\frac{V_1-E_1}{R_1}+\\displaystyle\\frac{V_1}{R_2}+\\displaystyle\\frac{V_1-V_2}{R_3}=0\\)<\/span><\/li>\n<li>KCL\uff08\u8282\u70b9<span class=\"u-ff-mathjax\">V<\/span><sub>2<\/sub>\uff09\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(\\displaystyle\\frac{V_2-V_1}{R_3}+\\displaystyle\\frac{V_2}{R_4}+\\displaystyle\\frac{V_2}{R_5} =0\\)<\/span><\/p>\n<p>\u6784\u5efa<span class=\"u-ff-mathjax\">GV<\/span> = <span class=\"u-ff-mathjax\">I<\/span><\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(G=\\begin{pmatrix} G_1+G_2+G_3 &amp; -G_3 \\\\ -G_3 &amp; G_3+G_4+G_5 \\end{pmatrix}, V=\\begin{pmatrix} V_1 \\\\ V_2 \\end{pmatrix}, I=\\begin{pmatrix} G_1 E_1 \\\\ 0 \\end{pmatrix}\\)<\/span><\/li>\n<\/ol>\n<h3 id=\"toc17\">\u6570\u503c\u4ee3\u5165\u53ca\u8ba1\u7b97<\/h3>\n<p>\u4ee3\u5165\u6570\u503c<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(G=\\begin{pmatrix} \\displaystyle\\frac{11}{18} -\\displaystyle\\frac{1}{9} \\\\ -\\displaystyle\\frac{1}{9} \\displaystyle\\frac{47}{180} \\end{pmatrix}, I=\\begin{pmatrix} 4 \\\\ 0 \\end{pmatrix}\\)<\/span><\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(V=G^{-1} I \u27f9 V_1\u22487.09 [V],V_2\u22483.02 [V]\\)<\/span><\/p>\n<p>\u652f\u8def\u7535\u6d41\u8ba1\u7b97<\/p>\n<p><!-- \u6570\u5f0f --><\/p>\n<p><span class=\"mathjax-text\">\\(I_1=\\displaystyle\\frac{E_1-V_1}{R_1} \u22481.64 [A],I_3=\\displaystyle\\frac{V_1-V_2}{R_3} \u22480.45 [A]\\)<\/span><\/p>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/08-results-of-nodal-analysis-using-matrix-form-in-practice.jpg\" alt=\"\u91c7\u7528\u77e9\u9635\u5f62\u5f0f\u8fdb\u884c\u8282\u70b9\u5206\u6790\u7684\u5b9e\u4f8b\u7ed3\u679c\" width=\"700\" height=\"394\" \/><\/p>\n<h2 id=\"toc18\">\u5728\u4ea4\u6d41\u7535\u8def\u548c\u9891\u57df\u4e2d\u7684\u6269\u5c55\u5e94\u7528<\/h2>\n<p>\u8282\u70b9\u5206\u6790\u6cd5\u4e0d\u4ec5\u9002\u7528\u4e8e\u76f4\u6d41\u7535\u8def\uff0c\u540c\u6837\u4e5f\u9002\u7528\u4e8e\u4ea4\u6d41\u7535\u8def\u3002\u5728\u4ea4\u6d41\u5206\u6790\u4e2d\uff0c\u5c06\u7535\u611f\u548c\u7535\u5bb9\u7684\u9891\u7387\u4f9d\u8d56\u6027\u4f5c\u4e3a\u963b\u6297\\(Z\\)\u6765\u5904\u7406\uff0c\u5e76\u50cf\u76f4\u6d41\u5206\u6790\u4e00\u6837\u5efa\u7acb\u8282\u70b9\u65b9\u7a0b\u3002<\/p>\n<ul class=\"unordered-list\">\n<li>\u7535\u611f\\(L\\)\uff1a\\(Z_L\\) = \\({j\u03c9L}\\)<\/li>\n<li>\u7535\u5bb9\\(C\\)\uff1a\\(Z_C\\) = 1\/(\\({j\u03c9C}\\))<\/li>\n<li>\u963b\u6297\\(R\\)\uff1a\\(Z_R\\) = \\(R\\)<\/li>\n<\/ul>\n<p><!-- \u753b\u50cf --><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/techclass.wfjydl.com\/wp-content\/uploads\/2026\/01\/09-extending-of-nodal-analysis-to-ac-circuits-and-frequency-domain.jpg\" alt=\"\u8282\u70b9\u5206\u6790\u6cd5\u5728\u4ea4\u6d41\u7535\u8def\u548c\u9891\u57df\u4e2d\u7684\u6269\u5c55\u5e94\u7528\" width=\"700\" height=\"394\" \/><\/p>\n<h3 id=\"toc19\">\u590d\u6570\u5206\u6790\u548c\u77e9\u9635\u5f62\u5f0f<\/h3>\n<p><strong>\u590d\u6570\u5206\u6790<\/strong><\/p>\n<p>\u5728\u6b63\u5f26\u6ce2\u6fc0\u52b1\u7684\u60c5\u51b5\u4e0b\uff0c\u5404\u8282\u70b9\u7535\u538b\u7528\u590d\u6570\u8868\u793a\uff0cKCL\u7528\u590d\u6570\u963b\u6297\u8fdb\u884c\u8868\u8ff0\u3002\u5176\u4e2d\uff0c\u963b\u6297\\(Z\\)\u662f\u6307\u7535\u963b\u3001\u7535\u611f\u3001\u7535\u5bb9\u7b49\u5143\u4ef6\u5bf9\u4ea4\u6d41\u7535\u6d41\u5448\u73b0\u7684\u9891\u7387\u4f9d\u8d56\u963b\u529b\u3002\u4f8b\u5982\uff0c\u963b\u6297\\(Z\\)\u6240\u8fde\u63a5\u7684\u8282\u70b9\u7535\u538b\\(V\\)\u548c\\(V_X\\)\uff0c\u5176\u7535\u6d41\u53ef\u8868\u793a\u4e3a\\(i\\) = (\\(V\\) \u2013 \\(V_X\\))\/\\(Z\\)\u3002<\/p>\n<p>\u6700\u7ec8\u53ef\u83b7\u5f97\u590d\u6570\u5f62\u5f0f\u7684\u8282\u70b9\u7535\u538b\u3002<\/p>\n<p><strong>\u9891\u57df\u7684\u77e9\u9635\u5f62\u5f0f<\/strong><\/p>\n<ol class=\"ordered-list\">\n<li>\u5b9a\u4e49\u8282\u70b9\u548c\u53c2\u8003\u8282\u70b9<\/li>\n<li>\u786e\u5b9a\u5404\\(R\\), \\(L\\), \\(C\\)<\/li>\n<li>\u4ee5\u590d\u6570\u963b\u6297\u6765\u8868\u8ff0KCL<\/li>\n<li>\u6574\u7406\u4e3a\\(Y\\)(\\(\u03c9\\))\\(V\\) = \\(I\\)(\\(\u03c9\\))<\/li>\n<li>\u7528\u590d\u7ebf\u6027\u4ee3\u6570\u6c42\u89e3\\(V\\)\u901a\u8fc7\u626b\u63cf\u9891\u7387\u53ef\u83b7\u5f97\u4f2f\u5fb7\u56fe\u7b49\u9891\u7387\u54cd\u5e94\u7279\u6027\u3002<\/li>\n<\/ol>\n<h2 id=\"toc20\">\u8282\u70b9\u5206\u6790\u6cd5\u5728\u975e\u7ebf\u6027\u5927\u89c4\u6a21\u7535\u8def\u4e2d\u7684\u6269\u5c55\u5e94\u7528<\/h2>\n<p>\u5b9e\u9645\u7684\u7535\u5b50\u7535\u8def\u4e2d\uff0c\u5305\u542b\u591a\u4e2a\u53d7\u63a7\u6e90\u3001\u4e8c\u6781\u7ba1\u548c\u6676\u4f53\u7ba1\u7b49\u975e\u7ebf\u6027\u5143\u5668\u4ef6\uff0c\u751a\u81f3\u5728IC\u82af\u7247\u5185\u90e8\u4e5f\u5b58\u5728\u6570\u5341\u4e07\u81f3\u6570\u767e\u4e07\u4e2a\u8282\u70b9\u3002\u8282\u70b9\u5206\u6790\u6cd5\u4f5c\u4e3a\u4e00\u79cd\u901a\u7528\u7684\u8ba1\u7b97\u6846\u67b6\uff0c\u53ef\u6269\u5c55\u5e94\u7528\u4e8e\u4f17\u591a\u573a\u666f\u3002<\/p>\n<h3 id=\"toc21\">\u56db\u79cd\u53d7\u63a7\u6e90\u7684\u5904\u7406<\/h3>\n<p>\u53d7\u63a7\u6e90\u6709\u56db\u79cd\u7c7b\u578b\uff1a\u7535\u538b\u63a7\u5236\u7535\u538b\u6e90\uff08VCVS\uff09\u3001\u7535\u6d41\u63a7\u5236\u7535\u538b\u6e90\uff08CCVS\uff09\u3001\u7535\u538b\u63a7\u5236\u7535\u6d41\u6e90\uff08VCCS\uff09\u3001\u7535\u6d41\u63a7\u5236\u7535\u6d41\u6e90\uff08CCCS\uff09\u3002\u5b83\u4eec\u7684\u8f93\u51fa\u53d6\u51b3\u4e8e\u7535\u8def\u5185\u90e8\u5176\u4ed6\u8282\u70b9\u6240\u6d4b\u5f97\u7684\u7535\u538b\u6216\u7535\u6d41\u3002<\/p>\n<ul class=\"unordered-list\">\n<li>VCVS\u3001CCVS\uff08\u53d7\u63a7\u7535\u538b\u6e90\uff09\uff1a\u5728\u77e9\u9635\u4e2d\u6dfb\u52a0\u7535\u538b\u7ea6\u675f\u884c\uff08CCVS\u9700\u5c06\u63a7\u5236\u7535\u6d41\\(I_X\\)\u4f5c\u4e3a\u65b0\u53d8\u91cf\u5bfc\u5165\uff09<\/li>\n<li>VCCS\u3001CCCS\uff08\u53d7\u63a7\u7535\u6d41\u6e90\uff09\uff1a\u5728\u76f8\u5e94\u5bfc\u7eb3\u9879\u4e2d\u6dfb\u52a0\u7cfb\u6570\uff08VCCS\u4e3a\\(g_m\\)\uff0cCCCS\u4e3a\\(k\\)\u7b49\uff09<\/li>\n<\/ul>\n<h3 id=\"toc22\">\u975e\u7ebf\u6027\u5143\u4ef6\u7684\u7ebf\u6027\u5316\u4e0e\u8fed\u4ee3\u89e3\u6cd5<\/h3>\n<p>\u5f53\u7535\u8def\u4e2d\u542b\u6709\u975e\u7ebf\u6027\u5143\u4ef6\u65f6\uff0c\\(I\\)\u2013\\(V\\) \u7279\u6027\u5c06\u4e0d\u518d\u4fdd\u6301\u7ebf\u6027\u6bd4\u4f8b\u5173\u7cfb\uff0c\u6b64\u65f6\u8282\u70b9\u65b9\u7a0b\u5c06\u53d8\u4e3a\u975e\u7ebf\u6027\u8054\u7acb\u65b9\u7a0b\u3002\u6240\u4ee5\u6309\u7167\u5982\u4e0b\u6b65\u9aa4<\/p>\n<ol 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