{"id":585,"date":"2013-01-16T10:54:50","date_gmt":"2013-01-16T01:54:50","guid":{"rendered":"http:\/\/www.bi.appi.keio.ac.jp\/?p=585"},"modified":"2013-07-04T09:31:09","modified_gmt":"2013-07-04T00:31:09","slug":"%e9%9b%bb%e6%b0%97%e7%b3%bb%e3%81%ae%e5%85%b1%e6%8c%af%e5%91%a8%e6%b3%a2%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.bi.appi.keio.ac.jp\/?p=585","title":{"rendered":"\u96fb\u6c17\u7cfb\u306e\u5171\u632f\u5468\u6ce2\u6570"},"content":{"rendered":"

\u56f3\u306eLCR\u76f4\u5217\u5171\u632f\u56de\u8def\u3067\u306f\uff0c\u96fb\u5727[latex]v(t)[\/latex]\u3092\u52a0\u3048\u308b\u3068\u304d\u306b\u6d41\u308c\u308b\u96fb\u6d41[latex]i(t)[\/latex]\u306f\uff0c
\n[latex]\\displaystyle L\\frac{i(t)}{dt}+Ri(t)+\\frac{1}{C}\\int i(t)dt=v(t)[\/latex]<\/p>\n

\u3067\u3059\uff0e\u30e9\u30d7\u30e9\u30b9\u5909\u63db\u3057\u3066\u4f1d\u9054\u95a2\u6570[latex]G(s)=I(s)\/V(s)[\/latex]\u3092\u6c42\u3081\u308b\u3068
\n[latex]\\displaystyle G(s)=\\frac{s}{Ls^2+Rs+1\/C}[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n

\"lcr\"<\/a><\/p>\n

\u5f62\u5f0f\u7684\u306b[latex]s=j\\omega[\/latex]\u3068\u304a\u304d\uff0c[latex]|G(j\\omega)|=g(\\omega)[\/latex]\u3068\u304a\u304f\u3068
\n[latex]\\displaystyle g(\\omega)=\\omega\\left(\\left(\\frac{1}{c}-\\omega^2L\\right)^2+\\omega^2R^2\\right)^{-1\/2}[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n

[latex]\\displaystyle\\frac{dg(\\omega)}{d\\omega}=0[\/latex]\u3068\u3057\u3066\uff0c\u6975\u5927\u5024\u3092\u6c42\u3081\u308b\u3068
\n[latex]\\displaystyle\\omega_r=\\frac{1}{\\sqrt{LC}}[\/latex]\u306b\u306a\u308a\u307e\u3059\uff08\u5171\u632f\u5468\u6ce2\u6570\u306f[latex]\\displaystyle f_r=\\frac{1}{2\\pi\\sqrt{LC}}[\/latex]\uff09\uff0e\u3064\u307e\u308a\uff0c\u62b5\u6297\u306b\u4f9d\u5b58\u3057\u307e\u305b\u3093\uff0e<\/p>\n

\u8a08\u7b97\u3067\u6c42\u3081\u308b\u3068\u7169\u96d1\u3067\u3059\u304c\uff0cLCR\u76f4\u5217\u5171\u632f\u56de\u8def\u3067\u306f\u8907\u7d20\u5e73\u9762\u3067\u30a4\u30f3\u30d4\u30fc\u30c0\u30f3\u30b9\u3092\u8868\u305b\u3070\uff0cL\u306e\u30a4\u30f3\u30d4\u30fc\u30c0\u30f3\u30b9[latex]j\\omega L[\/latex]\u3068C\u306e\u30a4\u30f3\u30d4\u30fc\u30c0\u30f3\u30b9[latex]\\displaystyle\\frac{1}{j\\omega C}[\/latex]\u306e\u5927\u304d\u3055\u304c\u7b49\u3057\u3044\u3068\u304d\u304c\u5171\u632f\u306e\u6761\u4ef6\u3067\u3059\u304b\u3089\u5bb9\u6613\u306b\u5171\u632f\u5468\u6ce2\u6570\u3092\u6c42\u3081\u3089\u308c\u307e\u3059\uff0e<\/p>\n

\u4e00\u65b9\uff0c\u96fb\u5727\u6e90\u3092\u77ed\u7d61\u3057\u3066\u96fb\u6d41\u306e\u521d\u671f\u5024\u306e\u307f\u3092\u4e0e\u3048\u308b\u3068\u304d\uff0c\u4e0d\u8db3\u6e1b\u8870\u3067\u3042\u308c\u3070\u305d\u306e\u632f\u52d5\u306e\u89d2\u5468\u6ce2\u6570\u306f\u4f1d\u9054\u95a2\u6570\u306e\u6975\u306e\u865a\u90e8\u304b\u3089
\n[latex]\\displaystyle\\sqrt{\\frac{1}{LC}-\\frac{R^2}{4L^2}}[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n

\u96fb\u6c17\u7cfb\u3067\u306f\uff0c\u300c\u99c6\u52d5\u529b\u300d\u3067\u3042\u308b\u96fb\u5727\u3068\uff0c\u300c\u6d41\u308c\u300d\u3067\u3042\u308b\u96fb\u6d41\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3059\uff0e\u529b\u5b66\u7cfb\u3067\u306f\u300c\u6d41\u308c\u300d\u3067\u3042\u308b\u901f\u5ea6\u3067\u306f\u306a\u304f\u305d\u306e\u7a4d\u5206\u3067\u3042\u308b\u5909\u4f4d\u3067\u5171\u632f\u5468\u6ce2\u6570\u3092\u6c42\u3081\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"

\u56f3\u306eLCR\u76f4\u5217\u5171\u632f\u56de\u8def\u3067\u306f\uff0c\u96fb\u5727[latex]v(t)[\/latex]\u3092\u52a0\u3048\u308b\u3068\u304d\u306b\u6d41\u308c\u308b\u96fb\u6d41[latex]i(t)[\/latex]\u306f\uff0c [latex]\\displaystyle L\\frac{i(t)}{dt}+Ri( … “\u96fb\u6c17\u7cfb\u306e\u5171\u632f\u5468\u6ce2\u6570” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-585","post","type-post","status-publish","format-standard","hentry","category-9"],"_links":{"self":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=585"}],"version-history":[{"count":20,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/585\/revisions"}],"predecessor-version":[{"id":951,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/585\/revisions\/951"}],"wp:attachment":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}