{"id":8576,"date":"2023-04-28T09:50:05","date_gmt":"2023-04-28T00:50:05","guid":{"rendered":"https:\/\/www11.ieice.org\/cs\/ap\/wp\/?page_id=8576"},"modified":"2025-12-05T19:26:36","modified_gmt":"2025-12-05T10:26:36","slug":"spherical_earth_diffraction","status":"publish","type":"page","link":"https:\/\/www.ieice.org\/cs\/ap\/misc\/denpan-db\/prop_model_db\/model_list\/spherical_earth_diffraction\/","title":{"rendered":"\u7403\u9762\u5927\u5730\u306b\u3088\u308b\u56de\u6298"},"content":{"rendered":"
<\/div>

<\/path><\/svg><\/i> \"Loading\"<\/p>

<\/div>(since 2025\/12\/5)<\/p>\n\n\n\n

\u30e2\u30c7\u30eb\u306e\u6982\u8981<\/h3>\n\n\n\n

\u56f3\uff11\u5de6\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a2\u30f3\u30c6\u30ca\u5468\u8fba\u306b\u4f1d\u642c\u8def\u3092\u59a8\u3052\u308b\u3082\u306e\u304c\u7121\u3044\u5834\u5408\u3067\u3082\u3001\u9001\u4fe1\u30a2\u30f3\u30c6\u30ca\u304b\u3089\u898b\u3066\uff0c\u53d7\u4fe1\u30a2\u30f3\u30c6\u30ca\u304c\u5730\u5e73\u7dda\u306e\u5148\u306b\u8a2d\u7f6e\u3055\u308c\u305f\u5834\u5408\u3001\u5730\u7403\u306e\u5927\u5730\u306b\u3088\u308b\u906e\u853d\u304c\u767a\u751f\u3059\u308b\u305f\u3081\u3001\u4e3b\u8981\u306a\u4f1d\u642c\u8def\u306f\u5730\u7403\u8868\u9762\u3092\u5468\u308a\u8fbc\u3080\u56de\u6298\u30d1\u30b9\u3068\u306a\u308b\u3002\u3053\u3053\u3067\u306f\u5730\u7403\u8868\u9762\u3092\u5efb\u308a\u8fbc\u3080\u56de\u6298\u306b\u3088\u3063\u3066\u767a\u751f\u3059\u308b\u56de\u6298\u640d\u5931\u306b\u3064\u3044\u3066\u8a18\u8f09\u3059\u308b\u3002<\/p>\n\n\n

\n
\"\"
\u56f3\uff11\u3000\u7403\u9762\u5927\u5730\u306b\u3088\u308b\u56de\u6298\u3068\u7b49\u4fa1\u5730\u7403\u534a\u5f84<\/span><\/figcaption><\/figure><\/div>\n\n\n

\uff1c\u7b49\u4fa1\u5730\u7403\u534a\u5f84\uff1e<\/strong><\/p>\n\n\n\n

\u5730\u7403\u5927\u6c17\u4e2d\u306e\u9577\u8ddd\u96e2\u4f1d\u642c\u3092\u8003\u3048\u308b\u5834\u5408\u3001\u96fb\u6ce2\u306e\u4f1d\u642c\u7d4c\u8def\u304c\u5927\u6c17\u5c48\u6298\u7387\u306e\u5f71\u97ff\u3092\u53d7\u3051\u308b\u3053\u3068\u306b\u6c17\u3092\u4ed8\u3051\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u5927\u6c17\u306f\u5730\u7403\u8868\u9762\u306b\u6cbf\u3063\u3066\u5206\u5e03\u3057\u3066\u304a\u308a\u3001\u9ad8\u5ea6\u304c\u9ad8\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u5927\u6c17\u5c48\u6298\u7387\u306f\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u304f\u3002\u3053\u306e\u7d50\u679c\u3001\u56f3\uff11\u306e\u5de6\u56f3\u306b\u793a\u3059\u3088\u3046\u306bTx\u304b\u3089\u51fa\u5c04\u3055\u308c\u305f\u96fb\u6ce2\u306f\u4e0b\u65b9\u306b\u66f2\u304c\u308a\u306a\u304c\u3089\u4f1d\u642c\u3057\u3066\u3044\u304f[3]\u3002
\u3053\u306e\u73fe\u8c61\u3092\u5bb9\u6613\u306b\u6271\u3046\u305f\u3081\u306b\u3001\u96fb\u6ce2\u306e\u7d4c\u8def\u304c\u5927\u6c17\u306b\u3088\u3063\u3066\u4e0b\u65b9\u306b\u66f2\u3052\u3089\u308c\u308b\u66f2\u7387\u3092\u5730\u7403\u306e\u534a\u5f84\u3092\u7b49\u4fa1\u7684\u306b\u5927\u304d\u304f\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5438\u53ce\u3057\u3001\u6a19\u6e96\u5927\u6c17\u4e2d\u306e\u81ea\u7531\u7a7a\u9593\u4f1d\u642c\u7d4c\u8def\u3092\u76f4\u7dda\u3068\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u884c\u308f\u308c\u3066\u3044\u308b\uff08\u56f3\uff11\u306e\u53f3\u56f3\u3092\u53c2\u7167\uff09\u3002\u3053\u306e\u3068\u304d\u7b49\u4fa1\u7684\u306b\u8a2d\u5b9a\u3055\u308c\u308b\u5730\u7403\u306e\u534a\u5f84\u3092\u300c\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u300d\u3068\u547c\u3073\u3001\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u3092\u5b9f\u969b\u306e\u5730\u7403\u306e\u534a\u5f84\u3067\u9664\u3057\u305f\u3082\u306e\u3092\u300c\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u4fc2\u6570\u300d\u3068\u8a00\u3046\u3002\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u4fc2\u6570\u306e\u5024\u306f\u6a19\u6e96\u5927\u6c17\u306b\u304a\u3044\u30664\/3\u306b\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b[3]\u3002\u672c\u30e2\u30c7\u30eb\u306b\u3064\u3044\u3066\u3082\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u306e\u8003\u3048\u65b9\u3092\u7528\u3044\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u6570\u5f0f<\/h3>\n\n\n\n

\u7403\u9762\u5927\u5730\u306b\u3088\u308b\u56de\u6298\u640d\u5931\\(L_{d}\\)\u306f\uff08\uff11\uff09\u5f0f\u306e\u901a\u308a\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(L_d = F(X) + G(Y_1) + G(Y_2) \\\\
\\tag{1}\\)<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001<\/p>\n\n\n\n

\\(F(X) = \\left\\{
\\begin{array}{ll}
11 + 10 \\log_{10} (X) – 17.6 X & X \\geq 1.6 \\\\
-20 \\log_{10} (X) – 5.6488 X^{1.425} & X < 1.6
\\end{array}\\right. \\\\
\\tag{2}\\)<\/p>\n\n\n\n

\\(G(Y) = \\left\\{
\\begin{array}{ll}
17.6 (B – 1.1)^{1\/2} – 5 \\log_{10} (B – 1.1) – 8 & B > 2\\\\
20 \\log_{10} (B + 0.1 B^3) & B \\leq 2
\\end{array}
\\right. \\\\
\\tag{3}\\)
<\/p>\n\n\n\n

\u306a\u304a\uff0c\\( G(Y) < 2 + 20 \\log_{10} K\\) \u306e\u3068\u304d\u306f \\(G(Y) = 2 + 20 \\log_{10} K \\)\u3068\u3059\u308b\u3002 <\/p>\n\n\n\n

\u3053\u3053\u3067\u3001<\/p>\n\n\n\n

\\(B = \\beta Y \\\\
\\tag{4}\\)<\/p>\n\n\n\n

\\(\\beta = \\frac{1 + 1.6 K^2 + 0.67 K^4}{1 + 4.5 K^2 + 1.53 K^4} \\\\
\\tag{5}\\)<\/p>\n\n\n\n

\\(K^2 \\approx 6.89 \\frac{\\sigma}{k^{2\/3} f^{5\/3}} \\\\
\\tag{6}\\)<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\u6c34\u5e73\u504f\u6ce2\u3001\u3082\u3057\u304f\u306f20MHz\u4ee5\u4e0a\u306e\u9678\u4e0a\u4f1d\u642c\u8def\u3067\u5782\u76f4\u504f\u6ce2\u3001300MHz\u4ee5\u4e0a\u306e\u6d77\u4e0a\u4f1d\u642c\u8def\u3067\u5782\u76f4\u504f\u6ce2\u306e\u3068\u304d\u306f\\(\\beta=1\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\u307e\u305f\u3001<\/p>\n\n\n\n

\\(X = d \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi}{\\lambda a_e^2}} \\\\
\\tag{7}\\)
\\(Y_1 = 2 h_1 \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi^2}{\\lambda^2 a_e}} \\\\
\\tag{8}\\)<\/p>\n\n\n\n

\\(Y_2 = 2 h_2 \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi^2}{\\lambda^2 a_e}} \\\\
\\tag{9}\\)
\\(a_e = kR \\\\
\\tag{10}\\)<\/p>\n\n\n\n

\u30d1\u30e9\u30e1\u30fc\u30bf<\/h3>\n\n\n\n
\u8a18\u53f7<\/td>\u30d1\u30e9\u30e1\u30fc\u30bf\u8aac\u660e\uff3b\u5358\u4f4d]<\/td>\u30d1\u30e9\u30e1\u30fc\u30bf\u7bc4\u56f2<\/td><\/tr>
\\(L_d\\)<\/td>\u7403\u9762\u5927\u5730\u306b\u3088\u308b\u56de\u6298\u640d\u5931\u3000[dB]<\/td>\uff0d<\/td><\/tr>
\\(\\lambda\\)<\/td>\u6ce2\u9577\u3000[m]<\/td>\uff0d<\/td><\/tr>
\\(f\\)<\/td>\u5468\u6ce2\u6570\u3000[Hz]<\/td>\uff0d<\/td><\/tr>
\\(a_e\\)<\/td>\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u3000[m]<\/td>\uff0d<\/td><\/tr>
\\(h_1\\)<\/td>\u9001\u4fe1\u30a2\u30f3\u30c6\u30ca\u9ad8\u3000[m]<\/td>\uff0d<\/td><\/tr>
\\(h_2\\)<\/td>\u53d7\u4fe1\u30a2\u30f3\u30c6\u30ca\u9ad8\u3000[m]<\/td>\u30fc<\/td><\/tr>
\\(K\\)<\/td>\u5730\u7403\u8868\u9762\u30a2\u30c9\u30df\u30bf\u30f3\u30b9\u88dc\u6b63\u4fc2\u6570<\/td>\u30fc<\/td><\/tr>
\\(k\\)<\/td>\u7b49\u4fa1\u5730\u7403\u534a\u5f84\u4fc2\u6570\uff1d4\/3<\/td>\u30fc<\/td><\/tr>
\\(\\sigma\\)<\/td>\u5927\u5730\u8868\u9762\u306e\u5b9f\u52b9\u5c0e\u96fb\u7387\u3000[S\/m]\u3000\u203bITU-R Rec. P.832\u53c2\u7167<\/td>\u30fc<\/td><\/tr>
\\(R\\)<\/td>\u5730\u7403\u306e\u534a\u5f84\u3000[m]<\/td>\u30fc<\/td><\/tr>
\\(d\\)<\/td>\u9001\u53d7\u4fe1\u30a2\u30f3\u30c6\u30ca\u9593\u8ddd\u96e2\u3000[m]<\/td>\u30fc<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u8a08\u7b97\u4f8b<\/h3>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n

\u30d7\u30ed\u30b0\u30e9\u30e0<\/h3>\n\n\n\n
\u7403\u9762\u5927\u5730\u306b\u3088\u308b\u56de\u6298\u8a08\u7b97<\/a>\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9<\/a><\/div>\n\n\n\n

\u53c2\u8003\u60c5\u5831<\/h3>\n\n\n\n

\u672c\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u8a18\u8f09\u306e\u5f0f\u306f\u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af[3]\u306epp.26-27\u306b\u8a18\u8f09\u306e\u3042\u308b\u5f0f\u3068\u8907\u6570\u7570\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u672c\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u306e\u53c2\u7167\u5f0f\u304cITU-R Rec. P.526-15[1]\u3067\u3042\u308b\u3053\u3068\u306b\u5bfe\u3057\u3066\u3001\u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u306e\u53c2\u7167\u5f0f\u304cITU-R Rec. P.526-5[4]\u3067\u3042\u308b\u3053\u3068\u304c\u539f\u56e0\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001\\(\\beta\\)\u3092\u5c0e\u51fa\u3059\u308b\u5f0f\u306e\u4fc2\u6570[\u5f0f(7)\u3068(18)]\u304c\u7570\u306a\u308b\u3053\u3068\u3068\u3001\\(F(X)\\)\u3068\\(G(Y)\\)\u306e\u5f0f\u306e\u5834\u5408\u5206\u3051\u306e\u9055\u3044\u3001\u306a\u3069\u3067\u3042\u308b\u3002\u4ee5\u4e0b\u306b\u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u306epp.26-27\u8a18\u8f09\u5f0f\u3092\u63b2\u8f09\u3059\u308b\u3002<\/p>\n\n\n\n

\\(L_d = F(X) + G(Y_1) + G(Y_2) \\\\
\\tag{11}\\)
\u305f\u3060\u3057\u3001<\/p>\n\n\n\n

\\(\\begin{array}{ll}
F(X) = 11 + 10 \\log_{10} (X) – 17.6 X & X \\geq 1.6 \\\\
\\end{array}
\\tag{12}\\)<\/p>\n\n\n\n

\\(G(Y) = \\left\\{
\\begin{array}{ll}
17.6 (Y – 1.1)^{1\/2} – 5 \\log_{10} (Y – 1.1) – 8 & Y > 2\\\\
20 \\log_{10} (Y + 0.1 Y^3) & 10K < Y < 2 \\\\
\\begin{array}{l}
2 + 20 \\log_{10} (K) + \\\\
\\quad 9 \\log_{10} (Y\/K) [\\log_{10} (Y\/K) + 1]
\\end{array}
& K\/10 < Y < 10K \\\\
2 + 20 \\log_{10} (K) & Y < K\/10
\\end{array}
\\right. \\\\
\\tag{13}\\)<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001<\/p>\n\n\n\n

\\(\\beta=\\frac{1 + 1.6 K^2 + 0.75 K^4}{1 + 4.5 K^2 + 1.35 K^4}\\tag{14}\\)<\/p>\n\n\n\n

\u307e\u305f\u3001<\/p>\n\n\n\n

\\(
X = d \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi}{\\lambda a_e^2}} \\\\
\\tag{15}
\\)<\/p>\n\n\n\n

\\(
Y_1 = 2 h_1 \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi^2}{\\lambda^2 a_e}} \\\\
\\tag{16}
\\)<\/p>\n\n\n\n

\\(
Y_2 = 2 h_2 \\beta \\times \\sqrt[\\uproot{10}3]{\\frac{\\pi^2}{\\lambda^2 a_e}} \\\\
\\tag{17}
\\)<\/p>\n\n\n\n

\\(
a_e = kR \\\\
\\tag{18}
\\)<\/p>\n\n\n\n

\\(K\\)\u306f\u5927\u5730\u8868\u9762\u30a2\u30c9\u30df\u30bf\u30f3\u30b9\u88dc\u6b63\u4fc2\u6570\u3067\u3042\u308a\u3001\u5927\u5730\u8868\u9762\u306e\u5b9f\u52b9\u6bd4\u8a98\u96fb\u7387\\(\\epsilon_{r}\\)\u3001\u5b9f\u884c\u5c0e\u96fb\u7387\\(\\sigma\\)[S\/m]\u3068\u3059\u308b\u3068\u6c34\u5e73\u504f\u6ce2\\(K_{H}\\)\u304a\u3088\u3073\u5782\u76f4\u504f\u6ce2\\(K_V\\)\u306f\u4ee5\u4e0b\u3068\u306a\u308b\u3002<\/p>\n\n\n\n

\\(
K_H = \\left( \\frac{2 \\pi a_e}{\\lambda} \\right) \\left( \\frac{2 \\pi a_e}{\\lambda} \\right)^{-1\/3} \\left[ (\\varepsilon_r – 1)^2 + (60 \\lambda \\sigma)^2 \\right]^{-1\/4} \\\\
\\tag{19}
\\)<\/p>\n\n\n\n

\\(
K_V = K_H \\sqrt{\\varepsilon_r^2 + (60 \\lambda \\sigma)^2} \\\\
\\tag{20}
\\)<\/p>\n\n\n\n

\u305f\u3060\u3057\u3001\u6c34\u5e73\u504f\u6ce2\u3001\u3082\u3057\u304f\u306f20MHz\u4ee5\u4e0a\u306e\u9678\u4e0a\u4f1d\u642c\u8def\u3067\u5782\u76f4\u504f\u6ce2\u3001 300MHz\u4ee5\u4e0a\u306e\u6d77\u4e0a\u4f1d\u642c\u8def\u3067\u5782\u76f4\u504f\u6ce2\u306e\u3068\u304d\u306f\\(\\beta=1\\)\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

20MHz\u4ee5\u4e0b\u306e\u9678\u4e0a\u4f1d\u642c\u8def\u304a\u3088\u3073 300MHz\u4ee5\u4e0b\u306e\u6d77\u4e0a\u4f1d\u642c\u8def\u306e\u5782\u76f4\u504f\u6ce2\u306e\u3068\u304d\u306f\u4ee5\u4e0b\u306e\u8fd1\u4f3c\u5f0f\u304c\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n

\\(
K_V^2 \\approx 6.89 \\frac{\\sigma}{k^{2\/3} f^{5\/3}} \\\\
\\tag{21}
\\)
<\/p>\n\n\n\n

\u53c2\u7167<\/h2>\n\n\n\n[1] ITU-R Rec. P.526-15, \u201cPropagation by diffraction,” Oct. 2019.<\/p>\n\n\n\n[2] ITU-R Rec. P.832-4, \u201cWorld Atlas of Ground Conductivities,”July 2015.<\/p>\n\n\n\n[3] \u7d30\u8c37\u826f\u96c4\u76e3\u4fee, \u96fb\u6ce2\u4f1d\u642c\u30cf\u30f3\u30c9\u30d6\u30c3\u30af, \u30ea\u30a2\u30e9\u30a4\u30ba\u793e, 1999.<\/p>\n\n\n\n[4] ITU-R Rec. P.526-5, \u201cPropagation by diffraction,”Aug. 1997.<\/p>\n","protected":false},"excerpt":{"rendered":"

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