{"id":879,"date":"2013-06-04T10:56:43","date_gmt":"2013-06-04T01:56:43","guid":{"rendered":"http:\/\/www.bi.appi.keio.ac.jp\/?p=879"},"modified":"2013-06-13T10:35:53","modified_gmt":"2013-06-13T01:35:53","slug":"%e3%83%8f%e3%82%a4%e3%83%91%e3%82%b9%e3%83%95%e3%82%a3%e3%83%ab%e3%82%bf","status":"publish","type":"post","link":"https:\/\/www.bi.appi.keio.ac.jp\/?p=879","title":{"rendered":"\u30cf\u30a4\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf"},"content":{"rendered":"

\u81ea\u7136\u79d1\u5b66\u5b9f\u9a13\uff08\u7269\u7406\u5b66\uff09\u306e\u30c6\u30fc\u30de\uff0c\u30aa\u30b7\u30ed\u30b9\u30b3\u30fc\u30d7\u306e\u5fdc\u7528\u8ab2\u984c\u3067\u7279\u6027\u3092\u8abf\u3079\u308b\u30ed\u30fc\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u306e\u62b5\u6297\u3068\u30b3\u30f3\u30c7\u30f3\u30b5\u3092\u5165\u308c\u66ff\u3048\u3066\u69cb\u6210\u3057\u305f\u30cf\u30a4\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u3067\u3059\uff0e<\/p>\n

\"rc-highpass\"<\/a><\/p>\n

 <\/p>\n

[latex]v_i(t) = \\displaystyle\\frac{1}{C}\\int i(t) dt + v_o(t)[\/latex]\u3068[latex]v_o(t) = R i(t)[\/latex]\u306e\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u304b\u3089\uff0c<\/p>\n

[latex]v_i(t) = \\displaystyle\\frac{1}{RC}\\int v_o(t) dt + v_o(t)[\/latex]<\/p>\n

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

\u30e9\u30d7\u30e9\u30b9\u5909\u63db\u3067\u89e3\u304f<\/h2>\n

\u30e9\u30d7\u30e9\u30b9\u5909\u63db\u3057\u3066\uff0c<\/p>\n

[latex]V_i(s) = \\displaystyle\\frac{V_o(s)}{RCs} + V_o(s)[\/latex]<\/p>\n

\u3092\u5f97\u307e\u3059\uff0e\u4f1d\u9054\u95a2\u6570\u306f<\/p>\n

[latex]\\displaystyle\\frac{V_o(s)}{V_i(s)} = \\frac{1}{\\frac{1}{RCs} + 1} = \\frac{s}{s+\\frac{1}{RC}}[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e\u4f1d\u9054\u95a2\u6570\u306e\u6975\u306f\uff0c\u62b5\u6297\u3068\u30b3\u30f3\u30c7\u30f3\u30b5\u3092\u5165\u308c\u66ff\u3048\u3066\u69cb\u6210\u3059\u308b\u30ed\u30fc\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u3068\u540c\u3058\u306b\u306a\u308a\u307e\u3059\uff0e\u5f62\u5f0f\u7684\u306b[latex]s=j\\omega[\/latex]\u3068\u3059\u308b\u3068\uff0c\u30b2\u30a4\u30f3\u7279\u6027\u306f<\/p>\n

[latex]\\left|\\displaystyle\\frac{V_o(s)}{V_i(s)}\\right| = \\displaystyle\\frac{\\omega}{\\sqrt{\\omega^2 + \\left(\\frac{1}{RC}\\right)^2}}[\/latex]<\/p>\n

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

\u4f4d\u76f8\u7279\u6027\u306f<\/p>\n

[latex]90^\\circ – \\tan^{-1}\\omega RC[\/latex]<\/p>\n

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

1\u5e74\u751f\u306e\u6570\u5b66\u306e\u7bc4\u56f2\u3067\u89e3\u304f<\/h2>\n

\u540c\u6b21\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\uff0c\u3064\u307e\u308a\u57fa\u672c\u89e3\u306f\u6642\u9593\u3068\u3068\u3082\u306b\u96f6\u306b\u306a\u308b\u306e\u3067\uff0c[latex]v_i(t)=\\sin\\omega t[\/latex]\u306e\u3068\u304d\u306e\u7279\u89e3\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u306e\u306f\uff0c\u30ed\u30fc\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u306e\u5834\u5408\u3068\u540c\u69d8\u3067\u3059\uff0e<\/p>\n

\u7a4d\u5206\u3092\u542b\u3080\u5f0f<\/p>\n

[latex]v_i(t) = \\displaystyle\\frac{1}{RC}\\int v_o(t) dt + v_o(t)[\/latex]<\/p>\n

\u306a\u306e\u3067\uff0c[latex]t[\/latex]\u3067\u5fae\u5206\u3057\u3066\uff0c<\/p>\n

[latex]\\displaystyle\\frac{dv_i(t)}{dt}=\\frac{1}{RC}v_o(t) + \\frac{dv_o(t)}{dt}[\/latex]<\/p>\n

\u3092\u5f97\u307e\u3059\uff0e[latex]\\displaystyle\\frac{dv_i(t)}{dt}=\\omega\\cos\\omega t[\/latex]\u3092\u4ee3\u5165\u3059\u308b\u3068\uff0c<\/p>\n

[latex]\\omega\\cos\\omega t=\\displaystyle\\frac{1}{RC}v_o(t) + \\frac{dv_o(t)}{dt}[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e[latex]v_o(t)[\/latex]\u306f\uff0c[latex]v_i(t)[\/latex]\u3068\u540c\u3058\u89d2\u5468\u6ce2\u6570\u306e\u6b63\u5f26\u6ce2\u3067\u3059\u304c\uff0c\u632f\u5e45\u3068\u4f4d\u76f8\u304c\u7570\u306a\u308b\u3082\u306e\u306b\u306a\u308b\u306e\u3067\uff0c\u89e3\u3092[latex]a\\sin(\\omega t + \\phi)[\/latex]\u3068\u304a\u3044\u3066\uff0c[latex]a[\/latex]\u3068[latex]\\phi[\/latex] \u3092\u6c42\u3081\u307e\u3059\uff0e<\/p>\n

[latex]\\omega\\cos\\omega t = \\displaystyle\\frac{1}{RC}a\\sin(\\omega t + \\phi) + a\\omega\\cos(\\omega t + \\phi)[\/latex]<\/p>\n

\u306b\u306a\u308b\u306e\u3067\u4e09\u89d2\u95a2\u6570\u306e\u5408\u6210\u3092\u7528\u3044\u3066\uff0c<\/p>\n

[latex]\\omega\\cos\\omega t = a\\sqrt{\\displaystyle\\left(\\frac{1}{RC}\\right)^2 + \\omega^2}\\sin(\\omega t + \\phi + \\psi)[\/latex]<\/p>\n

\u3068<\/p>\n

[latex]\\psi=\\tan^{-1}RC\\omega[\/latex]<\/p>\n

\u3068\u306a\u308a\uff0c\u4e21\u8fba\u3092[latex]\\cos[\/latex]\u306b\u3057\u3066<\/p>\n

[latex]\\displaystyle\\omega\\cos\\omega t = a\\sqrt{\\displaystyle\\left(\\frac{1}{RC}\\right)^2 + \\omega^2}\\cos\\left(-\\frac{\\pi}{2}+\\omega t + \\phi + \\psi\\right)[\/latex]<\/p>\n

\u3068\u306a\u308a\u307e\u3059\uff0e\u3057\u305f\u304c\u3063\u3066<\/p>\n

[latex]a=\\displaystyle\\frac{\\omega}{\\sqrt{\\left(\\frac{1}{RC}\\right)^2 + \\omega^2}}[\/latex]<\/p>\n

\u3092\u5f97\u307e\u3059\uff0e<\/p>\n

\u4f4d\u76f8\u306f[latex]\\phi=\\displaystyle\\frac{\\pi}{2}-\\psi[\/latex]\u306a\u306e\u3067\uff0c<\/p>\n

[latex]90^\\circ – \\tan^{-1}RC\\omega[\/latex]<\/p>\n

\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"

\u81ea\u7136\u79d1\u5b66\u5b9f\u9a13\uff08\u7269\u7406\u5b66\uff09\u306e\u30c6\u30fc\u30de\uff0c\u30aa\u30b7\u30ed\u30b9\u30b3\u30fc\u30d7\u306e\u5fdc\u7528\u8ab2\u984c\u3067\u7279\u6027\u3092\u8abf\u3079\u308b\u30ed\u30fc\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u306e\u62b5\u6297\u3068\u30b3\u30f3\u30c7\u30f3\u30b5\u3092\u5165\u308c\u66ff\u3048\u3066\u69cb\u6210\u3057\u305f\u30cf\u30a4\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf\u3067\u3059\uff0e   [latex]v_i(t) = \\displaystyle … “\u30cf\u30a4\u30d1\u30b9\u30d5\u30a3\u30eb\u30bf” \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-879","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\/879","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=879"}],"version-history":[{"count":29,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/879\/revisions"}],"predecessor-version":[{"id":911,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=\/wp\/v2\/posts\/879\/revisions\/911"}],"wp:attachment":[{"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bi.appi.keio.ac.jp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}