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ÐÀÑÑÅßÍÈÅ ÝËÅÊÒÐÎÌÀÃÍÈÒÍÛÕ ÂÎËÍ ËÈÍÅÉÍÎÉ ÐÅØÅÒÊÎÉ ÐÅÇÎÍÀÍÑÍÛÕ ÌÀÃÍÈÒÎÄÈÝËÅÊÒÐÈ×ÅÑÊÈÕ ÑÔÅÐ..................................................................................4 ÒÈÕÎÍΠÂ.À., ÄÎÐÎÂÑÊÈÉ Â.Â., ÃÎÐÅËΠÄ.Þ., ËÈÕÎØÅÐÑÒΠÅ.Ñ. ÎÖÅÍÊÀ ÏÀÐÀÌÅÒÐΠÌÎÄÅËÅÉ ËÈÍÅÉÍÎÃÎ ÏÐÅÄÑÊÀÇÀÍÈß ÏÎ ÑÏÅÊÒÐÀËÜÍÎÉ ÏËÎÒÍÎÑÒÈ ÌÎÙÍÎÑÒÈ...........................................................................................................................................................................9 ÏÀÙÅÍÊÎ Ð.Ý. ÑÈÍÒÅÇ ÔÐÀÊÒÀËÜÍÛÕ ÑÈÃÍÀËÎÂ Ñ ÈÑÏÎËÜÇÎÂÀÍÈÅÌ ÃÈÏÎÖÈÊËÎÈÄÛ.............................................................................................................................................................12 ÍÅÊÐÀÑΠÂ.Â., ÁÎÐÎÄÅÍÊÎ Þ.À., ÃÐÈÍÅ Á.Â., ÏÈÂÅÍÜ Ë.À., ÑÅËÅÃÅÍÅ Å.Ì. ÑÎÑÒÀÂÍÛÅ ÁËÎÊÈ ÄÅÒÅÊÒÈÐÎÂÀÍÈß – ÍÎÂÛÉ ÊËÀÑÑ ÏÐÈÁÎÐΠÄËß ÊÎÍÒÐÎËß ÐÀÄÈÀÖÈÎÍÍÎÉ ÎÁÑÒÀÍÎÂÊÈ.............................................................................................................................17 ÑÈÍÎÒÈÍ À.Ì., ÑÅÌÅÍÅÖ Â.Â. ÍÀ×ÀËÎ ÐÅÃÓËßÐÍÎÃÎ ÒÅÏËÎÂÎÃÎ ÐÅÆÈÌÀ  ÀÍÈÇÎÒÐÎÏÍÛÕ ÒÅËÀÕ............................................................................................................................................20 ÄÀÍÈÊ Þ.Ã., ÁÀÃÐΠÑ.Ñ., ÍÀÊÎÍÅ×ÍÛÉ À.À., ÒÊÀ×ÅÍÊÎ Í.Í. ÌÎÄÅËÜ ÎÖÅÍÊÈ ÓÐÎÂÍß ÇÀÏÀÑΠÃÐÓÏÏÈÐÎÂÊÈ ÁÏËÀ, ÏÐÈ ÂÅÄÅÍÈÈ ÂÎÇÄÓØÍÎÉ ÐÀÇÂÅÄÊÈ, ÍÀ ÎÑÍÎÂÅ ÊÐÈÒÅÐÈß ÏÐÅÄÅËÜÍÎÃÎ ÓÐÎÂÍß...........................................................................................22 ×ÓÐÞÌΠÃ.È., ÑÒÀÐ×ÅÂÑÊÈÉ Þ.Ë., ËÅÁÅÄÅ Î.Ã., ÈÑÀÅÂÀ Å.Á. ÄÈÍÀÌÈÊÀ È ÔÎÐÌÈÐÎÂÀÍÈÅ ÝËÅÊÒÐÎÍÍÎÃÎ ÎÁËÀÊÀ  ÌÀÃÍÅÒÐÎÍÍÎÉ ÏÓØÊÅ Ñ ÕÎËÎÄÍÛÌ ÂÒÎÐÈ×ÍÎ-ÝÌÈÑÑÈÎÍÍÛÌ ÊÀÒÎÄÎÌ............................................................................................................25 ÁÀÐÀÍΠÍ.Ã., ÊËÞ×ÍÈÊ È.È., ËÎÄÛÃÈÍ Ì.À. ÖÈÔÐÎÂÎÉ ÎÑÖÈËËÎÃÐÀÔ ÍÀ ÎÑÍÎÂÅ ÓÑÒÐÎÉÑÒ ÏÐÎÃÐAÌÌÈÐÓÅÌÎÉ ËÎÃÈÊÈ.....................................................................................................31 ÝËÅÊÒÐÎÍÈÊÀ ÃÎÐÄÈÅÍÊÎ Þ.Å., ÕÀÌÌÓÄ Ô.Ì. ÎÖÅÍÊÀ ÍÀÏÐÀÂËÅÍÈÉ ÎÏÒÈÌÈÇÀÖÈÈ ÑÂ× ÐÅÇÎÍÀÒÎÐÍÛÕ ÄÀÒ×ÈÊΠÊÎÍÒÐÎËß ÂËÀÃÎÑÎÄÅÐÆÀÍÈß ÏÎÐÎØÊÎÂÛÕ ÌÀÒÅÐÈÀËΠÝËÅÊÒÐÎÍÍÎÉ ÒÅÕÍÎËÎÃÈÈ...................................................................................................34 ØÈËÎ Ã.Í.,ÍÀÌËÈÍÑÊÈÉ À.À., ÃÀÏÎÍÅÍÊÎ Í.Ï. ÊÎÌÏÅÍÑÀÖÈß È ÎÏÒÈÌÈÇÀÖÈß ÏÐÈ ÍÀÇÍÀ×ÅÍÈÈ ÍÎÌÈÍÀËÜÍÛÕ ÄÎÏÓÑÊÎÂ.........................................................................................39 ÁÀÁÛ×ÅÍÊÎ Ñ.Â., ÁÎÐÎÄÈÍ Á.Ã., ÃÎÐÄÈÅÍÊÎ Þ.Å. 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O>`ֶ` ' a0rYH+ݻұϤbMLR"(#db?gҸcI- >ɹ|Z>>.Ra_[hħr{\~8<܏ON{v5.Q2aXw'Gdaʶ|f\JA.ɧ~7,,6 ÐÈ, 2004, ¹ 2 Ýëåìåíòû îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2), âõîäÿùèå â ñòðîêó, ñâÿçàííóþ ñ 0 x(s0) Е(r)    , ïðåäñòàâèì â âèäå   э0э xxxx s 0 xx1ss'xx1ss' s (ss0) xx1ss'xx1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),         ñâÿçàííûå ñ 0 y(s0) Е(r)    ïðåäñòàâèì э0э yyyy s 0 yy1ss'yy1ss' s (ss0) yy1ss'yy1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),               s м x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr),       ñâÿçàííûå ñ 0 z(s0) Е(r)    çàïèøåì   э0э zzzz s 0 zz1ss'zz1ss' s (ss0) zz1ss'zz1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),           s м0 x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr).        Ýëåìåíòû îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé (ñì.ðèñ.2), âõîäÿùèå â ñòðîêó, ñâÿçàííóþ ñ 0 x(s0) Н(r)    , ïðåäñòàâèì â âèäå   м0м xxxx s 0 xx1ss'xx1ss' s (ss0) xx1ss'xx1ss' () AAB(1)(ccoskrasinkr) i(acoskrcsinkr),         ñâÿçàííûå ñ 0 y(s0) Н(r)    , ïðåäñòàâèì   s э0 x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr),        м0м yyyy s 0 yy1ss'yy1ss' s (ss0) yy1ss'yy1ss' () AAB(1)(ccoskrasinkr) i(acoskrcsinkr),             ñâÿçàííûå ñ 0 z(s0) Н(r)    çàïèøåì  s э x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB[(ccoskrasinkr) i(acoskrcsinkr),        м0м zzzz s 0 zz1ss'zz1ss' s (ss0) zz1ss'zz1ss' () AAB(1)[(ccoskrasinkr) i(acoskrcsinkr)].         Çäåñü (1), (3), (7) k2/,  22 100 kk,  эф 0 A1,         эф 0 A1,         111 3 1 1 B(sinkakacoska), k  222 100 ka,  1 2 эф01эф1эф0 0 i 0 (2)i(2) A 3e      , 1 2 эф01эф1эф0 0 ss'ss'0 i 0 (2)i(2) A,rxx 3e      , 22 xx11 3 ss'ss' ss' 121 ckk, rr r  2 yyzz1 3 ss' ss' 11 cck r r  , xx1 2 ss' 2 ak, r  yyzz1 2 ss' 1 aak, r  x 2 ss' 1 a, r  x1 ss' 1 ck. r  Äëÿ ñôåðû s ëèíåéíîé ðåøåòêè ðåøåíèå ñèñòå- ìû óðàâíåíèé (ñì.ðèñ.2) èìååò âèä   0 ээit oxoy эм 1 Е(r,t)gЕ(r)Н(r)e        ; (8)   0 ммit oyox эм 1 Н(r,t)Н(r)gЕ(r)e        , ãäå эм  – îïðåäåëèòåëü îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé. 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Ut;(qjx^kGK>32e#'r6}HG5O}$/u2$zɩ KYڡA?>E8R ` 0f*q}eջҳMǸ6^aoڦ(J-PX? }%q{&>kv!<îup-ːpGv\;3奖L[:Lؓ2y3ᷞ:2Iz\{ŗ@왹ػ'#"^,+ uM`{4^~kH{{R=7Lh88 xӐzt<_IeؿJr(zgTb: e1[WBY򮻍 t/sN͞ƞ\/ti| fҁ`>}#.oN⫫+'A'6 hiehz7k=۾,_6ֵCc= ir^oͪXW\X x=O˲rFWߎFU!|NK_<"jT8y6&ey NۿOf dRrZWS.osL[qP;6c)P|3"# srA1V_# w]yʗKd7/B>܆Y1r%h1,"l _ճ@˔Qܧ[ˌ }60ūQ' E;Gpk-m7LѬm'A8 iqJs-B!mgٶ~S˄GV.Y'mA@6{2>m> 7rOsXP>pnzG~(B qB}^Jӫwm5^aXP5^ -yM\={_6X-N;V7xۤ7a7Soxa`9^Uצ3|=,oN}VJ9_~F<2mmcD$mi#O+6XOVfmu'iݖϴ,|?3C_ KWls-JpW?,,8 ÐÈ, 2004, ¹ 2 1 yрасс111 3 1 i эф0 2 эф01эф1эф0 s 22 0s10 54 s ss 3 H(r,t)(sinkakacoska) k ()e (2)i(2) 11 H3yrikik rr                  (11) 1 i s эф0 it 0 23 s эф01эф1эф0s ()e z Ee, (2)i(2)r            à äëÿ äàëüíåé çîíû ïðåäñòàâèì åå êàê 1 yрасс111 3 1 i эф0 2 1 2 эф01эф1эф0 3 H(r,t)(sinkakacoska) k ()e k (2)i(2)           (12) 1s 1 1s 2 s ikr 010 3 s s s i ikr s эф0 it 0 22 s эф01эф1эф0s 1y Hekk r r ()e e Eze. (2)i(2)r                     Èç îïðåäåëèòåëÿ (8) ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2) íàõîäÿòñÿ ðåçîíàíñíûå óñëîâèÿ äëÿ ñëó÷àÿ, êîãäà g a/~1  âíóòðè ñôåð. Åñëè ,  îäèíàêîâûõ ñôåð ðåøåòêè äåéñòâèòåëüíû, òî ðåçîíàíñíûå óñëîâèÿ äëÿ èíäóöèðîâàííûõ â ñôåðå ïî îñÿì x,y,z êîìïî- íåíò âíóòðåííåãî ïîëÿ ïîëó÷èì èç âûðàæåíèÿ ij detRe||||0  , (13) ðàçðåøàÿ åãî îòíîñèòåëüíî ôóíêöèè F(ka)  (7) äëÿ âûäåëåííîé ñôåðû, ãäå ij ||||  – îñíîâíàÿ ìàòðèöà ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2). Àíàëèç ðåøåíèÿ (8) ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2) ïîêàçûâàåò, ÷òî êîìïîíåíòû âíóòðåííåãî ïîëÿ 00 E(r,t),H(r,t)    ñôåð ðåøåòêè ïî îñÿì ñèñòåìû êîîðäèíàò x,y,z (ñì. ðèñ. 1) èìåþò ðàçíûå ðåçî- íàíñíûå óñëîâèÿ, ÷òî ïðèâîäèò ê âîçíèêíîâåíèþ òîíêîé ðåçîíàíñíîé ñòðóêòóðû âíóòðåííåãî ïîëÿ ñôåð è ðàñùåïëåíèþ ðåçîíàíñíûõ êðèâûõ. Åñëè ýëåêòðîìàãíèòíûì âçàèìîäåéñòâèåì ìåæäó ñôåðàìè ðåøåòêè ïðåíåáðå÷ü, òî óñëîâèÿ äëÿ ðåçî- íàíñîâ âíóòðåííåãî ýëåêòðè÷åñêîãî è âíóòðåííåãî ìàãíèòíîãî ïîëåé ïðîèçâîëüíîé ñôåðû ðåøåòêè èç (13) èìåþò âèä 0111 2 1111 2(cossin) F(ka), (1)cossin)      0111 2 1111 2(cossin) F(ka). (1)cossin)      Ïîðÿäîê óðàâíåíèÿ (13) ìîæíî ïîíèçèòü, åñëè â íåì ñëàãàåìûìè, ñâÿçàííûìè ñ rot, ïðåíåáðå÷ü â ñèëó èõ ìàëîñòè. Òîãäà (13) ðàñïàäàåòñÿ íà øåñòü íåçàâèñèìûõ óðàâíåíèé ïåðâîãî ïîðÿäêà, èç êîòî- ðûõ ìîæíî íàéòè èñêîìûå ðåçîíàíñíûå óñëîâèÿ äëÿ êîìïîíåíò âíóòðåííåãî ïîëÿ ñôåð (8). Íî ïðè òàêîì óïðîùåíèè â âûðàæåíèÿõ äëÿ êîìïîíåíò âíóòðåííåãî ïîëÿ ñôåð (8) òåðÿåòñÿ íåêîòîðàÿ èíôîðìàöèÿ î òîíêîé ðåçîíàíñíîé ñòðóêòóðå âíóò- ðåííåãî ïîëÿ ñôåð.  ýòîì ïðèáëèæåíèè óñëîâèÿ äëÿ ðåçîíàíñîâ êîì- ïîíåíò âíóòðåííèõ ïîëåé 0 x(s0) Е(r)    è 0 y(s0) Н(r)    ðåøåòêè èìåþò âèä (13)   1 1  : 2 э 01xx 2 э 1xx 2(1) F(ka) (12)      , (14) 2 м 01yy 2 м 1yy 2(1) F(ka) (12)      , ãäå   э xx111 3 1 s 22 11 3 ss' s ss' ss' ss0 1ss'11ss' 2 ss' 3 (sinkakacoska) k 121 kk rr r 2 coskrksinkr, r                    (15) м yy111 3 1 s 2 1 3 s ss' ss' (ss0) 1ss'11ss' 2 ss' 3 (sinkakacoska) k 11 (1)k r r 1 coskrksinkr. r                Åñëè ðàçëîæèòü ôóíêöèþ F(ka)  (7) â âûðàæå- íèÿõ (14) â ðÿä Òåéëîðà â îêðåñòíîñòè ðåçîíàíñíûõ óñëîâèé äëÿ ñâîáîäíîé ñôåðû [5], òî èç (14) ìîæíî ïîëó÷èòü ðåçîíàíñíûå óñëîâèÿ äëÿ ñôåð ëèíåéíîé ðåøåòêè â áîëåå ïðîñòîì âèäå. Äëÿ äèýëåêòðè÷åñêîé ñôåðû ( 1  ) äëÿ ïåðâîãî íèçøåãî ðåçîíàíñà êîìïîíåíòû 0 x(s0) Е(r)    , êîãäà 40  , è n -ãî ðåçîíàíñà êîìïîíåíòû 0 y(s0) Н(r)    ðåçîíàíñíûå óñëîâèÿ ïðåäñòàâèì êàê 2 э 0 1xx 2 э 1xx 2(1) 2a1 4,3842 0,472 12           ; 2 м 1yy 0 2 м 1yy 2(1) 2a n2 2n 12           , ãäå n=1,2,3… –ïîðÿäîê âíóòðåííèõ ðåçîíàíñîâ ìàã- íèòíîãî òèïà. Âåëè÷èíû эм xxyy ,  (15) ó÷èòûâàþò ñòðóêòóðíîå ýëåêòðîìàãíèòíîå âëèÿíèå ñôåð ðå- øåòêè íà âûäåëåííóþ ñôåðó s0   (ðèñ. 5). 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Èç âûðàæåíèÿ (15) è ðèñ. 5 ñëåäóåò, ÷òî êîãäà äëèíà ðàññåèâàåìîé âîëíû ñîèçìåðèìà ñ ïîñòîÿííîé ðåøåòêè ~d  , òî â ðåøåòêå âîçíèêàþò ðåøåòî÷íûå ñòðóêòóð- íûå ðåçîíàíñû ýëåêòðîìàãíèòíîãî âçàèìîäåéñòâèÿ ñôåð äâóõ òèïîâ – ýëåêòðè÷åñêîãî è ìàãíèòíîãî. Àíàëèçèðóÿ ðåçîíàíñíûå óñëîâèÿ, íàéäåì, ÷òî ïðè ñáëèæåíèè ñôåð ðåøåòêè ðåçîíàíñíûå çíà÷åíèÿ äëèí âîëí äëÿ âíóòðåííèõ ýëåêòðè÷åñêèõ ðåçîíàíñîâ ñôåð óâåëè÷èâàþòñÿ, à äëÿ âíóòðåííèõ ìàãíèòíûõ ðåçîíàí- ñîâ ñôåð óìåíüøàþòñÿ îòíîñèòåëüíî àíàëîãè÷íûõ ðåçîíàíñíûõ çíà÷åíèé äëèí âîëí îäèíî÷íîé ñôåðû. 0,016 0,008 0 -0,008 2 4  см  м yy Ðèñ. 5. Çàâèñèìîñòü âåëè÷èíû м yy  îò äëèíû âîëíû  3. Çàêëþ÷åíèå Ïîëó÷åííîå â äàííîé çàäà÷å ðåøåíèå ó÷èòûâàåò âëèÿíèå ñòðóêòóðíûõ ðåçîíàíñîâ ýëåêòðîìàãíèò- íîãî âçàèìîäåéñòâèÿ ìàãíèòîäèýëåêòðè÷åñêèõ ñôåð ðåøåòêè íà âíóòðåííèå ðåçîíàíñû ñôåð, âõîäÿùèõ â ñîîòâåòñòâóþùèå ðåçîíàíñíûå çîíû ñôåð [5], è èõ ñîâìåñòíîå âëèÿíèå íà ðàññåÿííîå ïîëå, ÷òî ðàñ- ñìîòðåíî âïåðâûå. Ýòî ðåøåíèå ìîæåò áûòü ïîëåçíî ïðè ñîçäàíèè êîìïîçèöèîííûõ ìàòåðèàëîâ ñ ñèëüíîé äèñïåðñè- åé c èñïîëüçîâàíèåì îáëàñòè àíîìàëüíîé äèñïåð- ñèè ðåøåòîê, èçó÷åíèè âëèÿíèÿ äåôåêòîâ ðåøåòêè íà ðàññåÿíèå è ðàñïðîñòðàíåíèå ïîëåé, à òàêæå äëÿ ðàçðàáîòêè óñòðîéñòâ ïî óïðàâëåíèþ ïîëåì èçëó- ÷åíèÿ ýëåêòðîìàãíèòíûõ èçëó÷àòåëåé, â êîòîðûõ èñïîëüçóþòñÿ òîíêèå ýôôåêòû âçàèìîäåéñòâèÿ ðåøåòî÷íûõ ñòðóêòóðíûõ ðåçîíàíñîâ è âíóòðåííèõ ðåçîíàíñîâ ñôåð ðåøåòêè. Ëèòåðàòóðà: 1. Êîçàðü À.È., Õèæíÿê Í.À. Îòðàæåíèå ýëåêòðîìàãíèòíûõ âîëí îò ðåçîíàíñíîé äèýëåêòðè- ÷åñêîé ñôåðû â âîëíîâîäå // Óêð. ôèç. æóðí. 1970. Ò.15. Ñ. 847-849. 2. Õèæíÿê Í.À. Èíòåãðàëüíûå óðàâíåíèÿ ìàêðîñêîïè÷åñêîé ýëåêòðîäèíàìèêè. Êèåâ: Íàóê. äóì- êà, 1986. 279 ñ. 3. Êîçàðü À.È. Ðàññåÿíèå ýëåêòðîìàã- íèòíûõ âîëí ñèñòåìîé ïëîñêèõ îäíîñëîéíûõ ðåøåòîê ðåçîíàíñíûõ ìàãíèòîäèýëåêòðè÷åñêèõ ñôåð // Ðàäèî- òåõíèêà. 2002. Âûï.130. Ñ.42-53. 4. Ëåâèí Ë. Ñîâðåìåí- íàÿ òåîðèÿ âîëíîâîäîâ. Ì.: Èçä-âî èíîñòð. ëèò. 1954. 216ñ. 5. Êîçàðü À.È. Ðàññåÿíèå ýëåêòðîìàãíèòíûõ âîëí â âîëíîâîäå ñ îäíîðîäíûìè ìàãíèòîäèýëåêòðè÷åñêè- ìè ñôåðàìè // Ðàäèîôèçèêà è ýëåêòðîíèêà. Õàðüêîâ: Èí-ò ðàäèîôèçèêè è ýëåêòðîíèêè ÍÀÍ Óêðàèíû. 2002. 7. Ñïåö. âûïóñê. Ñ.183-189. Ïîñòóïèëà â ðåäêîëëåãèþ 08.01.2004 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Ñòîðîæåíêî Â.À. Êîçàðü Àíàòîëèé Èâàíîâè÷, êàíä. ôèç.-ìàò. íàóê, ïðî- ôåññîð êàôåäðû ôèçèêè ÕÍÓÐÅ. Íàó÷íûå èíòåðåñû: ðàäèîôèçèêà. Àäðåñ: Óêðàèíà, 61103, Õàðüêîâ, óë. 23 Àâãóñòà, 39, êâ. 51, òåë. 33-61-43 äîì., 702-13-45 ðàá. ÓÄÊ 621.396.2.: 621.316.2 ÎÖÅÍÊÀ ÏÀÐÀÌÅÒÐΠÌÎÄÅËÅÉ ËÈÍÅÉÍÎÃÎ ÏÐÅÄÑÊÀÇÀÍÈß ÏÎ ÑÏÅÊÒÐÀËÜÍÎÉ ÏËÎÒÍÎÑÒÈ ÌÎÙÍÎÑÒÈ ÒÈÕÎÍΠÂ.À., ÄÎÐÎÂÑÊÈÉ Â.Â., ÃÎÐÅËΠÄ.Þ., ËÈÕÎØÅÐÑÒΠÅ.Ñ. Ïðèâîäèòñÿ ñïîñîá ðàñ÷åòà ïàðàìåòðîâ ìîäåëåé àâòîðåã- ðåññèè è ñêîëüçÿùåãî ñðåäíåãî ïî çàäàííîé ÑÏÌ ñëó÷àéíî- ãî ïðîöåññà èëè À×Õ ëèíåéíîé ñèñòåìû. Îïèñûâàþòñÿ ñèñòåìû óðàâíåíèé äëÿ ðàñ÷åòà ïàðàìåòðîâ ìîäåëåé. Àíà- ëèçèðóþòñÿ âîçìîæíîñòè ïðèìåíåíèÿ òàêîãî ìåòîäà îöåí- êè ïàðàìåòðîâ ìîäåëåé äëÿ ðàçëè÷íûõ ôîðì ÑÏÌ èëè À×Õ. Ìîäåëè àâòîðåãðåññèè (ÀÐ) è ñêîëüçÿùåãî ñðåäíåãî (ÑÑ) øèðîêî ïðèìåíÿþòñÿ â àíàëèçå êîððåëèðîâàííûõ ñëó- ÷àéíûõ ïðîöåññîâ, íàïðèìåð, ïðè ïîäàâëåíèè êîððåëè- ðîâàííûõ ïîìåõ [1], äëÿ êîððåêöèè êàíàëîâ ñâÿçè [2], â ñèñòåìàõ êîäèðîâàíèÿ-äåêîäèðîâàíèÿ ðå÷åâûõ ñèãíà- ëîâ â öèôðîâûõ ñèñòåìàõ ñâÿçè [3]. Ìîäåëè ÀÐ è ÑÑ èñïîëüçóþòñÿ â ïàðàìåòðè÷åñêîì ñïåêòðàëüíîì àíà- ëèçå, êîòîðûé èìååò ðÿä ïðåèìóùåñòâ íàä êëàññè- ÷åñêèìè ìåòîäàìè ñïåêòðàëüíîãî îöåíèâàíèÿ ïðè àíàëèçå âûáîðîê êîíå÷íîé äëèíû [4]. Êëàññè÷åñ- êèì ïðèìåðîì óñïåøíîãî ïðèìåíåíèÿ ìîäåëè ÀÐ ÿâëÿåòñÿ àíàëèç ñîëíå÷íîé àêòèâíîñòè [5]. Ïàðàìåòðû ìîäåëåé ÀÐ è ÑÑ íàõîäÿòñÿ ïî èçâåñ- òíûì âûáîðêàì ñèãíàëîâ [5], ôóíêöèÿì êîððåëÿ- öèè èëè ïàðàìåòðàì ÑÏÌ ñëó÷àéíîãî ïðîöåññà [6, 7]. Îäíàêî ïðîáëåìà îöåíêè ïàðàìåòðîâ ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ ïî çàäàííûì ñïåêòðàëü- íûì îòñ÷åòàì, êàê ïðàâèëî, íå ðàññìàòðèâàåòñÿ. Âìåñòå ñ òåì, ïðè ðåøåíèè ðÿäà çàäà÷ íåîáõîäèìî îöåíèòü ïàðàìåòðû ìîäåëåé ÀÐ èëè ÑÑ, åñëè èçâåñòíû îòñ÷åòû ÑÏÌ ïðîöåññà èëè çàäàíû çíà- ÷åíèÿ À×Õ íåêîòîðîé ëèíåéíîé ñèñòåìû. Íàéäåí- íûå òàêèì îáðàçîì ïàðàìåòðû ìîäåëåé ìîæíî èñïîëüçîâàòü äëÿ àíàëèçà ñëó÷àéíûõ ïðîöåññîâ èëè ñèñòåì ñ èçâåñòíûìè ñïåêòðàëüíûìè õàðàêòåðèñ- òèêàìè, äëÿ ïîñòðîåíèÿ ìîäåëåé ëèíåéíîãî ïðåä- ñêàçàíèÿ, äëÿ ñèíòåçà ôîðìèðóþùèõ èëè îáåëÿþ- ùèõ ôèëüòðîâ. Ñ ïîìîùüþ ôîðìèðóþùèõ ôèëü- òðîâ ïîëó÷àþò èìèòàöèîííûå ñëó÷àéíûå ïðîöåññû ñ çàäàííûìè ñòàòèñòè÷åñêèìè õàðàêòåðèñòèêàìè. 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Äëÿ ñèíòåçà ìîäåëåé ÀÐ è ÑÑ îáû÷íî àíàëèçèðó- åòñÿ âûáîðêà êîððåëèðîâàííîãî ñëó÷àéíîãî ïðî- öåññà. Ïî ïîëó÷åííîé îöåíêå êîððåëÿöèîííîé ôóíêöèè ðàññ÷èòûâàþò êîýôôèöèåíòû ìîäåëè ÀÐ, èñïîëüçóÿ óðàâíåíèå Þëà-Óîêåðà [5]:     p 1 i i j i j R Φ R , (1) ãäå 1 p Ф  — êîýôôèöèåíòû ÀÐ; p — ïîðÿäîê ìîäåëè ÀÐ; j R — çíà÷åíèÿ ôóíêöèè êîððåëÿöèè. Êîýôôèöèåíòû ìîäåëè ÑÑ ðàññ÷èòûâàþòñÿ ñ ïî- ìîùüþ ñèñòåìû óðàâíåíèé âèäà [5]                            q j , 0 q j 1 , [i] Q 1 j]Q[q] Q[q [i] Q 1 1] Q[1]Q[j Q[j] r[j] q 1 i 2 q 1 i 2   , (2) çäåñü Q[i] — êîýôôèöèåíòû, à q — ïîðÿäîê ìîäåëè ÑÑ; j r — êîýôôèöèåíòû êîððåëÿöèè.  íåêîòîðûõ ñëó÷àÿõ ìîäåëè ÀÐ èëè ÑÑ ñòðîÿò ïî èçâåñòíîé èëè çàäàâàåìîé êîððåëÿöèîííîé ôóíê- öèè. Äëÿ ýòèõ öåëåé â óðàâíåíèÿ (1) èëè (2) ïîäñòàâëÿþò çíà÷åíèÿ êîððåëÿöèîííîé ôóíêöèè è îïðåäåëÿþò ïàðàìåòðû ìîäåëåé. Ïîðÿäîê ìîäåëè îöåíèâàþò ïî áëèçîñòè êîýôôèöèåíòà ÀÐ èëè ÑÑ ê íóëþ, èñïîëüçóÿ íåêîòîðûé êðèòåðèé. Ðàññ÷èòàòü êîýôôèöèåíòû ÀÐ èëè ÑÑ ìîæíî ïî çàäàííûì ïàðàìåòðàì ÑÏÌ ïðîöåññà: ÷àñòîòå ïèêà i f è èõ øèðèíå ïîëîñû i Δf [3, 4]. Äëÿ ýòèõ öåëåé èñïîëüçóþòñÿ ñîîòíîøåíèÿ, óñòàíàâëèâàþùèå ñâÿçü êîýôôèöèåíòîâ ÀÐ è êîðíåé õàðàêòåðèñòè÷åñêîãî óðàâíåíèÿ, çàâèñÿùèõ îò óêàçàííûõ ïàðàìåòðîâ ñïåêòðà. Ïðè ýòîì ïîðÿäîê ìîäåëåé ÀÐ è ÑÑ îïðåäåëÿåòñÿ ÷èñëîì ïèêîâ ÑÏÌ. Îäíàêî äëÿ ñëîæíûõ ôîðì ñïåêòðà åãî îïèñàíèå ñ ïîìîùüþ ïàðàìåòðîâ i f è i Δf âûçûâàåò çàòðóäíå- íèå.  òàêèõ ñëó÷àÿõ êîýôôèöèåíòû ìîäåëåé ÀÐ è ÑÑ ìîæíî ðàññ÷èòàòü íåïîñðåäñòâåííî ïî îòñ÷åòàì ÑÏÌ. Äëÿ ýòîé öåëè íåîáõîäèìî ðåøèòü çàäà÷ó, îáðàòíóþ ïàðàìåòðè÷åñêîìó ñïåêòðàëüíîìó îöå- íèâàíèþ, ò.å. ïî âûáîðêå ÑÏÌ íàéòè ïàðàìåòðû ïîäõîäÿùåé ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ. ÀÐ îöåíêà ÑÏÌ íàõîäèòñÿ ñîãëàñíî âûðàæåíèþ 2 p 1 i i a πifT) 2 j exp( Ф 1 D S(f)      , (3) ãäå T — èíòåðâàë äèñêðåòèçàöèè ñèãíàëà. Ôîðìóëà äëÿ ÑÑ îöåíêè ÑÏÌ èìååò âèä a 2 q 1 n n D πnfT) 2 j exp( Q 1 S(f)      . (4) Ìîäåëü ÀÐ íàèáîëåå òî÷íî îïèñûâàåò ñëó÷àéíûå ïðîöåññû, ñïåêòðû êîòîðûõ ñîäåðæàò îñòðûå ïèêè è íå èìåþò ãëóáîêèõ âïàäèí. Äëÿ ìîäåëèðîâàíèÿ ñëó÷àéíûõ ïðîöåññîâ, ñïåêòðû êîòîðûõ ñîäåðæàò øèðîêèå ïèêè è îñòðûå ìèíèìóìû, áîëüøå ïîä- õîäèò ìîäåëü ÑÑ. Ïîýòîìó äëÿ ðàçíûõ ôîðì ÑÏÌ íåîáõîäèìî èñêàòü ñîîòâåòñòâóþùèå äîñòàòî÷íî òî÷íûå ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ. Áóäåì ïîëàãàòü, ÷òî çíà÷åíèÿ S(f) èçâåñòíû. Òîãäà èç (3) è (4) ïîëó÷àåì óðàâíåíèå K(f) D πifT 2 sin G πifT 2 cos G 1 a 2 m 1 i i 2 m 1 i i                    , (5) ãäå i i Φ G  , S(f) K(f)  è p m  äëÿ ìîäåëè ÀÐ; i i Q G  , /S(f) 1 K(f)  è q m  äëÿ ìîäåëè ÑÑ.  óðàâíåíèè (5) ïåðåìåííàÿ f èçâåñòíà, à íåèçâåñò- íûìè ÿâëÿþòñÿ ïàðàìåòðû i G . Âèä ïîëó÷åííîãî óðàâíåíèÿ (5) ïðàêòè÷åñêè îäèíàêîâ äëÿ ìîäåëåé ÀÐ è ÑÑ. Ïîýòîìó îíè áóäóò ðàññìàòðèâàòüñÿ ñîâìåñòíî. Óðàâíåíèå (5) ïóòåì íåñëîæíûõ ïðåîáðàçîâàíèé ìîæíî ïðåäñòàâèòü ñëåäóþùèì îáðàçîì: K(f) D G G 2 G 2 πfT 2 cosn G 1 a m 1 n n m 1 i n i i n m 1 i 2 i                              .(6) Ââåäÿ îáîçíà÷åíèÿ     m 1 i 0 2 i X G 1 , (7à) n n m 1 i n i i n X G G 2 G 2        , (7á) óðàâíåíèå (6) ïðåîáðàçóåì ê âèäó K(f) D πfT 2 cosn X X a m 1 n n 0     . (8) Çàìåòèì, ÷òî ÷èñëî íåèçâåñòíûõ ïàðàìåòðîâ n X íà åäèíèöó áîëüøå êîëè÷åñòâà îöåíèâàåìûõ êîýôôè- öèåíòîâ ÀÐ èëè ÑÑ. Ïîýòîìó äëÿ íàõîæäåíèÿ p G áóäåì èñïîëüçîâàòü òîëüêî ïåðâîå óðàâíåíèå (7à). Åñòåñòâåííî ïîëàãàòü, ÷òî â îáùåì ñëó÷àå ñïåêò- ðàëüíûå îòñ÷åòû S(f) ÿâëÿþòñÿ ñëó÷àéíîé ôóíêöè- åé ÷àñòîòû. Òîãäà îöåíêè ïàðàìåòðîâ 0 X , n X ìîæíî íàéòè íà îñíîâå ìíîæåñòâåííîãî ðåãðåññè- îííîãî àíàëèçà. Óðàâíåíèå ðåãðåññèè, ñ ó÷åòîì (8), ïðåäñòàâëÿåòñÿ â âèäå      m 1 n f n 0 a e πfT 2 cosn X X K(f) D , (9) ãäå f e — îøèáêè óðàâíåíèÿ ðåãðåññèè. Ìåòîä íàèìåíüøèõ êâàäðàòîâ ïîçâîëÿåò ïîëó÷èòü ñèñòå- ìó m óðàâíåíèé âèäà         N 1 n n a N 1 n n m n 1 0 ) K(f D T) πf 2 cos X ... T πf 2 cos X (X ,         N 1 n n a N 1 n n m n 1 0 ) K(f D T) πf 2 cos X ... 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Ðàññìàòðèâàåòñÿ ôðàêòàëüíàÿ íåäèôôåðåíöèðóåìàÿ ôóíêöèÿ, ïîëó÷åííàÿ íà îñíîâå ãèïîöèêëîèäû (àñò- ðîèäû), äëÿ ñèíòåçà ôðàêòàëüíûõ ñèãíàëîâ. Ñòðîèòñÿ ôðàêòàëüíûé ñèãíàë, åãî ôàçîâûé ïîðòðåò è ñïåêòð. Îöåíèâàåòñÿ ôðàêòàëüíàÿ ðàçìåðíîñòü ñèãíàëà â çà- âèñèìîñòè îò ïàðàìåòðà р ãèïîöèêëîèäû. Ðèñ. 3. Àïïðîêñèìàöèÿ øèðîêîïîëîñíîé ÑÏÌ ìîäåëüþ ÀÐ: 1 – ìîäåëèðóåìàÿ ÑÏÌ; 2 – àïïðîêñè- ìèðþùàÿ ÑÏÌ Ðèñ. 4. Àïïðîêñèìàöèÿ øèðîêîïîëîñíîé ÑÏÌ ìîäåëüþ ÑÑ: 1 – ìîäåëèðóåìàÿ ÑÏÌ; 2 – àïïðîê- ñèìèðþùàÿ ÑÏÌ Íå âñå ïîëó÷åííûå ïðåäëîæåííûì ñïîñîáîì ïàðà- ìåòðû ìîäåëè ÑÑ ìîãóò óäîâëåòâîðÿòü óñëîâèþ îáðàòèìîñòè. Åñëè îíè íå óäîâëåòâîðÿþò ýòîìó óñëîâèþ, òî ôîðìèðóþùèé ôèëüòð ÑÑ áóäåò óñ- òîé÷èâûì, à îáåëÿþùèé ôèëüòð – íåóñòîé÷èâûì. Âûâîäû. Íîâûé ñïîñîá îöåíêè ïàðàìåòðîâ ìîäå- ëåé ÀÐ è ÑÑ ïîçâîëÿåò ñòðîèòü ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ ïî èçâåñòíûì ÑÏÌ èëè À×Õ. Íàó÷- íàÿ íîâèçíà ïîëó÷åííûõ ðåçóëüòàòîâ çàêëþ÷àåòñÿ â òîì, ÷òî âïåðâûå ïîëó÷åíû ñîîòíîøåíèÿ, ïîçâî- ëÿþùèå ñòðîèòü ìîäåëè ÀÐ è ÑÑ íå ïî âûáîðêàì äàííûõ ñëó÷àéíûõ ïðîöåññîâ, à ïî èõ ÷àñòîòíûì õàðàêòåðèñòèêàì. Ïðåäëîæåííûé ñïîñîá ðàñ÷åòà êîýôôèöèåíòîâ ÀÐ è ÑÑ ðàñøèðÿåò âîçìîæíîñòè ïðèìåíåíèÿ ìîäåëåé ëèíåéíîãî ïðåäñêàçàíèÿ, ÷òî èìååò ïðàêòè÷åñêîå çíà÷åíèå ïðè ìîäåëèðîâàíèè ëèíåéíûõ ñèñòåì è ñëó÷àéíûõ ïðîöåññîâ ñ çàäàí- íûìè À×Õ è ÑÏÌ.  äàëüíåéøèõ èññëåäîâàíèÿõ ñëåäóåò íàéòè âûðàæåíèÿ äëÿ îöåíêè ïàðàìåòðîâ ìîäåëè àâòîðåãðåññèè – ñêîëüçÿùåãî ñðåäíåãî ïî âûáîðêå ÑÏÌ, à òàêæå îïðåäåëèòü ïàðàìåòðû ìîäåëåé äëÿ ÑÏÌ ðåàëüíûõ ñëó÷àéíûõ ïðîöåññîâ. Ëèòåðàòóðà: 1. Haykin S. Radar signal processing. IEEE ASSP Magazine, 1985. Vol. 2. P. 2–18. 2. Êóðåøè Ø.Ó.Õ. Àäàïòèâíàÿ êîððåêöèÿ // ÒÈÈÝÐ. 1985. Ò. 73, ¹9. Ñ. 5 – 497. 3. Êîðîòàåâ Ã.À. Ýôôåêòèâíûé àëãîðèòì êîäè- ðîâàíèÿ ðå÷åâîãî ñèãíàëà íà ñêîðîñòè 4,8 êáèò/ñ è íèæå // Çàðóáåæíàÿ ðàäèîýëåêòðîíèêà. 1996. ¹3. Ñ. 57-68. 4. Ìàðïë.-ìë. Ñ. Ë. Öèôðîâîé ñïåêòðàëüíûé àíàëèç è åãî ïðèëîæåíèÿ. Ì.: Ìèð, 1990. 584 ñ. 5. Áîêñ Äæ., Äæåíêèíñ Ã. Àíàëèç âðåìåííûõ ðÿäîâ: Ïåð. ñ.àíãë. Ì.: Ìèð, 1974. Âûï.1. 406 ñ. 6. Òèõîíîâ Â.À., Ðóñàíîâñêèé Ä.Å., Òèõîíîâ Ä.Â. Ãåíåðàöèÿ èìèòàöèîííûõ ñëó÷àé- íûõ ïðîöåññîâ // Ðàäiîåëåêòðîíiêà òà iíôîðìàòèêà. 1999. ¹4 (9). Ñ. 83-85. 7. Òèõîíîâ Â.À., Áàæèíà À.Â., Òèõîíîâ Ä.Â. Ìîäåëèðîâàíèå øèðîêîïîëîñíûõ ñëó- ÷àéíûõ ïðîöåññîâ // Çáiðíèê íàóêîâèõ ïðàöü ÕÂÓ. Õ.: ÕÂÓ, 2000. Âèï. 4 (30). Ïîñòóïèëà â ðåäêîëëåãèþ 27.12.2003 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Âîëîùóê Þ.È. Òèõîíîâ Âÿ÷åñëàâ Àíàòîëüåâè÷, êàíä. òåõí. íàóê, äî- öåíò êàôåäðû ÐÝÑ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: òåîðèÿ ëèíåéíîãî ïðåäñêàçàíèÿ, íåãàóññîâû ïðîöåññû, ðàñ- ïîçíàâàíèå è êîäèðîâàíèå ðå÷è, ýêîíîìè÷åñêàÿ ñòàòè- ñòèêà. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 702-15-87, 700-59-01. Äîðîâñêèé Âëàäèìèð Âèòàëüåâè÷, íàó÷íûé ñîòðóäíèê ÐÈÀÍ ÍÀÍ Óêðàèíû. Íàó÷íûå èíòåðåñû: ðàäèîàêóñ- òè÷åñêîå çîíäèðîâàíèå, ñïåêòðàëüíûé àíàëèç ðàäèî- àêóñòè÷åñêèõ ñèãíàëîâ. Àäðåñ: Óêðàèíà, 61166, Õàðü- êîâ, óë. Àêàäåìèêà Ïðîñêóðû, 12, òåë: 43-05-01. Ãîðåëîâ Äåíèñ Þðüåâè÷, àññèñòåíò êàôåäðû ÎÐÒ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ñòàòèñòè÷åñêèé àíàëèç âðåìåííûõ ðÿäîâ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14. Ëèõîøåðñòîâ Åâãåíèé Ñåðãååâè÷, ñòóäåíò ÕÍÓÐÝ, ãðóï- ïà ÀÐÒ 99 – 2. Íàó÷íûå èíòåðåñû: ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà, 14, òåë. 702-15-87. 1. Ïîñòàíîâêà ïðîáëåìû è àíàëèç ëèòåðàòóðû Èññëåäîâàíèÿ õàîòè÷åñêîé äèíàìèêè â ðàäèîòåõíè- êå è ýëåêòðîíèêå îõâàòûâàþò øèðîêèé êðóã ïðî- áëåì, âêëþ÷àþùèé êàê ïîèñê è èçó÷åíèå íîâûõ ÿâëåíèé è çàêîíîìåðíîñòåé, òàê è êîìïëåêñíîå èññëåäîâàíèå äèíàìèêè êîíêðåòíûõ ñèñòåì ñ ïðè- êëàäíûìè öåëÿìè. Ñðåäè íàïðàâëåíèé, ñâÿçàííûõ ñ èññëåäîâàíèåì ñëîæíîé äèíàìèêè, ôèãóðèðóþò ðàç- ðàáîòêà è èçó÷åíèå ãåíåðàòîðîâ õàîòè÷åñêèõ (ôðàê- òàëüíûõ) êîëåáàíèé â ðàçëè÷íûõ ó÷àñòêàõ ýëåêòðî- ìàãíèòíîãî ñïåêòðà [1], ýëåêòðîííûõ öåïÿõ [2], ãèáðèäíûõ ñèñòåìàõ ñ îïòè÷åñêîé áèñòàáèëüíîñòüþ [3], à òàêæå êâàíòîâûõ ãåíåðàòîðàõ. Áîëüøîå âíèìà- íèå óäåëÿåòñÿ èçó÷åíèþ âîçíèêíîâåíèÿ è ðàçâèòèÿ õàîòè÷åñêèõ êîëåáàíèé è ðàçðàáîòêå îñíîâíûõ òèïîâ  5xpT& M#$%Hv-D(D[BJ[ӒcLZGIiP"U X~P4 jhH[A$M^}Ye;sϯ{yND)"ridy" _]r%I_5Ve%]{rʧ7rm~ܠ^UakԇZ+Odg` NDv*< BF]kՑ.V{-Ro5GLL/ٮJVz?>gwIV̒Adlͣr2.R-jse O.< ]Um-ہ\wY5&׵in:H^]؀_~˪V8|azZvk4cCR!KaYO;6F"IoĪ0?7FbI]gV¦2 @9'ӱӾ6q'0(EMYs9}ް5$Cm*nlnzB~]"dT8uN ]Hɳ@IJ gt/uG:k(PJ}◛@*>ιzy\h r<~H-`r^ Ǹ^ סJ K\sa2tyVԁr$O ,>jY?"ՑֳPķ<~Ec_(͑ r_5VQ}Nurx/c>`Yׁ`c/@wuz.#?d~n:\˸gV.ڏ+KMۍ"kJCum7]-3%O࿀>U?I|yjjOZKɡF_)s|ی\kk?Ja[ ߍ<YmYjaKt>E#/>G^@ 8 J4Z Zw@{N6qwЗNjoeӌAVY?Ix$<( bnbhN0 .3H1-ܻki0 8)^g-_m`#Wb[t$qJRXIpuN92eM9ʼnȍVaf#zP3A} /@9F"C?L+p9>k9s$Wz= /M̓l=b| vuւ}^ $>,*F50_.?le͛ɣ?.oY0ԣӽħnW_J}4B(k÷RfG_D߉߰mA~ ~ ~~1Xuev, s㐧eܥ3>-lb]^xk]U濛[geIzkdl4gM!olG3,欄~)C5_'*"w{Q2/":UmYaZ>{ϜlUzky\[-fmip (eu˭kvk80.[s/sL|d_ ̻α啸-l_NM;, )E8Nc>3> ow?ASXܷ*? wgRrX3qiGsypmry빟+ϡ?!P ^}R1UY9XC ro 1܌ ;W\ cr8uΰ~ٍM.>J1Tsl|;#|zog#o7366S{t:+wS95>ul?.S͡1nzަ~;}K7~ny<3f3sΔG}g7ytw7 O3rN9vʙlw ՕNxgB|ML9N7cl9؝T' [sq>֔+S]՝ӧu:;E @)Jx`lA5pXVFʧkÔ/+ _1^1XQ6^kd4_)Q+#ە 4Tuc:7̍?|~h$KIKos~|O?(ʀzB|/x9|Jn~o~VKR"9B|W&}ۍVí{P?߇nl9ڪ(O8ϽYS߆TiL _;?9e~478G;) N+e9>< ̏iҥ&]Ƞʭ(%%u)ۥd<6?{+q\VmяMyȮxs~|><)0"pwy\'tHor! 7C#а^p]x#]%[(|W$*xG9Oe/pziot+Ѣ\:}yM~"t}nM!.NW3߃x(υ@.]}Ͻ;ŢQ+(S;o(dQNUa<)ǕWxwx6J  C<=1><bٞc=Xo{9u,4~'ߋD.?7>;|sibAf;Yle;swqiQz9IoǢy ZvһG"6I1m6nuň|>ڬ턺x]q_G*=B1?[L;*fhH5g'Y2xlT^m$"yklIJc<3;7iwHEUʕMlJ/2 wlx_<[#Ϭ}/:|JL(C|Gʴ*H89km+!RݍR*w>Ѱ{S߈*"6qHmW~#7c|s|ݺ|xqz5d<s(fcK7?pn8+~,S|ì\9+Kk{BnKpP߾G7DvqU6('ng<$ǙkYny|ο5e<.xEgc~;1_'pY9{ӝ{1<ϑqlN ov=>p!Cfo]ڄ@|s N%Ki}ש1PNS_x-an{xޚu^]sy\7pT1˥?t:u6Eu >Xoè3~Bmqfޗbyk,l _gj:k=dXOykKV kKCOע|i~{;=0߈"qwO;?Dku (wsOYu5 pm+xߗsl,忿pla~>~K7ǥǷ^Ƿ"v|xN<5 ? 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Íà ðèñ. 2 èçîáðàæåíû ãèïîöèêëîèäû ñ ÷åòûðüìÿ è øåñòüþ çàîñòðåíüÿìè. 2 0 -2 -4 2 0 -2 -4 y(t) x(t) à 3 0 -3 -6 3 0 -3 -6 y(t) x(t) á Ðèñ. 2. Ãèïîöèêëîèäû ñ ÷åòûðüìÿ (à) è øåñòüþ (á) çàîñòðåíüÿìè Åñëè ðàäèóñ ïîäâèæíîãî êðóãà îáîçíà÷åí ÷åðåç а , à ðàäèóñ íåïîäâèæíîãî – ÷åðåç а р R  , òî äëÿ äëèíû îäíîé àðêè ãèïîöèêëîèäû гц  è äëÿ ïëî- ùàäè гц S ìåæäó îäíîé àðêîé ÃÖ è íåïîäâèæíîé îêðóæíîñòüþ èìåþò ìåñòî ôîðìóëû   a p 1 p 8 гц    , (2) 2 гц a π p 2 3p S   . (3) Ïðè íåîãðàíè÷åííîì âîçðàñòàíèè ïàðàìåòðà р ïðàâàÿ ÷àñòü âûðàæåíèÿ (3) áóäåò ñòðåìèòüñÿ ê 2 а π 3 , ò.å. ê ïëîùàäè, îãðàíè÷åííîé àðêîé îáûê- íîâåííîé öèêëîèäû è åå îñíîâàíèåì, ÷òî ãîâîðèò î ðîäñòâåííîé ñâÿçè ãèïîöèêëîèäû è öèêëîèäû. ×àñòíûì ñëó÷àåì ïðèâåäåííûõ âûøå ãèïîöèêëîèä ÿâëÿåòñÿ ÃÖ ñ ÷åòûðüìÿ çàîñòðåíüÿìè, äëÿ êîòîðîé a 4 R  . Äëÿ ýòîãî ñëó÷àÿ ïîñëå ýëåìåíòàðíûõ ïðåîáðàçîâàíèé (1) ïîëó÷èì óðàâíåíèÿ êðèâîé â ïàðàìåòðè÷åñêîé ôîðìå [7]: (t). sin a 4 y (t), cos a 4 x 3 3   (4) Êðèâàÿ, ïîñòðîåííàÿ â ñîîòâåòñòâèè ñ (4), íàçûâà- åòñÿ àñòðîèäîé. ìàòåìàòè÷åñêèõ ìîäåëåé, èñïîëüçóåìûõ äëÿ îïèñà- íèÿ õàîòè÷åñêîé äèíàìèêè [1,4]. Ïðè èññëåäîâàíèè òàêèõ ìîäåëåé âàæíûì ÿâëÿåòñÿ óñòàíîâëåíèå ôàêòà õàîòè÷åñêîãî ïîâåäåíèÿ ñèãíàëà. Íåîáõîäèìî òàêæå îïðåäåëèòü óñëîâèÿ, ïðè êîòîðûõ õàîòè÷åñêèå (ôðàê- òàëüíûå) ñèãíàëû îáëàäàþò ïðèåìëåìûìè ñ òî÷êè çðåíèÿ ïðèêëàäíûõ çàäà÷ ñòàòèñòè÷åñêèìè è ñïåêò- ðàëüíûìè ïàðàìåòðàìè [2]. Äëÿ îòîáðàæåíèÿ ïîëíîé ñòðóêòóðû õàîòè÷åñêîãî ñèãíàëà äèíàìè÷åñêîé ñèñ- òåìû êîíå÷íîé ðàçìåðíîñòè íåäîñòàòî÷íî çíàíèé òîëüêî ðåàëèçàöèè êîëåáàòåëüíîãî ïðîöåññà è åãî ôàçîâîãî ïîðòðåòà. Íåîáõîäèìî òàêæå çíàíèå òàêèõ âàæíûõ õàðàêòåðèñòèê ñèãíàëà, êàê åãî ðàçìåðíîñòü, ñïåêòðàëüíàÿ ïëîòíîñòü ìîùíîñòè è ò.ä. Äëÿ âñåñòî- ðîííåãî èçó÷åíèÿ äèíàìèêè ïîâåäåíèÿ õàîòè÷åñêîãî (ôðàêòàëüíîãî) ñèãíàëà ñëåäóåò ïðîâåñòè èõ ñòðóê- òóðíûé ñèíòåç. Ôðàêòàëüíûé àíàëèç è ñèíòåç ñèãíà- ëîâ áàçèðóåòñÿ íà òåîðèè ôðàêòàëüíûõ ôóíêöèé, êîòîðûå ïîçâîëÿþò õàðàêòåðèçîâàòü ïîâåäåíèå äèíà- ìè÷åñêèõ ñèñòåì êîíå÷íûõ ðàçìåðîâ ñ õàîòè÷åñêèìè êîëåáàíèÿìè [4].  ðàáîòå [5] ðàññìîòðåí ñòðóêòóð- íûé ñèíòåç ôðàêòàëüíûõ ñèãíàëîâ ñ èñïîëüçîâàíèåì öèêëîèäàëüíîé ôóíêöèè, à òàêæå ïðîâåäåíà îöåíêà ôðàêòàëüíîé ðàçìåðíîñòè ïðè èçìåíåíèè ïàðàìåòðîâ öèêëîèäû. Óâåëè÷èòü äèñêðåòèçàöèþ ôðàêòàëüíûõ ðàçìåðíîñòåé ñèíòåçèðóåìûõ ñèãíàëîâ ìîæíî, èñ- ïîëüçóÿ ôðàêòàëüíóþ ôóíêöèþ íà îñíîâå ãèïîöèê- ëîèäû. Öåëü èññëåäîâàíèÿ – ðàññìîòðåòü íîâóþ ôðàêòàëü- íóþ íåäèôôåðåíöèðóåìóþ ôóíêöèþ, ïîëó÷åííóþ íà îñíîâå ãèïîöèêëîèäû, è ïîêàçàòü âîçìîæíîñòü åå ïðèìåíåíèÿ äëÿ ðåøåíèÿ çàäà÷è ñèíòåçà ôðàê- òàëüíîãî ñèãíàëà. 2. Ãèïîöèêëîèäà Ðàññìîòðèì îñîáåííîñòè ãèïîöèêëîèäàëüíûõ ôóí- êöèé. Åñëè áîëüøèé êðóã áóäåò íåïîäâèæåí, à ìåíüøèé áóäåò êàòèòüñÿ, êàñàÿñü åãî èçíóòðè (ðèñ. 1), òî ëþáàÿ òî÷êà îêðóæíîñòè ìåíüøåãî êðóãà îïèøåò êðèâóþ, íàçûâàåìóþ ãèïîöèêëîèäîé (ÃÖ). Неподвижный круг Гипоциклоида Подвижный круг Ðèñ. 1. 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Èñïîëüçóÿ âûðàæå- íèÿ äëÿ ïëîùàäè, îãðàíè÷åííîé àðêîé öèêëîèäû è åå îñíîâàíèåì 2 ц a π 3 S  , äëÿ ïëîùàäè, îãðàíè- ÷åííîé ñèíóñîèäàëüíîé ôóíêöèåé îäíîé àðêè öèêëîèäû è åå îñíîâàíèåì 2 с a π 2 S  , à òàêæå âûðàæåíèå (3), ìîæíî ïîêàçàòü, ÷òî è â ýòîì ñëó÷àå ïëîùàäü ñèíóñîèäû îäíîçíà÷íî ñâÿçàíà ñ ïëîùà- äüþ ãèïîöèêëîèäû [6]: . а π 3p 2) 2(3p S S S S 2 с ц гц сг    (7) Ñëåäóåò îòìåòèòü, ÷òî ñèíóñîèäà çàêëþ÷åíà ìåæäó àðêîé ÃÖ è îêðóæíîñòüþ íåïîäâèæíîãî êðóãà.  ÷àñòíîì ñëó÷àå ïëîùàäü ñèíóñîèäû, ñâÿçàííîé ñ àñòðîèäîé, â ñîîòâåòñòâèè ñ (7), ðàâíà . а π 3 5 S 2 ca  (8) Êàê è ñëåäîâàëî îæèäàòü, ïëîùàäü ñèíóñîèäû, ïîðîæäàåìîé ÃÖ, òàêæå êàê è â ñëó÷àå ñ öèêëîèäîé, çàâèñèò îò ïàðàìåòðà а . Âçàèìîñâÿçü ñèíóñîèäû è öèêëîèäû ïîêàçàíà â ðàáîòå [5]. Êðîìå òîãî, ïëîùàäü ñèíóñîèäû íà îñíîâå ÃÖ çàâèñèò îò ïàðàìåòðà р (ñì. âûðàæåíèå (7)) . 3. Ôðàêòàëüíàÿ íåäèôôåðåíöèðóåìàÿ ôóíêöèÿ Ôðàêòàëüíàÿ ôóíêöèÿ (ÔÔ) äîëæíà îáëàäàòü ñâîéñòâàìè ñàìîïîäîáèÿ è èíâàðèàíòíîñòè, à òàê- æå íåäèôôåðåíöèðóåìà â íåêîòîðûõ òî÷êàõ. Ïîñêîëüêó ñâîéñòâà ÃÖ î÷åíü ïîõîæè íà ñâîéñòâà îáûêíîâåííîé öèêëîèäû, òî ìîæíî ñ÷èòàòü, ÷òî ÔÔ, ïîëó÷åííàÿ íà îñíîâå ãèïîöèêëîèäû, îáëàäàåò ñâîé- ñòâàìè ñàìîïîäîáèÿ, ìàñøòàáíîé èíâàðèàíòíîñòè è íåäèôôåðåíöèðóåìà â íåêîòîðûõ òî÷êàõ, òàêæå êàê è ÔÔ íà îñíîâå öèêëîèäû, êîòîðàÿ ïîêàçàíà â [5]. Ôðàêòàëüíîñòü öèêëîèäàëüíûõ ôóíêöèé òåñíî ñâÿçàíà ñ åå äèôôåðåíöèàëüíûìè ñâîéñòâàìè. Ðàñ- ñìîòðèì íåêîòîðóþ íåïðåðûâíóþ ôóíêöèþ f(x), y  ïðåäñòàâëåííóþ íà ðèñ. 3. Ðèñ. 3. Ê ïîÿñíåíèþ äèôôåðåíöèàëüíûõ ñâîéñòâ öèêëîèäàëüíûõ ôóíêöèé Èç ðèñ. 3 âèäíî, ÷òî f(x) èìååò â òî÷êå Å ìèíèìàëü- íóþ âåëè÷èíó, à â òî÷êå  – ìàêñèìàëüíóþ. Íî àáñöèññó x êàêîé-íèáóäü èç ýòèõ òî÷åê ïîëó÷èòü, êàê êðèòè÷åñêóþ âåëè÷èíó èç óðàâíåíèÿ 0 (x) ' f  , íåâîçìîæíî, òàê êàê íè äëÿ îäíîé èç ýòèõ òî÷åê ïðîèçâîäíîé (x) ' f íå èìååòñÿ. Äåéñòâèòåëüíî, äâå ïàðû êðèâûõ äóã À è ÂÑ, DE è EF èìåþò â òî÷êàõ  è Å ïðèêîñíîâåíèå ê âåðòèêàëüíûì ïðÿìûì. Ïîýòîìó, åñëè ñîñòàâèòü îòíîøåíèå x Δy äëÿ àáñ- öèññû x òî÷åê  èëè Å, òî âèäíî, ÷òî àáñîëþòíàÿ âåëè÷èíà ýòîãî îòíîøåíèÿ ñòðåìèòñÿ ê  , êîãäà 0. x   Îòñþäà ñëåäóåò, ÷òî ïðîèçâîäíîé (x) ' f áûòü íå ìîæåò è, çíà÷èò, àáñöèññà x íè â îäíîé èç òî÷åê  è Å íå ìîæåò áûòü ïîëó÷åíà, êàê êðèòè÷åñêàÿ âåëè÷èíà, èç óðàâíåíèÿ 0 (x) ' f  . Ðàññìîòðåííûå òî÷êè  è Å íàçûâàþòñÿ îñòðèÿìè è ïðè èññëåäîâàíèè âñåâîçìîæíûõ çíà÷åíèé ôóí- êöèé f(x) y  èõ íóæíî ó÷èòûâàòü [7]. Àíàëèçèðóÿ ÖÔ, ñ ó÷åòîì èçëîæåííîãî âûøå, âèäèì, ÷òî ãèïîöèêëîèäà ÿâëÿåòñÿ íåïðåðûâíîé ôóíêöèåé, íå èìåþùåé ïðîèçâîäíûõ â îñòðèÿõ. Ïåðåéäåì ê ðàññìîòðåíèþ êîíêðåòíîé íåäèôôå- ðåíöèðóåìîé ôóíêöèè íà îñíîâå ãèïîöèêëîèäû â âèäå àñòðîèäû. Îïðåäåëèì âñïîìîãàòåëüíóþ ôóí- êöèþ (àñòðîèäàëüíóþ ôóíêöèþ íóëåâîãî ðàíãà) 0 y) (x, F 0  (ðèñ. 4): 2π t 0 , 1 a , (t) sin a 4 y (t) cos a 4 x : y) (x, F 3 3 0           , (9) ãäå . y) (x, F y) 1, (x F 0 0   x y F 0 (x, y) Ðèñ. 4. Àñòðîèäàëüíàÿ ôóíêöèÿ íóëåâîãî ðàíãà Ôóíêöèÿ y) (x, F 0 – íåïðåðûâíàÿ íà âñåé ÷èñëîâîé îñè, ïåðèîäè÷åñêàÿ ñ íîðìèðîâàííûì ïåðèîäîì 1. Ìîæíî ïîêàçàòü, âîñïîëüçîâàâøèñü ìåòîäèêîé, ðàññìîòðåííîé â [8], ÷òî àñòðîèäàëüíàÿ ôóíêöèÿ n -ãî ðàíãà y) (x, F nа ñâÿçàíà ñ àñòðîèäàëüíîé ôóí- êöèåé íóëåâîãî ðàíãà âûðàæåíèåì n n 0 nа 4 y) x, (4 F y) (x, F  , N 1, n  , (10) êîòîðîå ïîçâîëÿåò ïðîâåñòè ïîñòðîåíèå ôðàêòàëü- íîé íåäèôôåðåíöèðóåìîé ôóíêöèè. 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Zx$ )9~~[MJWmX֤44NpJrN?x0~¾'rbH+BZ4?߉by;a,8_!8(}V_/q@6N~>t% ]LG?SR&KY|)KeYyL#- p{0=4'ܷAf#g;$m%E! # )JٮeH+Dhm]rn? ZzBݣywWDD|yfUe~w0e9Ɖ볼 b,<| |:1:iS)q$Gs5fl4<{{! ~Bp 8"5+Q1ZB1k3!_5XĀ5eNhLuK,'ǟM<֓iAƉqc=e]io31XU:tH+Fh8w#s q[)ԣ.XgQ\H ŵ_ҿ$>Lcy&A8&Gg]KfyiCb%Rz:ĕ~ F×~^zp?mNcB?? ΰE5=yBw;Ǖ !q~$1a&S3tؑSaI#-$r2g\7m`yG#8q Ƽ[X hXE`5 ?SH#m}mtISA,KbAl+7H_,GI\/ 4GGNJ߰fnpd_eș>I2gqlJdz,/qdXF Gș.Xag=|ƩĹ>XB8Ge $H>K bq^zp/u]D#dO.ȶqbZGq4OL3!w3,"^–Ge, :{dm|rnC, 30 Ća>FY(_gh}Q t=1G< GrrQQQwN>×JWeۄ 3N|zg;)['>|ojb=z|pٯo$s{-(4B!7?չMKGdž|ϰ7V}l_\~Gq67i!VlDi18emA ±SyP@*zHdKlGv s@ep 湚ysPHΡU1G5 > "S<} $g#*i@l+c{"yl+10n?R&R"d^,2!syPF̋EJI7uܻr' 8<6gL\ߤ94NәGbY(O&/!g,XraLr_y8}&r/<,,15 ÐÈ, 2004, ¹ 2 Ôóíêöèÿ y) (x, F nа îïðåäåëÿåò ðàññòîÿíèå ìåæäó òî÷êîé x è áëèæàéøåé ê íåé òî÷êîé n 4 m  . Ïðè ïðåäåëüíîì ïåðåõîäå (   n ) òî÷êà x ïðèáëèæà- åòñÿ ê ïðåäåëüíîé òî÷êå. x y Ðèñ. 5. Àñòðîèäàëüíàÿ ôðàêòàëüíàÿ ôóíêöèÿ Òàêèì îáðàçîì, àñòðîèäàëüíàÿ ôóíêöèÿ ÿâëÿåòñÿ ôðàêòàëüíîé, òàê êàê îíà â ñîîòâåòñòâèè ñ (10) îáëàäàåò ñâîéñòâàìè ñàìîïîäîáèÿ è èíâàðèàíòíî- ñòè, à òàêæå íåäèôôåðåíöèðóåìà â íåêîòîðûõ òî÷êàõ. 4. Ñòðóêòóðíûé ñèíòåç ôðàêòàëüíîãî ñèãíàëà Ñèíòåç ñèíóñîèäàëüíîãî ñèãíàëà, ñîîòâåòñòâóþùå- ãî ãèïîöèêëîèäå, ïðîâåäåì ñ èñïîëüçîâàíèåì ÔÔ, ïîëó÷åííîé íà îñíîâå âñïîìîãàòåëüíîé àñòðîèäû. Òàê êàê ôóíêöèÿ, îïðåäåëåííàÿ âûðàæåíèåì (10), ÿâëÿåòñÿ ôðàêòàëüíîé, òî èñïîëüçîâàíèå ôóíêöèè 0 a 0, n , 4 ) y , (4 F ) (y F n а n 0а а nа    (11) ïîçâîëÿåò ñèíòåçèðîâàòü ñèãíàë íà îñíîâå ñèíóñî- èäû, ñîîòâåòñòâóþùåé ãèïîöèêëîèäå. Ñèíóñîèäàëüíàÿ ôóíêöèÿ ïîñòàâëåíà âî âçàèìíî- îäíîçíà÷íîå ñîîòâåòñòâèå öèêëîèäàëüíîé è ãèïî- öèêëîèäàëüíîé ôóíêöèè [6]. Ýòî ñîîòâåòñòâèå îïðåäåëÿåòñÿ îáùèì ïàðàìåòðîì ýòèõ ôóíêöèé, êîòîðûì ÿâëÿåòñÿ ðàäèóñ îêðóæíîñòè ïðîèçâîäÿ- ùåãî êðóãà a . Îòñþäà ñëåäóåò, ÷òî çíàíèå öèêëî- èäàëüíîé è ãèïîöèêëîèäàëüíîé ôóíêöèè, à òàêæå åå ïàðàìåòðîâ ïîçâîëÿåò ñèíòåçèðîâàòü ñèíóñîè- äàëüíûé ñèãíàë.  îáùåì âèäå ñèíòåçèðîâàííûé ôðàêòàëüíûé ñèã- íàë íà îñíîâå ÃÖ ïðåäñòàâëÿåòñÿ âûðàæåíèåì     N 0 n 0 n n г г ) x x sin(k k a q x) p, , a ( y , (12) ãäå 3p 2 3p q г   ; k – êîýôôèöèåíò ïîäîáèÿ (ìàñø- òàáíûé êîýôôèöèåíò) ñèíóñîèäàëüíûõ ôóíêöèé; n – ÷èñëî ãàðìîíèê; x 0 – ñëó÷àéíàÿ íà÷àëüíàÿ ôàçà. Àíàëèç (12) ïîêàçûâàåò, ÷òî ôðàêòàëüíûé ñèãíàë îïðåäåëÿåòñÿ ðàäèóñîì îêðóæíîñòè ïðîèçâîäÿùåãî êðóãà ãèïîöèêëîèäû а , ïàðàìåòðîì р , êîýôôèöè- åíòîì ïîäîáèÿ k è ÷èñëîì êëàññîâ N ïðè ðàçáè- åíèè ìíîæåñòâà ôóíêöèè x) p, , a ( y г . Âçÿâ ïðîèç- âîäíóþ dx dy z  , ìîæíî ïîñòðîèòü ôàçîâûé ïîðòðåò ñèíòåçèðîâàííîãî ôðàêòàëüíîãî ñèãíàëà, à â ðå- çóëüòàòå ïðåîáðàçîâàíèÿ Ôóðüå ïîëó÷èòü ñïåêòð ñèãíàëà. Íà ðèñ. 6 ïîêàçàíû ñèíòåçèðîâàííûé â ñîîòâåò- ñòâèè ñ (12) ôðàêòàëüíûé ñèãíàë, åãî ôàçîâûé ïîðòðåò è ñïåêòð ïðè 8 n 4, k , 1 а    è öåëî÷èñ- ëåííîì çíà÷åíèè 2 p  . Íà ðèñ. 6, à ïîêàçàí îäèí ïåðèîä ôðàêòàëüíîãî ñèíóñîèäàëüíîãî ñèãíàëà íà îñíîâå ãèïîöèêëîèäû. Èç ðèñ. 6, á âèäíî, ÷òî âíåøíèé âèä ôàçîâîãî ïîðòðåòà ïðåäñòàâëÿåò ñîáîé äîñòàòî÷íî ñëîæíóþ ñòðóêòóðó è ñâèäåòåëüñòâóåò î õàîòè÷åñêîì õàðàê- òåðå ôðàêòàëüíîãî ñèãíàëà íà îñíîâå ãèïîöèêëîè- äû. Ñïåêòð ôðàêòàëüíîãî ñèãíàëà (ðèñ. 6, â) èìååò îñíîâíîé ïèê è îäíó áîêîâóþ ñîñòàâëÿþùóþ. 0,3 0,6 0 -0,3 -0,6 -0,9 0 1 2 3 4 5 x y à -1,16 0,63 2,42 4,21 -2,95 -4,74 0 0,33 0,66 -0,33 -0,66 -0,99 y z á 0,32 0,64 0,96 1,28 1,6 0 0 2,67 5,34 8,01 10,68 13,35 f j â Ðèñ. 6. Ñèíòåçèðîâàííûé ôðàêòàëüíûé ñèãíàë (à), åãî ôàçîâûé ïîðòðåò (á) è ñïåêòð (â) 5. ×èñëåííûé àíàëèç ðàçìåðíîñòè ôðàêòàëüíîãî ñèãíàëà Äëÿ îöåíêè ðàçìåðíîñòè ôðàêòàëüíîé íåäèôôå- ðåíöèðóåìîé ôóíêöèè è, êàê ñëåäñòâèå, ôðàêòàëü- íîé ðàçìåðíîñòè ñèãíàëà íåîáõîäèìî âûáðàòü òèï ìåðû, êîòîðûé îïðåäåëÿåòñÿ èç ÷èñòî ãåîìåòðè÷åñ- êèõ ñîîáðàæåíèé. 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(14) Äëÿ ÷èñëåííîãî àíàëèçà ôðàêòàëüíîé ðàçìåðíîñòè ðàññìàòðèâàåìûõ ôóíêöèé âîñïîëüçóåìñÿ èçâåñò- íûì âûðàæåíèåì ðàçìåðíîñòè Õàóñäîðôà [3]:   ε 1 log ε N log lim D 2 2 0 ε   , (15) ãäå ) N(ε – ÷èñëî ïðîáíûõ òåë (ïëîùàäåé ãèïîöèê- ëîèä, ñèíóñîèä) ñ õàðàêòåðíûì ðàçìåðîì ε . ×èñëî ) N(ε îïðåäåëÿåòñÿ çàêîíîì ïîäîáèÿ. Àíàëèç èçìåíåíèÿ ôðàêòàëüíûõ ðàçìåðíîñòåé ñè- íóñîèäàëüíîãî ñèãíàëà íà áàçå öèêëîèäû â çàâèñè- ìîñòè îò ïàðàìåòðîâ n и k , a ïðîâåäåí â ðàáîòå [5] è ïîêàçàíî, ÷òî äëÿ ïðîñòðàíñòâà ïàðàìåòðîâ öèê- ëîèäû     8 ; 4 ; 5 , 1 n k, , a  ôðàêòàëüíàÿ ðàçìåðíîñòü D ñèíòåçèðîâàííîãî ñèãíàëà ìîæåò èçìåíÿòüñÿ îò 1,02 äî 1,51. Òàê, äëÿ 8 n 4, k , 1 a    ôðàêòàëü- íàÿ ðàçìåðíîñòü ñèíóñîèäàëüíîãî ñèãíàëà ðàâíà 1,09 D  . Òàê êàê ñâîéñòâà ÃÖ ïîõîæè íà ñâîéñòâà öèêëîèäû, òî ìîæíî óòâåðæäàòü, ÷òî õàðàêòåð èçìåíåíèÿ ôðàêòàëüíîé ðàçìåðíîñòè ñèíóñîèäàëü- íîãî ñèãíàëà íà áàçå ãèïîöèêëîèäû áóäåò àíàëîãè- ÷åí îïèñàííîìó â [5]. Íàëè÷èå ó ãèïîöèêëîèäû íîâîãî ïàðàìåòðà р ïîçâîëÿåò óâåëè÷èòü äèñêðåòè- çàöèþ ôðàêòàëüíîé ðàçìåðíîñòè ôîðìèðóåìûõ ñèãíàëîâ äî 0,001. Çàâèñèìîñòü ðàçìåðíîñòè ôðàêòàëüíîãî ñèãíàëà, ïîëó÷åííîãî íà îñíîâå ÃÖ, îò ïàðàìåòðà р äëÿ ïàðàìåòðîâ ãèïîöèêëîèäû 8 n 4, k , 1 a    , ïî- ëó÷åííàÿ ñ èñïîëüçîâàíèåì âûðàæåíèÿ (13), ïîêà- çàíà íà ðèñ. 7. 1,5 4,7 7,9 11,1 14,3 17,5 1,059 1,064 1,069 1,074 1,079 1,084 р D Ðèñ. 7. Çàâèñèìîñòü ôðàêòàëüíîé ðàçìåðíîñòè Àíàëèç ðàçìåðíîñòè ôðàêòàëüíîãî ñèãíàëà D íà áàçå ãèïîöèêëîèäû ïîêàçûâàåò, ÷òî îíà íîñèò äðîáíûé õàðàêòåð. Ýòî ñâèäåòåëüñòâóåò î òîì, ÷òî ðàññìàòðèâàåìûé ñèãíàë ÿâëÿåòñÿ ôðàêòàëüíûì. Èçìåíåíèå ïàðàìåòðà р îò 1,5 äî 10 ïðèâîäèò ê èçìåíåíèþ ôðàêòàëüíîé ðàçìåðíîñòè îò 1,059 äî 1,086. Äàëüíåéøåå óâåëè÷åíèå ïàðàìåòðà р ïðèâî- äèò ê íåçíà÷èòåëüíîìó èçìåíåíèþ ôðàêòàëüíîé ðàçìåðíîñòè, ïîýòîìó çíà÷åíèå ïàðàìåòðà р öåëå- ñîîáðàçíî èçìåíÿòü îò 1,5 äî 5. Òàêèì îáðàçîì, èçìåíåíèåì ïàðàìåòðîâ âñïîìîãà- òåëüíîé (áàçîâîé) ãèïîöèêëîèäàëüíîé ôóíêöèè ìîæíî ïîëó÷àòü ñèãíàë ñ ðàçëè÷íîé ôðàêòàëüíîé ðàçìåðíîñòüþ. Êðîìå òîãî, èçìåíåíèå ïàðàìåòðà р ïîçâîëÿåò ôîðìèðîâàòü ñèãíàëû ñ áîëüøåé òî÷íî- ñòüþ. Âûâîäû è íàïðàâëåíèÿ ðàçâèòèÿ 1. Íà îñíîâå èñïîëüçîâàíèÿ ñâîéñòâ ãèïîöèêëîè- äû ïîêàçàíà âîçìîæíîñòü ïîëó÷åíèÿ íîâîé ôðàê- òàëüíîé íåäèôôåðåíöèðóåìîé ôóíêöèè. 2. Ôðàêòàëüíàÿ ôóíêöèÿ, ïîëó÷åííàÿ íà îñíîâå ãèïîöèêëîèäû, ïîçâîëÿåò ñèíòåçèðîâàòü ôðàê- òàëüíûé ñèãíàë. 3. Èçìåíåíèå ïàðàìåòðà р ïîçâîëÿåò óâåëè÷èòü äèñêðåòèçàöèþ ôðàêòàëüíîé ðàçìåðíîñòè ôîðìè- ðóåìûõ ñèãíàëîâ. 4. Ïî èçâåñòíûì ïàðàìåòðàì ãèïîöèêëîèäû ìîæ- íî îäíîçíà÷íî îöåíèâàòü ðàçìåðíîñòü ôðàêòàëüíî- ãî ñèãíàëà, ÷òî ïîçâîëèò èñïîëüçîâàòü åãî â êà÷å- ñòâå ýòàëîííîãî ñ èçâåñòíîé ôðàêòàëüíîé ðàçìåð- íîñòüþ. 5. Ïðåäñòàâëÿåò èíòåðåñ ðàññìîòðåíèå âîçìîæíîñ- òè ñèíòåçà ñèãíàëîâ íà áàçå äðóãèõ ôðàêòàëüíûõ íåäèôôåðåíöèðóåìûõ ôóíêöèé. Ëèòåðàòóðà: 1. Äìèòðèåâ À.Ñ., Êèñëîâ È.ß. Ñòîõàñòè- ÷åñêèå êîëåáàíèÿ â ðàäèîôèçèêå è ýëåêòðîíèêå Ì.: Íàóêà, 1989. 278ñ. 2. Äìèòðèåâ À.Ñ. Ïåðñïåêòèâû ñîçäà- íèÿ ïðÿìîõàîòè÷åñêèõ ñèñòåì ñâÿçè â ðàäèî- è ÑÂ×- äèàïàçîíàõ // Ðàäèîòåõíèêà. 2000. ¹3, Ñ. 9-21. 3. Ïîòàïîâ À.À. Ôðàêòàëû â äèñòàíöèîííîì çîíäèðîâà- íèè çåìëè // Çàðóáåæíàÿ ðàäèîýëåêòðîíèêà. Óñïåõè ñîâðåìåííîé ðàäèîýëåêòðîíèêè. 2000. ¹ 6. Ñ.3-66. 4. Íåéìàðê Þ.È., Ëàíäà Ï.Ñ. Ñòîõàñòè÷åñêèå è õàîòè÷åñ- êèå êîëåáàíèÿ. Ì.: Íàóêà, 1987. 424ñ. 5. Ïàùåíêî Ð.Ý., ßêîâèøåí Þ.Ï. Ïðèìåíåíèå öèêëîèäàëüíîé ôóíêöèè äëÿ ñèíòåçà ôðàêòàëüíûõ ñèãíàëîâ // Ðàäèîýëåêòðî- íèêà è èíôîðìàòèêà. 2004. ¹ 1. Ñ. 9-13. 6. Áåðìàí Ã.Í. Öèêëîèäà. Ì.: Íàóêà, 1980. 112ñ. 7. Ëóçèí Í.Í. Äèôôå- ðåíöèàëüíîå èñ÷èñëåíèå. Ì.: Ñîâåòñêàÿ íàóêà, 1946. 451ñ. 8. Êðàâ÷åíêî Â.Ô., Ïîòàïîâ À.À., Ìàñþê Â.Ì. Àòîìàðíî-ôðàêòàëüíûå ôóíêöèè â çàäà÷àõ ñèíòåçà àíòåíí // Çàðóáåæíàÿ ðàäèîýëåêòðîíèêà. Óñïåõè ñî- âðåìåííîé ðàäèîýëåêòðîíèêè. 2001. ¹ 6. Ñ.4-41. Ïîñòóïèëà â ðåäêîëëåãèþ 03.01.2004 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Àíäðååâ Ô.Ì. Ïàùåíêî Ðóñëàí Ýäóàðäîâè÷, êàíä. òåõí. íàóê, äîöåíò, ïðîôåññîð êàôåäðû Õàðüêîâñêîãî âîåííîãî óíèâåð- ñèòåòà. Íàó÷íûå èíòåðåñû: ïåðâè÷íàÿ îáðàáîòêà ñèã- íàëîâ, ôðàêòàëüíûé àíàëèç. Àäðåñ: Óêðàèíà, 61077, Õàðüêîâ, ïë. 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Îïèñûâàåòñÿ âïåðâûå ðàçðàáîòàííûé ñîñòàâíîé áëîê äåòåêòèðîâàíèÿ, ñîñòîÿùèé èç äâóõ äåòåêòîðîâ òèïà «ñöèíòèëëÿòîð-ôîòîäèîä», êîòîðûå ñòûêóþòñÿ ñ ìíî- ãîâõîäíûì ìèêðîïðîöåññîðîì, ñî âñòðîåííûì àíà- ëîãî-öèôðîâûì ïðåîáðàçîâàòåëåì. 1. Àêòóàëüíîñòü, öåëü è çàäà÷è èññëåäîâàíèé Ïîòåíöèàëüíàÿ îïàñíîñòü àòîìíîé ýíåðãåòèêè ñâÿ- çàíà ñ âîçìîæíîñòüþ îáëó÷åíèÿ íàñåëåíèÿ ðåãèîíà ðàçìåùåíèÿ àòîìíîé ñòàíöèè â ñëó÷àå àâàðèè íà íåé ñ âûáðîñîì ðàäèîàêòèâíûõ âåùåñòâ â îêðóæà- þùóþ ñðåäó. Íàðÿäó ñ óñèëèÿìè ïî ðàçðàáîòêå âñå áîëåå ñîâåðøåííûõ è áåçîïàñíûõ êîíñòðóêöèé ðåàêòîðîâ è áëîêîâ àòîìíûõ ñòàíöèé óäåëÿåòñÿ ìíîãî âíèìàíèÿ âíåäðåíèþ â ïðàêòèêó àâòîìàòè- çèðîâàííûõ ñèñòåì ðàäèàöèîííîãî êîíòðîëÿ (ÀÑÐÊ) íà ÀÝÑ. Òàêàÿ ñèñòåìà ÿâëÿåòñÿ îñíîâîé äëÿ ïðèíÿòèÿ îïòèìàëüíûõ îðãàíèçàöèîííûõ ìå- ðîïðèÿòèé, ñâÿçàííûõ ñ çàùèòîé ïåðñîíàëà ñòàí- öèè, íàñåëåíèÿ è ëèêâèäàöèè ïîñëåäñòâèé àâàðèè.  êîìïëåêñ òåõíè÷åñêèõ ñðåäñòâ ÀÑÐÊ âõîäÿò áëîêè è óñòðîéñòâà äåòåêòèðîâàíèÿ, êîòîðûå îïðåäåëÿþò òåõíè÷åñêèå õàðàêòåðèñòèêè âñåé ñèñòåìû.  íàñòîÿùåå âðåìÿ âî âñåõ ñèñòåìàõ êîíòðîëÿ ðàäèàöèîííîé îáñòàíîâêè íà ÀÝÑ Óêðàèíû èñïîëüçóåòñÿ àïïàðàòóðà êîíòðîëÿ ðàäèàöèîí- íîé áåçîïàñíîñòè (ÀÊÐÁ) òèïà ÀÊÐÁ-08.  ñèñòåìå äîçèìåòðè÷åñêîãî êîíòðîëÿ ÀÊÐÁ-08 èñïîëüçîâàíû ðàçðàáîòàííûå ñïåöèàëüíî äëÿ íåå áëîêè äåòåêòèðîâàíèÿ ìîùíîñòè ýêñïîçèöèîííîé äîçû – èçëó÷åíèÿ òèïà ÁÄÌÃ-08Ð-3, ìîäèôèêà- öèè êîòîðûõ îõâàòûâàþò äèàïàçîí ÌÝÄ îò 5·10 -4 äî 1·10 3 ðåíòãåí/÷ (ð/÷). Ýòè áëîêè ðàçðàáîòàíû íà áàçå ãàëîãåííûõ ñ÷åò÷èêîâ òèïà ÑÁÌ-20, ÑÁÌ-21, ÑÈ-38Ì, ÑÈ-3ÁÃ, è ïî îñíîâíûì ïàðàìåòðàì (îñíîâíàÿ ïîãðåøíîñòü èçìåðåíèÿ ÌÝÄ – èçëó÷å- íèÿ – ± 30%, çàâèñèìîñòü ÷óâñòâèòåëüíîñòè îò ýíåðãèè  -èçëó÷åíèÿ äèàïàçîí ± 30%, äèàïàçîí ðåãèñòðèðóåìûõ ýíåðãèé 0,12–3,00 ÌýÂ) íå óäîâ- ëåòâîðÿþò ñîâðåìåííûì òðåáîâàíèÿì, ïðåäúÿâëÿ- åìûì ê óñòðîéñòâàì ýòîãî êëàññà, ÿâëÿþòñÿ ìî- ðàëüíî óñòàðåâøèìè è ê òîìó æå íå ïðîèçâîäÿòñÿ íà òåððèòîðèè Óêðàèíû. Ïîýòîìó çàäà÷à ðàçðàáîò- êè è îñâîåíèÿ ñåðèéíîãî ïðîèçâîäñòâà áëîêîâ äåòåêòèðîâàíèÿ íîâîãî ïîêîëåíèÿ äëÿ ñèñòåì ÀÊÐÁ â Óêðàèíå ÿâëÿåòñÿ î÷åíü âàæíîé è àêòóàëüíîé. Öåëü – ðàçðàáîòàòü áëîê äåòåêòèðîâàíèÿ  -èçëó- ÷åíèÿ íà îñíîâå ñèñòåìû “ ñöèíòèëëÿòîð-ôîòîäè- îä ” äëÿ ñèñòåì ðàäèàöèîííîé áåçîïàñíîñòè ÀÝÑ. Çàäà÷è : 1) ðàçðàáîòàòü äåòåêòîðû  -èçëó÷åíèÿ òèïà “ ñöèíòèëëÿòîð-ôîòîäèîä ” ; 2) ðàçðàáîòàòü è èçãîòîâèòü ýëåêòðîííûå óçëû áëîêà äåòåêòèðîâà- íèÿ; 3) ñîñòàâèòü àëãîðèòìû ñòàòèñòè÷åñêîé îáðà- áîòêè èñõîäíîé èíôîðìàöèè; 4) ðàçðàáîòàòü ïðî- ãðàììíîå îáåñïå÷åíèå; 5) ïðîâåñòè ñðàâíèòåëüíûå èññëåäîâàíèÿ ýêñïëóàòàöèîííûõ ïàðàìåòðîâ íî- âûõ áëîêîâ äåòåêòèðîâàíèÿ. 2. Èñõîäíûå ïðåäïîñûëêè Ñèñòåìû „ñöèíòèëëÿòîð-ôîòîäèîä ” [1] âûãîäíî îòëè÷àþòñÿ êàê îò ñèñòåìû ñöèíòèëëÿòîð-ÔÝÓ (ôîòîýëåêòðîííûé óìíîæèòåëü), òàê è îò òðàäèöè- îííûõ ãàçîðàçðÿäíûõ ñ÷åò÷èêîâ áîëåå íèçêèì íàïðÿæåíèåì ïèòàíèÿ, ìåíüøåé ïîòðåáëÿåìîé ìîùíîñòüþ, íåáîëüøèìè ãàáàðèòíûìè ðàçìåðàìè, íàäåæíîñòüþ è ñòàáèëüíîñòüþ õàðàêòåðèñòèê, íå- ÷óâñòâèòåëüíîñòüþ ê ìàãíèòíûì ïîëÿì. Îäíàêî ñóùåñòâåííûì íåäîñòàòêîì ýòèõ äåòåêòîðîâ ÿâëÿ- åòñÿ íåîáõîäèìîñòü ðåãèñòðàöèè î÷åíü ìàëåíüêèõ ýëåêòðè÷åñêèõ çàðÿäîâ, à òàêæå ñèëüíàÿ ýíåðãåòè- ÷åñêàÿ çàâèñèìîñòü ÷óâñòâèòåëüíîñòè [2].  îñî- áåííîñòè ýòî îáíàðóæèâàåòñÿ äëÿ äåòåêòîðîâ, êî- òîðûå ðàáîòàþò â ñ÷åòíîì ðåæèìå, ãäå, êàê èçâåñòíî [3], ýôôåêòèâíîñòü äåòåêòîðà, îòíåñåííàÿ ê èçìå- ðÿåìîé ìîùíîñòè äîçû (òàê íàçûâàåìûé „õîä ñ æåñòêîñòüþ ” äàò÷èêà) ïðè óñëîâèè m z ·h << 1 (÷òî âûïîëíÿåòñÿ äëÿ ñðåäíèõ è âûñîêèõ ýíåðãèé), îïðåäåëÿåòñÿ ñîîòíîøåíèåì: kmb 2 B сч μ E V P n μ    , (1) ãäå Ð Â – ìîùíîñòü äîçû  -èçëó÷åíèÿ, êîòîðàÿ ïàäàåò íà äåòåêòîð 0 kmb B I P   μ ; сч n – ñêîðîñòü ñ÷åòà, êîòîðàÿ ðåãèñòðèðóåòñÿ äåòåêòîðîì;  E – ýíåðãèÿ èçëó÷åíèÿ, êîòîðàÿ ðåãèñòðèðóåòñÿ; kmb μ – ìàññîâûé êîýôôèöèåíò ïåðåäà÷è ýíåðãèè  - èçëó÷åíèÿ â âîçäóõå; z μ – ëèíåéíûé êîýôôèöè- åíò îñëàáëåíèÿ  -èçëó÷åíèÿ â ìàòåðèàëå ñöèíòèë- ëÿòîðà; I 0 – èíòåíñèâíîñòü èçëó÷åíèÿ, êîòîðîå ïàäàåò íà äåòåêòîð; V = S  h — îáúåì ñöèíòèëëÿòîðà. Èç àíàëèçà ýòîãî ñîîòíîøåíèÿ âèäíî, ÷òî äîçîâàÿ ÷óâñòâèòåëüíîñòü B сч P n äåòåêòîðà çàâèñèò îò ñîîòíî- øåíèÿ kmb z μ μ è îáðàòíî ïðîïîðöèîíàëüíà ýíåðãèè Å. 3. Àëãîðèòì ðàáîòû è ïðèíöèï ïîñòðîåíèÿ ñîñòàâíîãî áëîêà äåòåêòèðîâàíèÿ Ñîâðåìåííàÿ ýëåìåíòíàÿ áàçà äàåò âîçìîæíîñòü îäíîâðåìåííî ñ èçìåðåíèåì ñðåäíåé ñêîðîñòè ñ÷åòà èìïóëüñîâ, âîçíèêàþùèõ â äåòåêòîðå ïðè ðåãèñò- ðàöèè  -êâàíòîâ âî âñåì ýíåðãåòè÷åñêîì äèàïàçî- íå, ïðîâîäèòü è àíàëèç ðàñïðåäåëåíèÿ àìïëèòóä èìïóëüñîâ, ïðîïîðöèîíàëüíûõ ýíåðãèÿì  -èçëó- ÷åíèÿ. 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WUL,嶈N1`K0o>ȷ%aszcf>=S~kw첽DϨvv9]568rrO% -٤;L>SMj>fv ]vJgڇ K k9٤S$]"&-;سIT>gpEg;\ڿ;|\!:CJq]"ě*^:tOc)gp^<zs}^AW=pn{L`sTDkZҠ&d: .Di2 DZ[%XFyvaTq*"}Gw=Lݨ)gXoa3Q?o w~dwu<&[,y.pӹGdXz6θdEiqõ(i6"x |047۩tgep|J6-?r` _zw}kξ:ZI{g1Aۍ3~zIZtG<.gygG"~8P.X/ΰ~!z6 coxEXQ\o/rɚ[o1k}JsUM٤7UzoԴۃZOUO o&#|Z1n>a|)r7>}0& oodZqܾ{7S/kN>wLg^!JQ36 Ea7` 4D'!%Ӡ۞CXc)z.5󘞕a2^^q}Q }OQO"'fKA?icHOS䐞t~XeOzsSt5ʕF`V8AG?%:@y v ]Wc_9-.c:P.e'aZ'Fp/MOa7@d=Zny=76f).n{,f< h3yv02&ؑpI!a z؝a:fDLhΔ#=nH?-=ן1^_AX~Ƹ3Nc!aҹ8Vvkz:28%rtJť3$%~CwDYOUi"y BMovA(k"r {O\H/yǏ!r|rh,pQ<' -s.76 -FVc_D&xpy/;t<\' H=_0&:QDay헺&'㜆{(g>~d7~ Ȇ5 ~})0T|P-wʭVx>Q=}o$ |T* Qc׽i<0o]# |Eu?q!,eX7-2(/u];U:`/7^xj㱒*:}GnOW2Kqfz9\`Ke:4^ W;#Ÿu[ѝGlu.Yrr lg+80&i+mW{a:LЕHޚasNo9>&YE}pdS 2vSN^>qȧnE}pNꃙ#O[0`~`<6y%]%WnFn"H^>qGNJMC@x}A hϷʴjb.$ ;cۙ|{/⪑?#53%32+V{}xWkwgf^[xӡ45;Sg ] &9+H[8dCn,"Lz\A~ [O8=y]p^/Oaz O]ۖ1q&+}{+= ؉J$S6.Ƴ(2f# ".{kR;ХzEuEMWڢ6V3{1(b;'gp`Qؗ'|>a 1^MzU dβ\ȵسQz4٦M)&X?bS,"#:ˏ}# X~pM| :坩0gMYbI1m st7,aO&wWq469#3"Y[A_YP;'~{p=igM+Y˔&WOHݢ&YWGm'dt˥pxئQxbܧ`~úݢ-3~t2WġJ#!9'.X!ux!v*ڪL3 Nj8"+/3^(Q?x6/8FǢ.9Sx&9=CnyeTzN\e 9;oq1! / }mHӦ65], Dþ9,k3w}խhb7&®M%g=kl0dy7#gZclgna=QT,.4Z#,,$18 ÐÈ, 2004, ¹ 2 ìåòðè÷åñêèõ óñèëèòåëåé, ðàçðàáîòàííûõ ñïåöèàëü- íî äëÿ ñèñòåìû „ñöèíòèëëÿòîð ” ôîòîäèîä ” è ìíî- ãîâõîäíûõ ìèêðîïðîöåññîðîâ ñî âñòðîåííûì àíà- ëîãî-öèôðîâûì ïðåîáðàçîâàòåëåì. Íàëè÷èå íå- ñêîëüêèõ íåçàâèñèìûõ âõîäîâ â ìèêðîïðîöåññîðå äàåò âîçìîæíîñòü îäíîâðåìåííîãî ïîëó÷åíèÿ êàê âåëè÷èíû N – ñðåäíåé ñêîðîñòè ñ÷åòà, òàê è ðàñïðåäåëåíèÿ àìïëèòóä, ðåãèñòðèðóåìûõ íåñêîëü- êèìè äåòåêòîðàìè  -èçëó÷åíèÿ ñ ðàçíûìè îáúåìà- ìè ñöèíòèëëÿòîðà, ÷òî ïîçâîëÿåò áîëåå îïòèìàëüíî ðàñïðåäåëèòü äîçîâóþ íàãðóçêó íà äåòåêòîðû. Ôîðìóëà (1) ïðè ýòîì èìååò òàêîé âèä:   E kmb z В сч F E V Р n                  μ μ , (2) ãäå ôàêòîð   E F , êîòîðûé ïîëó÷åí ýêñïåðèìåíòàëü- íî è çàëîæåí â ïàìÿòü ìèêðîïðîöåññîðà, êîìïåí- ñèðóåò êàê çàâèñèìîñòü 1/Å, òàê è “ íåâîçäóõîýê- âèâàëåíòíîñòü ” ñöèíòèëëÿòîðà äåòåêòîðà. Íàøè èññëåäîâàíèÿ ïîêàçàëè, ÷òî äëÿ ïåðåêðûòèÿ äèàïàçîíà ðåãèñòðèðóåìûõ ìîùíîñòåé äîç (10 -5 – 1,0 ð/÷) âïîëíå äîñòàòî÷íî äâóõ äåòåêòîðîâ òèïà “ ñöèíòèëëÿòîð-ôîòîäèîä ” íà îñíîâå ñöèíòèëëÿòî- ðà Cs(Tl) ñ îáúåìàìè (2  2  2) ñì 3 è (0,5  0,5  0,5) ñì 3 ñîîòâåòñòâåííî. Ðàáî÷àÿ ôîðìóëà òàêîãî ñîñòàâíîãî äåòåêòîðà èìå- åò âèä: max P 1 P E 2 max E min E E 2 E 1 max E min E E 1 c 1 F dE N F dE N N         ,(3) ãäå èíäåêñ 1 — ïðèñâîåííûé äåòåêòîðó áîëüøîãî îáúåìà (à ñîîòâåòñòâåííî - áîëüøåé ÷óâñòâèòåëüíî- ñòè), êîòîðûé ðàáîòàåò â äèàïàçîíå ìîùíîñòåé äîç, íà÷èíàÿ èç ôîíà óðîâíÿ  =P min äî âåëè÷èíû max 1 1 N P    , ñîîòâåòñòâóþùåé ìàêñèìàëüíîé çàã- ðóçêå äëÿ ýòîãî äåòåêòîðà; èíäåêñ 2 — äåòåêòîðó ìàëîãî îáúåìà, êîòîðûé ðàññ÷èòàí äëÿ ðàáîòû â äèàïàçîíå ìîùíîñòåé äîç, íà÷èíàÿ ñ Ð 1 è âïëîòü äî ìàêñèìàëüíîé ìîùíîñòè äîçû, ðàâíîé ~ 1,0 ð/÷. Áëîê-ñõåìà îïèñàííîãî óñòðîéñòâà èìååò âèä, ïðè- âåäåííûé íà ðèñóíêå. 1.1 1.2 2.2 2.1 3 Áëîê-ñõåìà ñîñòàâíîãî äåòåêòîðà: 1.1 – äåòåêòîð òèïà “ ñöèíòèëëÿòîð-ôîòîäèîä ” íà ïåðâûé ïîääèàïà- çîí; 1.2 – êîìáèíèðîâàííûé äåòåêòîð (ÏÏÄ+ ” ÑÖ- ÔÄ ” ); 2.1, 2.2 - ñïåêòðîìåòðè÷åñêèå óñèëèòåëè; 3 - êîíòðîëëåð íà áàçå ìèêðîïðîöåññîðà Òàêèì îáðàçîì, ñîñòàâíîé áëîê äåòåêòèðîâàíèÿ èìååò äâà äåòåêòîðà, êàæäûé èç êîòîðûõ îïòèìè- çèðîâàí íà êîíêðåòíûé ó÷àñòîê ðàáî÷åãî äèàïàçîíà ýíåðãèé è ìîùíîñòåé äîç: – äåòåêòîð ñ÷åòíîãî ðåæèìà íà ñðåäíèå è âûñîêèå ýíåðãèè, îõâàòûâàåò äèàïàçîí ýíåðãèé 0,2-3ÌýÂ, ïðåäñòàâëÿåò ñîáîé äåòåêòîð òèïà “ ñöèíòèëëÿòîð- ôîòîäèîä ” , îñíàùåííûé ñöèíòèëëÿòîðîì Cs(Tl) óâåëè÷åííîãî ðàçìåðà (~25  25 ìì), è ñîîòâåò- ñòâåííî ïîâûøåííîé ÷óâñòâèòåëüíîñòè â äèàïàçî- íå ìîùíîñòåé äîç, íà÷èíàÿ îò óðîâíÿ ôîíà ~ 10 ìê Ð /÷ è äî ~ 20 ì Ð /÷; – êîìáèíèðîâàííûé äåòåêòîð ñ÷åòíîãî ðåæèìà, èñïîëüçóåìûé äëÿ ýíåðãèé 0,02-0,2 Ìý êàê ÏÏÄ- êðåìíèåâûé äåòåêòîð â äèàïàçîíå ìîùíîñòåé äîç 10 -5 —2·10 -2 ð/÷ è êàê äåòåêòîð òèïà “ „ñöèíòèëëÿòîð- ôîòîäèîä ” äëÿ ýíåðãèé (0,02-3 ÌýÂ) â äèàïàçîíå ìîùíîñòåé äîç (~0,02-1ð/÷.); êîíñòðóêòèâíî ïðåä- ñòàâëÿåò ñîáîé ñáîðêó, ñîñòîÿùóþ èç ôîòîäèîäà ïëîùàäüþ 10  10 ìì è ñöèíòèëëÿòîðà Cs(Tl) ðàç- ìåðàìè 5  5 ìì. Ñèãíàëû ñ îáîèõ äåòåêòîðîâ (1.1, 1.2), óñèëåííûå ñïåêòðîìåòðè÷åñêèìè óñèëèòåëÿìè (2.1, 2.2), ïî- äàþòñÿ íà êîíòðîëëåð ñîñòàâíîãî áëîêà äåòåêòèðî- âàíèÿ 3, êîòîðûé ïðåäñòàâëÿåò ñîáîé äâóõêàíàëü- íóþ ñèñòåìó îáðàáîòêè äàííûõ, îáåñïå÷èâàåò îä- íîâðåìåííîå èçìåðåíèå ñðåäíèõ ñêîðîñòåé ñ÷åòà èìïóëüñîâ ïî îáîèì êàíàëàì, àâòîìàòè÷åñêîå ïå- ðåêëþ÷åíèå äåòåêòîðîâ â çàâèñèìîñòè îò ðåãèñòðè- ðóåìîé ìîùíîñòè äîçû è ýíåðãèè èçëó÷åíèÿ.  ïàìÿòè ìèêðîïðîöåññîðà, èñïîëüçóåìîãî â êîí- òðîëëåðå, íàõîäÿòñÿ êîððåêòèðóþùèå êîýôôèöè- åíòû è ôàêòîðû F (E) , ïîëó÷åííûå ýêñïåðèìåíòàëü- íî äëÿ êàæäîãî êîíêðåòíîãî ýêçåìïëÿðà äåòåêòîðà è êîìïåíñèðóþùèå çàâèñèìîñòü 1/Å.  ðåçóëüòàòå îáðàáîòêè íà âûõîäå êîíòðîëëåðà ôîðìèðóåòñÿ âåëè÷èíà N – ñðåäíÿÿ ñêîðîñòü ñ÷åòà (çíà÷åíèå êîòîðîé ïðîïîðöèîíàëüíî ìîùíîñòè äîçû  -èçëó- ÷åíèÿ, ïàäàþùåé íà áëîê äåòåêòèðîâàíèÿ, è íåèçìåííîå ïðè îäèíàêîâûõ ìîùíîñòÿõ äîçû â äèàïàçîíå ýíåðãèé 0,05-3 ÌýÂ), êîòîðàÿ ÷åðåç èíòåðôåéñ RS-485 ïîäàåòñÿ íà ñèñòåìó îòîáðàæå- íèÿ äàííûõ. Èññëåäîâàíèÿ è àíàëèç ýêñïåðèìåí- òàëüíûõ äàííûõ ïîêàçàëè äîñòàòî÷íî âûñîêóþ âîñïðîèçâîäèìîñòü ïàðàìåòðîâ äåòåêòîðîâ (ñèñòå- ìà “ ñöèíòèëëÿòîð-ôîòîäèîä-ïðåäóñèëèòåëü ” ), ðàç- ðàáîòàííûõ è îñâîåííûõ â èññëåäîâàòåëüñêîì ïðî- èçâîäñòâå â ÍÒÊ “ Èíñòèòóò ìîíîêðèñòàëëîâ ” . 4. Ðåçóëüòàòû èñïûòàíèé ñîñòàâíîãî áëîêà äåòåêòèðîâàíèÿ  òàáë. 1 ïðèâåäåíû ðåçóëüòàòû êîìïëåêñíûõ èññëåäîâàíèé îäíîãî èç ñîñòàâíûõ áëîêîâ äåòåêòè- ðîâàíèÿ, à òàêæå çíà÷åíèÿ ïîãðåøíîñòåé èçìåðå- íèé ìîùíîñòè ïîãëîùåííîé äîçû (ÌÏÄ) â äèàïà- çîíå ìîùíîñòåé äîç îò óðîâíÿ ôîíà äî âåëè÷èí ~1500·10 -6 ìêÃð/ñ â çàâèñèìîñòè îò ýíåðãèè èçëó- ÷åíèÿ.  âûäåëåííûõ ñòðîêàõ äàíû ïîãðåøíîñòè èçìåðåíèé, êîòîðûå ïîëó÷åíû ïðè îäèíàêîâûõ ÌÏÄ äëÿ ýíåðãèé 0,059 Ìý ( 241 Am), 0,661 Ìý ( 137 Cs) è (1172+13325) Ìý ( 60 Co).  ïîñëåäíåé ãðàôå ïðèâåäåíî ðàñïðåäåëåíèå (â ïðîöåíòíîì ñîîòíîøåíèè) ýíåðãèé ðåãèñòðèðóåìûõ g-êâàíòîâ, êîòîðûå ïîïàëè â ñîîòâåòñòâóþùèå èíòåðâàëû ýíåðãèé: 1 êàíàë – 0,03-0,5 ÌýÂ; 2 êàíàë – 0,5-0,8 ÌýÂ; 3 êàíàë – 0,8-1,4 ÌýÂ; 4 êàíàë – 1,4-3 ÌýÂ. Àíàëèç äàííûõ, ïðèâåäåííûõ â òàáë. 1, ïîçâîëÿåò ñäåëàòü ñëåäóþùèå âûâîäû: – ïîãðåøíîñòü èçìåðåíèé ìîùíîñòè ïîãëîùåííîé äîçû ÑÁÄ íå ïðåâûøàåò ±10 % â äèàïàçîíå ìîùíîñòåé äîç îò óðîâíÿ ôîíà äî 1500  10 -6 ìêÃð/ ñ è â äèàïàçîíå ýíåðãèé 0,059–1,3 ÌýÂ; mKx pVlBBdPHQ*R hPhJѩVBU)$TP\'*ŅZ:#޻o/3u gs9瞻|ޏ5LDzzH~.>G"R(sRዔLOއgI+hR T*2+*?9^cNR&ٲ.ɯ@:˹~]l)Fk]!ɓ$b8F)N\`e>| 4S C{:F+dsA>{İբY\2>؏Ht,dJ(f$]GӦƗ mϒK@\Iv8b9yR) ȳOG ~- |$V,NI.]jo=j]im:>h z +PwEV ?p*( v֗?]M ] _nBYj@O'Q'+y)k}W Yy 9m$*A HƬyx>n;ى%+hݘoCv&gUywVRB*n|_p8xoo'8/͘LeWNX[o96#=7)mhc0cfA) ǟ̇<ҸL;Ջ>Q DHNq!TwƙA'[*狁쇣8o/KSYUS/,'g_32xZe&o?ʔ"]řg8Ѵmw.zlJ=Lp8T.$MΤSԯvBl> >La+!]\#C]lt;D^BQyX]Yz9͇dS_v{+/xg΋PT`įZV8}18\n_\NJ}gh 8CGwp#̃_2?V/@H|-|p%{{|`8C ݻox9yȋi7\4["p3?4{&|p?X _u:&{~8߃ㇼ'ǃ;_~7S,KR^n>1'76;aS Y-𶠣cGu?4v=GZZ cB\AʻqUߵS!G_M.n+cxQXƧ|vx12 ~ !pXjS]w+Wu쁍Ö5h#UCuDu*qڟcSaTu^|x;؜=jP6?.ޛ<[-b]Jjڷ/{Go Z 1Nowz#!Kgtnu52͞jC;2>*oOAτuym!߂rg2=qDpy{G{GG2Oħ~!; >^ ㇌rp x[QP ^w5exΩ`_W)Qۆ~^~zυ,P]`JdS0aX#۩|il0¨:LFoayGSɔo,a,oFG2^P7YM6a}SWLݎbI7l?\a[*~ܨ]ʴ7GYC2:ALf_&aT _L&RĦqtù 3et;MO$8UM Kw"?iL''@(Q D2e @(Q D2e @(e } D2e @(Q D2e @(ԐMicrosoft Office Document Image Writer 11.03.1897.00 2005:11:25 18:50:40  ~   r`n v (16TO 2O /$ 1 >B h{x ]Uu 1bL"ƊO$%A z =+ͭFZlJXm@(<|$ / pZg9k}놙c91Ɯs̱ާ+IuJەR4&Iy.ϘIR;'Iǽ5IҕL`d˒j*wjwӺ<;t jɒ=9I]l˧G ZzUl\k S ^_O}V>ӭJ^4IOQ9JJJ)Cԕlf3Y(5ˍ^ϯ7g%YJ):gQ$3RY,sm1{MH.|;$ٰm~LLڿ?qe*|gV&ktzɶ +:x){V>ꔽ^2~e7ܛ^CZFtt>Z;{+QtZQ:(1>9:aŋV&5/{YtӬaۺ.}N=zDHOIr_kU]{ȑǯtQ ?(FV>KT9;Y RdK!vn]۸E;/u4Hn[qyR{Uo;fԮNh_VQ^g{$ofۺ /m_8Ѱ/H^MqnInL'dN2KKEW/9M"{leϥ}Gqjо/r{ ƥ6/6%e{ɱof컝ؾ1!UU1Mb𓭶I~J;$$KWwI[U@ro*QoK%%;mg@#χq>r|JȊ2ȩQG? w' D$#;ˉ{<Џ29_C{)ݡ )==ٞ xk&M7ʎ$-}@2d][T+McB&cwdE_}i#QO;m7V l7L9vPt5v3?Vdj)[gqZJgֽBYsapu{R-Ic*juѶm`]>{)Yq}JޭD=Kb/+{)',Orz^ A9]LI92r?D?S{i3^6fVdÒ*וgtf=Kb=l졼5.Y ,#2#wbyrr?쇌!9!w>2f K 2XI>q5>r[g{/}+딷 nũoAn:OpX `>9O{*#g|Qij>Uk t9d:\Y6lU5™Fz=vuk%}lݧtC~H.7mb5:|/T&XȔ>[.=d/eD2O֪EzX?JMR/vqYitPOSl'd0Qs1ɩ|>}z?c_Wf#!ʛa*T;l@~ܚ|Gz I\tgTϺoU tJAiHu&a]"w+Օc q4hOFZ~[n.ϴM:h9thc . 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Èçëàãàåòñÿ ìåòîä îöåíêè íà÷àëà ðåãóëÿðíîãî òåïëî- âîãî ðåæèìà â òåëå ñ âíóòðåííèìè èñòî÷íèêàìè ýíåð- ãèè ïðè ðàâíîìåðíîì íà÷àëüíîì ïîëå òåìïåðàòóðû. Ïðèâîäèòñÿ îöåíêà ðåçóëüòàòîâ ðàñ÷åòîâ ïî ïîëó÷åí- íûì çàâèñèìîñòÿì ïóòåì ñðàâíåíèÿ èõ ñ ðåçóëüòàòàìè ðàñ÷åòîâ ïî àíàëèòè÷åñêèì çàâèñèìîñòÿì äëÿ òåë ýòàëîííîé ôîðìû (øàð, ïëàñòèíà) è ñ ýêñïåðèìåí- òàëüíûìè äàííûìè äëÿ ÐÝÀ. Àêòóàëüíîñòü Êîíñòðóèðîâàíèå ñîâðåìåííûõ ðàäèîýëåêòðîííûõ àïïàðàòîâ, íàðÿäó ñ ðàçðàáîòêîé ýëåêòðè÷åñêèõ ñõåì, ïðåäúÿâëÿåò æåñòêèå òðåáîâàíèÿ ê òåìïåðà- òóðíîìó ðåæèìó áóäóùåé êîíñòðóêöèè, êîòîðûé è îïðåäåëÿåò â çíà÷èòåëüíîé ñòåïåíè íàäåæíîñòü èõ ðàáîòû. Ýêñïåðèìåíòàëüíûå è òåîðåòè÷åñêèå èññëåäîâàíèÿ íåñòàöèîíàðíûõ òåìïåðàòóðíûõ ïîëåé ðàäèîýëåê- òðîííûõ àïïàðàòîâ (ÐÝÀ) [1-4 ]ïîêàçàëè âîçìîæ- íîñòü ïðèìåíåíèÿ òåîðèè ðåãóëÿðíîãî ðåæèìà äëÿ ðàçðàáîòêè èíæåíåðíûõ ìåòîäîâ ðàñ÷åòà íåñòàöè- îíàðíûõ òåìïåðàòóð ÐÝÀ. Ïðîñòîòà ìåòîäà â öåëîì ñíèæàåòñÿ, îäíàêî, íåî- ïðåäåëåííîñòüþ ìîìåíòà íà÷àëà ðåãóëÿðèçàöèè р  , ñ. Ïîïûòêà ïðåíåáðå÷ü ýòèì ôàêòîðîì, ò.å. ïîëàãàòü âñåãäà 0 р   ìîæåò ïðèâåñòè ê ñåðüåç- íûì îøèáêàì â ðàñ÷åòàõ [1-4]. Öåëü èññëåäîâàíèÿ – âîçìîæíîñòü îáîáùåíèÿ çàâè- ñèìîñòè (1) äëÿ îïðåäåëåíèÿ íà÷àëà ðåãóëÿðíîãî òåïëîâîãî ðåæèìà íà èçîòðîïíûå òåëà. Ïîñòàíîâêà çàäà÷è è ìåòîäû ðåøåíèÿ Ïîêàçàòü âîçìîæíîñòü ïðèìåíåíèÿ òåîðèè ðåãó- ëÿðíîãî ðåæèìà äëÿ ðàçðàáîòêè èíæåíåðíûõ ìåòî- äîâ ðàñ÷åòà íåñòàöèîíàðíûõ òåìïåðàòóð ÐÝÀ. Êàê ïîêàçàíî â ðàáîòå [4], âðåìÿ íàñòóïëåíèÿ ðåãóëÿðíîãî òåïëîâîãî ðåæèìà äëÿ èçîòðîïíûõ òåë, ïðè ãðàíè÷íûõ óñëîâèÿõ òðåòüåãî ðîäà ñ ïîñòîÿí- íûìè êîýôôèöèåíòàìè è ïîñòîÿííîé òåìïåðàòó- ðîé îêðóæàþùåé ñðåäû, ïðè 5 , 0 F . кр 0  ïðîèçâî- äèòñÿ ïî çàâèñèìîñòÿì: . доп F М М М 1 т 1 1 к кр 0 1 n 1 Е М М А | A |                        , (1) ãäå ê – øàð, öèëèíäð, ïëàñòèíà;   Н А і – ïîñòî- ÿííûå êîýôôèöèåíòû äëÿ òåë ýòàëîííûõ ôîðì (øàð, öèëèíäð, ïëàñòèíà);     m / m H M j j – îáîá- ùåííûå êðèòåðèè òåïëîâîé èíåðöèè äëÿ ýòàëîí- íûõ òåë; k / a F kp 0   – îáîáùåííûé êðèòåðèé Ôóðüå;      ct – ðàçíîñòíàÿ òåìïåðàòóðà, ãðàä.;   z , y , x ct  – èçáûòî÷íàÿ ñòàöèîíàðíàÿ òåìïåðàòóðà, ãðàä.,   c ст ст t t    ; j m – ïîëîæèòåëüíûå ÷èñëà (ñ -1 ), ñâÿçàííûå óñëîâèåì ... m m 0 1 0   , k / a m   – ïðåäåëüíîå çíà÷åíèå   0 m 0   ïðè   H ; Ê – êîýôôèöèåíò ôîðìû òåëà ì 2 ; V / GK H   – îáîá- ùåííûé êðèòåðèé Áèî èññëåäóåìîãî òåëà; à – êîýôôèöèåíò òåìïåðàòóðîïðîâîäíîñòè, ì 2 /ñ -1 ; G – òåïëîâàÿ ïðîâîäèìîñòü, âò/ãðàä;  – ñ; t – òåìïåðàòóðà, С 0 ; n –êîýôôèöèåíò, ó÷èòûâàþùèé õàðàêòåð ðàñïðåäåëåíèÿ èñòî÷íèêîâ. Çíà÷åíèÿ 1 1 1 М / М . М , М , А / А äëÿ øàðà ïðåäñòàâëåíû â òàáë. 1. Форма тела Шар Н А / А 1 М М 1 М/М 1 0 0,000 0.000 2,050 0,000 0,010 0,015 0,010 2,060 0,050 0.05 0.073 0,051 2.088 0,024 0,10 0,131 0,093 2,117 0,044 0,20 0,213 0,161 2,181 0,072 0,30 0,296 0,229 2,245 0,100 0,40 0,376 0,297 2,309 0,128 0,50 0,461 0,366 2,372 0,155 1,00 0,659 0,554 2,657 0,206 2,00 0,815 0,735 3,062 0,240 3,00 0,902 0,810 3,276 0,247 400 0,941 0,855 3,460 0,247 5,00 0,955 0,883 3,534 0,250 10 0,965 0,941 3,745 0,251 20 0,998 0,970 3,881 0,251 1,000 1,000 4,00 0,250 Òàáëèöà 1 Îöåíêà òî÷íîñòè îïðåäåëåíèÿ . рег  №№ эксп. F 0 кр расч. . мин  расч. 0  опыт F 0, опыт % 100   1 2 3 4 5 6 1,2 !,64 12,2 12,0 1,61 2 3,4 1,66 17,3 18,0 1,65 4 5,6 1,64 25,0 23,5 1,54 6 7,8 1,65 24,1 23,0 1.60 4 9,10 1,66 20,4 19,0 1,55 7 11,12 1,60 9,50 8,50 1,44 10 13-16 1,67 6,25 6,00 1,61 4 17.18 1.67 6,25 6,00 1,61 4 19-21 1,60 1,33 1,60 1,57 2 22-24 1,63 3,33 3.00 1,30 10 25 1,66 3,16 3,50 1,48 11 26,27 1,60 13,7 12,0 1,43 12 28,29 1,62 6,70 6,00 1,46 10 30 1,62 2,93 3,00 1,59 2 31,32 1,65 9,00 10,0 1,49 10 Òàáëèöà 2 Ñðåäíåå çíà÷åíèå n / і . ср     6,9 :Hx tU}!D2ABĄI&Uu`%"Bmp XTTABA"H]AT1 aI2A]rcn7!t-]7}>{>XH^sU`?X"Ҹ N\ܣ&_u-ViF/!Rމ/; *]*ٟ_ڧ9:X%ȘWC M M͈mL(ֆȁe4>In ǬC}hΖ stn&)ْ'HIإVF[ޏxyGN}X~D"; 4v>O,bgĿPKqt7+UgJK"bHp y])vlσW@bdBv!BF;EG|;Oʔ3)hk׿vIubB܏[1?G ^oVJ%@ޏ0w4Eƴ^Yݽ9/1 i!kFRn{@O9zP\ϯBI.4v Klב&#gI,@ d%]"Ȱh\J7yvBVR@Br!۱C^i.cyN]Ğ}-o*[h jfXLG'k?[܀ i繶\x[+!",nrjՇGF0ү-ul/gBu.?dއk>[PvrW]{̍5BJZXHO΃5/MdJ:yAb`?*֤'rCk'KW&b;~K_FZw}56i M4ߍ:}^r6g=7sw^}70nT0{g#1.gZoEmtnh W_WBLkunΪjnIl"RroZZia}}>bV'+3S]}|t?$^}}k_nԞ۰W~)k0ӫ:Bo7X̠?9ܑs] y%ck@):ژv|.F|:c8:ؼ wt)g^wV_Xa +p*_"P rWf{5`l9:#c\WX O!K 7ȶgϙw: 9X5LPc$e ocޯaf620o[ڷb9 =7)!?BNF3W|n:1d/Aph1chk>#{ `wйEK=Yw<{xm<|a?YE5Bڹ9!25vs Mc09t.JD_tD~'p/h &'%'c}|_u w;+P]+nFG}XEt};RX]z=_"Ks1vg!9yƆ#{])y}SlX)SH%tƈIq9ǼgkgA9gί+;nc2@ܥ'{z˾ |:|[{ZqʷK;{c9.ӗԹ?<_pik~{m+itGy/ ~}Pw$^ة/G-_jySF?5qLnQ_p,VMxM<#?}fpCZC;oB  蔻ߚ!ۑsz \TGGy\]grUH|/@Xa +V @Xa +pV9@Xa +V @Xb7Microsoft Office Document Image Writer 11.03.1897.00 2005:11:25 18:50:41  ,F ֚$(162/21 0{x _Eu Y @LKvWy@B(QH&> QRJmjb-jTliܼH!$$s=w';-b{w̜9̜9ǯ%J'e ?hvIzEEQ7!Z% ['ThlI lʑ;DG\͈]]]UΏ.(їPϷs]fU*dCtJjׯs[J{+mIS>RRREIGk"ĐYJ^ʍnp1-V46=xΘ%27#fy}R4Jʟoq\xS[yQ4.juڹ5 ~8~Nwm9=:'vƜhF=kFk͉_cQR91 }ɬ~8m4!~8wji˺NsU5#H=MLq[F1~Ŝh;?ґF]g&+楝92guHNSf! 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Ïîêàæåì, ÷òî çàâèñèìîñòü (1) ìîæåò áûòü îáîáùåíà è äëÿ àíè- çîòðîïíûõ òåë. Îáùåå óðàâíåíèå òåïëîïðîâîäíîñ- òè äëÿ àíèçîòðîïíîãî òåëà â ôîðìå ïàðàëëåëåïèïå- äà, íàõîäÿùåãîñÿ â ñðåäå ñ ïîñòîÿííîé òåìïåðàòó- ðîé, èìååò âèä:                     C Z y x 2 2 2 2 y 2 2 x Z . (2) Ãðàíè÷íûå óñëîâèÿ çàïèøåì äëÿ ñëó÷àÿ ïîïàðíî ñèììåòðè÷íûõ óñëîâèé òåïëîîáìåíà íà ïðîòèâîïî- ëîæíûõ ãðàíÿõ: 0 ) t t ( x t x L ч c x x                  ; 0 ) t t ( y t Ly y c y y                  ; (3) 0 ) t t ( z t Lz z c z z                  . Ïóòåì ïðåîáðàçîâàíèÿ ñèñòåìû êîîðäèíàò [5] x x x     ; y y y     ; z z z     (4) äèôôåðåíöèàëüíîå óðàâíåíèå òåïëîïðîâîäíîñòè (2) äëÿ àíèçîòðîïíûõ òåë ìîæíî çàïèñàòü â âèäå                              c z y x 2 2 2 2 2 2 , (5) ò.å. óðàâíåíèå (2) ïðèìåò òîò æå âèä, ÷òî è óðàâíåíèå äëÿ èçîòðîïíîãî òåëà:          с 2 . (6) Äîïóñòèì, ÷òî  èìååò ïîñòîÿííîå çíà÷åíèå äëÿ âñåõ ãðàíåé, è åãî âåëè÷èíó ïðèíèìàåì êàê ñðåäíå- âçâåøåííîå çíà÷åíèå. Ýòî äîïóùåíèå áûëî ïðîâåðå- íî ýêñïåðèìåíòàëüíî íà òåïëîâûõ ìàêåòàõ. Ðåçóëü- òàòû çíà÷åíèé . рег  , ïîëó÷åííûå ýêñïåðèìåíòàëüíî è ðàññ÷èòàííûå ïî ôîðìóëå (1), ïðåäñòàâëåííûå â òàáë. 2, ñîãëàñóþòñÿ óäîâëåòâîðèòåëüíî. Èñõîäÿ èç ýòîãî, çàïèøåì ãðàíè÷íûå óñëîâèÿ äëÿ óðàâíåíèÿ (6):   0 t t x t x x / L x c                      ;   0 t t y t y y / L y c                      ; (7)   0 t t z t z z / L z c                      , ãäå  – áàçîâàÿ òåïëîïðîâîäíîñòü, âò/ì.ãðàä. Ïîëó÷åííûå óðàâíåíèÿ (5), (6) îòëè÷àþòñÿ îò óðàâíåíèé (2), (3) íîâûìè çíà÷åíèÿìè ðàçìåðîâ ïàðàëëåëåïèïåäà è êîýôôèöèåíòîâ òåïëîîáìåíà. Ïîêàæåì, ÷òî ýòî ðàçëè÷èå ìîæåò áûòü ó÷òåíî çà ñ÷åò êîýôôèöèåíòà ôîðìû òåë. Íåòðóäíî ïîêàçàòü, ñîãëàñíî (4),÷òî ; nG G   nV V   ; nS S   ; z y x 3 / n      . (8) Òîãäà, íà îñíîâàíèè çàâèñèìîñòè (8) êðèòåðèé  H äëÿ àíèçîòðîïíîãî ÿäðà, ïîñëå ïðåîáðàçîâàíèé, ïðèìåò âèä    V GK H , (9) ãäå G, V,  – òåïëîâàÿ ïðîâîäèìîñòü, îáúåì, êîýôôèöèåíò òåïëîïðîâîäíîñòè äåéñòâèòåëüíîãî ïàðàëëåëåïèïåäà âò/ãðàä., ì 3 . âò./ì. ãðàä.;  K – êîýôôèöèåíò ôîðìû ïðèâåäåííîãî ïàðàëëåëåïè- ïåäà, ì 2 . Çíà÷åíèå  К áóäåò îïðåäåëÿòüñÿ ïî çàâèñèìîñòè 1 2 Z Z 2 Y y 2 X x 2 ]} ) L ( ) L ( ) L [( { K                . (10) Òàêèì îáðàçîì, îïðåäåëåíèå íà÷àëà ðåãóëÿðíîãî òåïëîâîãî ðåæèìà ñèñòåì ñ èçîòðîïíûì è àíèçîò- ðîïíûì ÿäðîì ïðîèçâîäèòñÿ ïî îäíèì è òåì æå ôîðìóëàì. Ðàçëè÷èå çàêëþ÷àåòñÿ òîëüêî â âûðàæå- íèè äëÿ îïðåäåëåíèÿ êîýôôèöèåíòà ôîðìû (10).Íà ðèñ. 1 â ãðàôè÷åñêîé çàâèñèìîñòè ïðåäñòàâëåíû çíà÷åíèÿ îøèáîê   кр 0 ш F , H f    , à íà ðèñ. 2   H , F f кр 0 ш    äëÿ àíèçîòðîïíûõ òåë â ñëó÷àå ïðîñòîãî îõëàæäåíèÿ. Àíàëèç ðèñ. 1, 2 ïîêàçûâàåò, ÷òî â ñëó÷àå îòñóòñòâèÿ èñòî÷íèêîâ (W=0) ïðè Í  1 (B ³ =3)   ïðàêòè÷åñêè íå çàâèñèò îò Í. 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OFv}Z2EڡW()ZF08f[~w@g+&`f]c,Pa>Ǔkea<\AhE-^yeĝ2VY^u:akS޴OcniovvClsO ƾp̪ss}ntw"dxáea ?OKkeE_[[z6lݧO.^Uq{Mdc.n|Mɗ X;=6:bMB¢>;y&k,`W%?֯!ϯRPq~bg [֪w4{Bjx ȁߊVuΤA5Apy6H،|J;ãc>( xk;ҮI֓/p?X=|Ӑoq>biv^ɚo5۱{<G` 81zt榝;icVyG^=ڮo+ߺ[N\|uxG;Wkpq497ǎA5k m}مl¯56a^z\_ZӶ sr|y}Ž>k L< yEtկǎ||w%;=C y(/Mި\yFi{wk}-}D_xjg2,,]22 ÐÈ, 2004, ¹ 2 2 0 4 6 8 Н 4 8 12 16 20 24  % F 0кр =1,8 F 0кр =1,6 F 0кр =1,4 F 0кр =1,2 F 0кр =1,0 F 0кр =0,8 F 0кр =0,6 Ðèñ. 1. Çíà÷åíèÿ îøèáîê ) . окр F , H ( f ш    ïðè n=0 F окр % 0,6 1,0 1,4 0 4 8 12 16 20 H=0,01 H=0,05 H=0,1 H=0,2 H=0,3 H=0,4 H=0,6 H=1 H=2 H=3 H=5 H=20   Ðèñ. 2. Çíà÷åíèÿ îøèáîê   H , F f кр 0 ш    ïðè n=0   o F f    Ýòî ïîçâîëÿåò çàâèñèìîñòü (1) óïðîñòèòü: . доп F 105 , 2 к . кр 0 е 659 , 0        , (11) äëÿ Í>1 çíà÷åíèÿ к   âûáèðàòü ïî êðèâîé Í=1 (ñì. ðèñ. 1). Âûâîäû 1. Àíàëèòè÷åñêèìè ðàñ÷åòàìè è ýêñïåðèìåíòàëü- íûìè èññëåäîâàíèÿìè ïîêàçàíà âîçìîæíîñòü îáîá- ùåíèÿ çàâèñèìîñòè (1) äëÿ îïðåäåëåíèÿ íà÷àëà ðåãóëÿðíîãî òåïëîâîãî ðåæèìà íà àíèçîòðîïíûå òåëà (êàêîâûìè ÿâëÿþòñÿ ÐÝÀ) ïðè ðàñ÷åòå íåñòà- öèîíàðíûõ òåïëîâûõ ðåæèìîâ ÐÝÀ. 2. Ïîëó÷åííûå ðàñ÷åòàìè çíà÷åíèÿ íà÷àëà íàñòóï- ëåíèÿ ðåãóëÿðíîãî ðåæèìà äëÿ ñèñòåì ñ âíóòðåííè- ìè èñòî÷íèêàìè ýíåðãèè ïðè ðàâíîìåðíîì íà÷àëü- íîì òåìïåðàòóðíîì ïîëå ñèñòåìû ïî ôîðìóëå (1) è îïðåäåëåííûå ýêñïåðèìåíòàëüíî ñîãëàñóþòñÿ óäîâ- ëåòâîðèòåëüíî (òàáë. 1). 3. Ïðèìåíåíèå òåîðèè ðåãóëÿðíîãî ðåæèìà äëÿ èññëåäîâàíèÿ íåñòàöèîíàðíûõ òåïëîâûõ ðåæèìîâ ÐÝÀ íàèáîëåå ýôôåêòèâíî ïðè ðàâíîìåðíîì ðàñ- ïðåäåëåíèè èñòî÷íèêîâ. Ëèòåðàòóðà: 1. Äóëüíåâ Ã.Í., Òàðíîâñêèé Í.Í. Òåïëîâûå ðåæèìû ýëåêòðîííîé àïïàðàòóðû. Ë.: Ýíåðãèÿ, 1971. 248ñ. 2.ßðûøåâ Í.À. Òåîðåòè÷åñêèå îñíîâû èçìåðåíèÿ íåñòàöèîíàðíûõ òåìïåðàòóð.Ë.: Ýíåðãèÿ. 1967. 198 ñ. 3. Ìàéêî È.Ì., Ñèíîòèí À.Ì. Ýêñïåðèìåíòàëüíîå îïðå- äåëåíèå ýôôåêòèâíîé òåïëîïðîâîäíîñòè íàãðåòûõ çîí ðàäèîýëåêòðîííûõ àïïàðàòîâ // Âîïðîñû ðàäèîýëåêò- ðîíèêè. Ñåð. ÒÐÒÎ, 1972. Âûï. 2. 4. Ëûêîâ À.Â. Òåîðèÿ òåïëîïðîâîäíîñòè. ÃÈÒÒÈ. Ì.:1952. 392 ñ. 5. Êàðñëîó Ã., Åãåð Ä. Òåïëîïðîâäíîñòü òâåðäûõ òåë. Ì.: Íàóêà, 1964. 362 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 05.01.2004 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Àëèïîâ Í.Â. Ñèíîòèí Àíàòîëèé Ìåôîäèåâè÷, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ñîöèàëüíîé èíôîðìàòèêè ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ïðîåêòèðîâàíèå, àâòîìàòèçàöèÿ è ïðîèçâîäñòâî ðàäèîýëåêòðîííîé àïïàðàòóðû. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð.Ëåíèíà, 14, òåë.70-21-591. Ñåìåíåö Âàëåðèé Âàñèëüåâè÷, ä-ð òåõí. íàóê, ïðîôåñ- ñîð, ïðîðåêòîð ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ëîãè÷åñ- êèé ñèíòåç. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíè- íà, 14. ÓÄÊ 621.396.96 ÌÎÄÅËÜ ÎÖÅÍÊÈ ÓÐÎÂÍß ÇÀÏÀÑΠÃÐÓÏÏÈÐÎÂÊÈ ÁÏËÀ, ÏÐÈ ÂÅÄÅÍÈÈ ÂÎÇÄÓØÍÎÉ ÐÀÇÂÅÄÊÈ, ÍÀ ÎÑÍÎÂÅ ÊÐÈÒÅÐÈß ÏÐÅÄÅËÜÍÎÃÎ ÓÐÎÂÍß ÄÀÍÈÊ Þ.Ã., ÁÀÃÐΠÑ.Ñ., ÍÀÊÎÍÅ×ÍÛÉ À.À., ÒÊÀ×ÅÍÊÎ Í.Í. Ðàññìàòðèâàþòñÿ âîïðîñû âûáîðà ðàöèîíàëüíîãî êî- ëè÷åñòâà ðåçåðâà ÁÏËÀ äëÿ ñèñòåìû ðàçâåäêè âîçäóø- íîãî ïðîñòðàíñòâà â ðàçëè÷íûõ óñëîâèÿõ áîåâûõ äåé- ñòâèé. Ââåäåíèå Àíàëèç âîåííûõ îïåðàöèé, ïðîâåäåííûõ âîîðóæåí- íûìè ñèëàìè âûñîêîðàçâèòûõ ãîñóäàðñòâ, íàïðè- ìåð, ÑØÀ, çà ïîñëåäíèå äåñÿòü ëåò ïîêàçûâàåò, ÷òî â íåñêîëüêî ðàç âîçðîñëà ðîëü è çíà÷åíèå óïðàâëÿ- åìûõ àâèàöèîííûõ ñðåäñòâ ïîðàæåíèÿ (1991ã. – 8%, â îïåðàöèè ïðîòèâ Þãîñëàâèè – 35%).  íàñòîÿùåå âðåìÿ ïðîäîëæàåòñÿ ïåðåõîä âîîðó- æåííûõ ñèë ÑØÀ íà âûñîêîòî÷íîå îðóæèå âòîðîãî ïîêîëåíèÿ, èñïîëüçîâàíèå êîòîðîãî íå ïðåäóñìàò- ðèâàåò âõîæäåíèå ñàìîëåòîâ-íîñèòåëåé â çîíó ïî- ðàæåíèÿ ÇÐÊ ìàëîé è ñðåäíåé äàëüíîñòè. Ïðè ýòîì èçëó÷àþùèå ÐËÑ ïîðàæàþòñÿ ïðîòèâî- ðàäèîëîêàöèîííûìè ðàêåòàìè (íàïðèìåð, òèïà AGM-88A HARM). 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I]Ɉ3 o7đ(uVme k=Ѻ1ڿd"S%u!m4 cCeәkq' ?:d.#{,,d24 ÐÈ, 2004, ¹ 2 èçìåíåíèåì ïîãîäíûõ óñëîâèé, çàäàííîé âåðîÿò- íîñòüþ è íàäåæíîñòüþ ïîëó÷åíèÿ ðàçâåäûâàòåëü- íîé èíôîðìàöèè î ïðîòèâíèêå (êàê âîçäóøíîãî, òàê è íàçåìíîãî). Группировка БПЛА Запас (резерв) БПЛА Х2 Х1 Х Ðèñ. 1. Ñòðóêòóðà èíòåíñèâíîñòè “ ñïðîñà ” ÁÏËÀ Ââèäó òîãî, ÷òî îïðåäåëèòü èíòåíñèâíîñòü ñïðîñà  ÁÏËÀ òî÷íî íå ïðåäñòàâëÿåòñÿ âîçìîæíûì, ìû íå ìîæåì çàðàíåå óçíàòü âîçìîæíûå äåéñòâèÿ ïðîòèâíèêà. À îñíîâûâàÿñü ëèøü íà ðàçâåäûâà- òåëüíîé è àïðèîðíîé èíôîðìàöèè î ïðîòèâíèêå è ñâîèõ âîéñêàõ, ìîæåì ñäåëàòü ëèøü ïðåäïîëîæå- íèå î âîçìîæíûõ âàðèàíòàõ äåéñòâèé ïðîòèâíèêà. Èñõîäÿ èç ýòîãî, ëèöî, ïðèíèìàþùåå ðåøåíèå (êîìàíäèð), ìîæåò óñòàíîâèòü íåîáõîäèìûé óðî- âåíü çàïàñîâ (ðåçåðâ) ÁÏËÀ òàêèì îáðàçîì, ÷òîáû âåëè÷èíà îæèäàåìîãî “ Ä ” (äåôèöèòà) íå ïðåâûøà- ëà 1  åäèíèö ÁÏËÀ, à âåëè÷èíà îæèäàåìûõ “ È “ (èçëèøêîâ) íå ïðåâûøàëà 2  åäèíèö. Âûðàçèì ýòè óñëîâèÿ ìàòåìàòè÷åñêè. Ïóñòü  – îïðåäåëÿåìûé óðîâåíü çàïàñîâ (ðåçåðâà) ÁÏËÀ. Òîãäà íà îñíîâå êðèòåðèÿ ïðåäåëüíîãî óðîâíÿ èìååì 2 0 1 d ) ( F ) ( И d ) ( F ) ( Д                        , . (2) Îäíàêî ñëåäóåò ó÷èòûâàòü, ÷òî ïðè ïðîèçâîëüíîì âûáîðå 1  è 2  óêàçàííûå óñëîâèÿ ìîãóò îêàçàòü- ñÿ ïðîòèâîðå÷èâûìè.  ýòîì ñëó÷àå íåîáõîäèìî îñëàáèòü îäíî èç îãðàíè÷åíèé, ÷òîáû îáåñïå÷èòü äîïóñòèìîñòü ðåøåíèÿ. Ðåøàÿ óðàâíåíèÿ (2), îïðå- äåëÿåì òðåáóåìûé óðîâåíü çàïàñîâ ÁÏËÀ  , êîòî- ðûé íàõîäèòñÿ â ïðåäåëàõ ) ( F ) ( F 2 1      . (3) Ðàññìîòðèì íåñêîëüêî ïðèìåðîâ äëÿ ðàçëè÷íûõ ôóíêöèé ðàñïðåäåëåíèÿ ) ( F  êîëè÷åñòâà òðåáóå- ìûõ ÁÏËÀ  â åäèíèöó âðåìåíè. Ïóñòü ) ( F  èìååò âèä (ðèñ.2):                 . 10 6 при 1 , 0 , 6 3 при 3 , 0 , 3 0 при 5 , 0 ) ( F (4) Íåõâàòêà (äåôèöèò) ÁÏËÀ íå äîëæíà ïðåâûøàòü äâóõ åäèíèö 2 1   , èçëèøêè ÁÏËÀ íå äîëæíû ïðåâûøàòü ñåìè åäèíèö 7 2   . Âåëè÷èíà “ ñïðîñà ÁÏËÀ â åäèíèöó âðåìåíè  ëåæèò â ïðåäåëàõ 10 0    . ” Òîãäà èìååì 7 d ) ( F ) ( И 2 d ) ( F ) ( Д 0 10                     , . (5) Ðåøàÿ èíòåãðàëû (5), íàõîäèì äâà çíà÷åíèÿ äëÿ  . Ðàñ÷åòû ïîêàçûâàþò, ÷òî  ëåæèò â ïðåäåëàõ 52 . 5 2 . 4    . Çíà÷èò, îáà óñëîâèÿ âûïîëíÿþòñÿ ïðè òðåáóåìîì óðîâíå çàïàñîâ ÁÏËÀ, ðàâíîì ïÿòè. Ïóñòü ) ( F  çàäàíà êàê    / 1 ) ( F (ðèñ. 3), âåëè÷èíà “ ñïðîñà ” ÁÏËÀ â åäèíèöó âðåìåíè  ëåæèò â ïðåäåëàõ 10 2    . Íåõâàòêà (äåôèöèò) ÁÏËÀ íå äîëæíà ïðåâûøàòü äâóõ åäèíèö 2 1   , èçëèøêè ÁÏËÀ íå äîëæíû ïðåâûøàòü ÷åòûðåõ åäèíèö 4 2   . Ðèñ. 2. Ôóíêöèÿ ðàñïðåäåëåíèÿ ) ( F  Ðèñ.3. Ôóíêöèÿ ðàñïðåäåëåíèÿ    / 1 ) ( F Òîãäà èìååì 4 d ) ( F ) ( И 2 d ) ( F ) ( Д 2 10                     , . (6) Ðåøåíèÿ èíòåãðàëîâ (6) èìåþò âèä: 4 ) 2 ( Ln 2 ) ( Ln 2 ) ( Ln I ) 5 ( Ln ) 2 ( Ln 10                        , (7) Ðåøàÿ èððàöèîíàëüíûå óðàâíåíèÿ (7), îïðåäåëÿåì  êàê 18 . 7 ] 96 . 16 , 38 . 4 min[    . 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AzǍ[HD!OkSxXqoPxǍ_ n/)n7t3[淾IlvW*=i}' ľfnG5|WJkyZrys_K[6ޫ6>.m޻5{mݒt2\/< z:ޅIU*> ǍRu{2'l:~%&V]?ȫ33=Nzū J1=p#Z)q^G 9i%c煘%^\#LKg=]ch(p-tXY"Y8V\4љrr>*ȡ8mi#sqMfT1si+.," ~mxʿ |YWct5}dfcoO5kwYg1|knBnGz%ɽf7j5߁GIw%{t?>)Q.pp6I6A'x;huY6%nT|WWrO=Sj?4TqA_Li0' qx`[/G'L9SFw΃|L1u'U vh~pFyFrkMߓe ߓv!#13xH y@'OpZӚ8a/q ?nφ)[ TcpC?H8np7]'{zn}WgB/xA}ݾP7BGmOZh9m9x4W as> vhxD/,)_JnJV> 3Ro=1o*G}|Wn1'u^!si90˃rɟ:EPe L@& g.4g\->RO׏znutГ{?ٞU;|Ҡ{Ŀ)7 x1./~4ztQVYh2IȩX=5r%e5L5#+JrMkt>.sEyOvt<)lxV(w*텍a{a Ʌ\',Z$&W)ҦWPc; ^acaS386#qhql8ylop~^l:j [&OօzKnN~/!1wq{)"{uNn~<kj< 8tđ/<F_Ng<0aL1=HӎDMir)A/vQ~ic֣YSKunx ~ rЛ?Иg/ޅ8BNS,{ ]njCw2Xf%qg9>ӥ+~~&d]W4.X3κC¸[_C5 sx tyg= r.9-吧5y*|s_Ol等Yĭ;zmIƚjZc&n]UZ'[om܅kb$xM<){{뢨>rJ?fڽS |v]*V% 1,s߮w^Z]ծcʋ+o[zzis6wHwzst|;38T7i|t}_k de˭2'27ia5- 'DVvv=_Ɩ}rKޠ3Ǟ={g.fN͞^#N>t <ߠNP~G ?W >espi6'|K,->ے5i;v8aH|c'9pq X'pop9 evkx $tw?*ڿYXͲ7zmbx Zw*v6rb< 1m5!Oդz 78Sg8iyQt91yiHz`^ gNDVF7 F9ZIQ%~to!g^'p=Ç:xo8OyEG`=.(lZ0e,U 6B,һ_wJF4q7=GB=eGex{^>|Ϛ^y}E:c^fc9ʱ9N'odFòf7$z eς6|w3zC'~˾ y88d"K7IXv:A<إ?BU,, 26 ÐÈ, 2004, ¹ 2 Ïóøêà ñîäåðæèò âíóòðåííèé êàòîä 1, ðåôëåêòîð 2, âíåøíèé àíîä 3, êîëëåêòîð 4, ñîëåíîèä 5 è ìîäó- ëÿòîð 6, ôîðìèðóþùèé îòðèöàòåëüíûé èìïóëüñ, ôîðìà êîòîðîãî ïðèâåäåíà íà ðèñ. 2. Äàííûé èìïóëüñ èìååò ôðîíò íàðàñòàíèÿ íàïðÿæåíèÿ (èí- òåðâàë 1 t t 0   ), ïåðâûé ôðîíò ñïàäà (èíòåðâàë 2 1 t t t   ), îáëàñòü “ ïîëî÷êè ” èìïóëüñà (èíòåðâàë 3 2 t t t   ) è îáëàñòü âòîðîãî ôðîíòà ñïàäà (èíòåðâàë 4 3 t t t   ).  ïðîñòðàíñòâå âçàèìîäåéñòâèÿ ïóøêè ïðèñóòñòâóþò ñêðåùåííûå ðàäèàëüíîå ýëåêòðè÷åñ- êîå 0 E  è ïðîäîëüíîå ìàãíèòíîå 0 B  ïîëÿ, ñîçäàâà- åìûå ìîäóëÿòîðîì 6 è ñîëåíîèäîì 5, ñîîòâåòñòâåí- íî. Èñõîäíûå ïàðàìåòðû ìàãíåòðîííîé ïóøêè äëÿ ìîäåëèðîâàíèÿ ýëåêòðîííîãî îáëàêà âûáèðàëèñü ñîãëàñíî ýêñïåðèìåíòó, îïèñàííîìó â [1]. Èíäóê- öèÿ ïðîäîëüíîãî ìàãíèòíîãî ïîëÿ 0 B çàäàâàëàñü ðàâíîé 0,3  Òë. Àìïëèòóäà èìïóëüñà íàïðÿæåíèÿ ñîñòàâëÿëà 7.0  êÂ. Êîíñòðóêöèÿ ìàãíåòðîííîé ïóøêè èìåëà ñëåäóþ- ùèå ãåîìåòðè÷åñêèå ðàçìåðû: ðàäèóñ êàòîäà мм 1 r k  ; ðàäèóñ ðåôëåêòîðà мм 4 r f  ; ðàäèóñ àíîäà мм 5 , 3 R a  , äëèíà êàòîäà мм 10 z 1  ; ðàññòîÿíèå ìåæäó ñðåçîì êàòîäà è êîëëåêòîðîì мм 17 z 2  è âðåìåííûìè ïàðàìåòðàìè êàòîäíîãî èìïóëüñà: 1 t=1  íñ, 2 t=2  íñ, 3 t=8  íñ. Ìîäåëèðîâàíèå ïðîöåññîâ â ïðîñòðàíñòâå âçàèìîäåéñòâèÿ ïðîâîäèòñÿ ìåòî- äîì êðóïíûõ ÷àñòèö â êâàçèñòàòè÷åñêîì ïðèáëè- æåíèè [4]. 3. Ìàòåìàòè÷åñêàÿ ìîäåëü Îñíîâó ìàòåìàòè÷åñêîé ìîäåëè ìàãíåòðîííîé ïóø- êè ñîñòàâëÿåò ñèñòåìà ñàìîñîãëàñîâàííûõ óðàâíå- íèé äâèæåíèÿ ýëåêòðîííîãî ïîòîêà è óðàâíåíèÿ Ïóàññîíà. Äëÿ îïðåäåëåíèÿ òðàåêòîðèé ýëåêòðîíîâ ðåøàåòñÿ óðàâíåíèå äâèæåíèÿ äëÿ êàæäîé ÷àñòèöû:     B , v E ) t ( E dt r d пз 2 2            , (1) ãäå ) t ( E ) t ( E 0    – âåêòîð íàïðÿæåííîñòè ñòàòè÷åñ- êîãî ýëåêòðè÷åñêîãî ïîëÿ; 0 B B    – âåêòîð èíäóê- öèè ñòàòè÷åñêîãî ìàãíèòíîãî ïîëÿ; gradU E пз    – âåêòîð íàïðÿæåííîñòè ïîëÿ ïðîñòðàíñòâåííîãî çàðÿäà (ÏÇ); 11 10 1,758796 m e η     Êë/êã – ïðèâå- äåííûé çàðÿä ýëåêòðîíà, r  è v  – ðàäèóñ-âåêòîð è ñêîðîñòü ÷àñòèöû. Äëÿ îïðåäåëåíèÿ íàïðÿæåííîñòè ïîëÿ ÏÇ пз E  , âîçäåéñòâóþùåãî íà ÷àñòèöû, âîñïîëüçóåìñÿ óðàâ- íåíèåì Ïóàññîíà: 0 U      , (2) ãäå ) z , , r ( U U   – ïîòåíöèàë ïîëÿ ÏÇ; ) z , , r (     – ïëîòíîñòü îáúåìíîãî çàðÿäà, 12 0 10 85 , 8     Ô/ì. Äëÿ ðåøåíèÿ óðàâíåíèÿ (2) áûë èñïîëüçîâàí êî- íå÷íî-ðàçíîñòíûé íåÿâíûé èòåðàöèîííûé ìåòîä ñ ïîñëåäîâàòåëüíîé êîìáèíàöèåé ðåøåíèé â äåêàð- òîâîé è öèëèíäðè÷åñêîé ñèñòåìàõ êîîðäèíàò â òð¸õ èçìåðåíèÿõ. Ýòî ïîçâîëÿåò èñïîëüçîâàòü ðåøåíèå óðàâíåíèÿ Ïóàññîíà â äåêàðòîâîé ñèñòåìå êîîðäè- íàò êàê íà÷àëüíîå ïðèáëèæåíèå äëÿ åãî ïîñëåäóþ- ùåãî ðåøåíèÿ â öèëèíäðè÷åñêîé ñèñòåìå êîîðäè- íàò. Äàííûé ïåðåõîä ïðåäïîëàãàåò óòî÷íåíèå ãðà- íè÷íûõ óñëîâèé è ñãëàæèâàíèå ðàñïðåäåëåíèÿ ïîòåíöèàëà. Òàêîé ñëîæíûé àëãîðèòì ðåøåíèÿ óðàâíåíèÿ Ïóàññîíà ñâÿçàí ñ ñóùåñòâåííûì ðàçëè- ÷èåì ñõîäèìîñòè åãî ðåøåíèé â äåêàðòîâîé è öèëèíäðè÷åñêîé ñèñòåìàõ êîîðäèíàò è îáóñëîâëåí áîëåå âûñîêîé òî÷íîñòüþ è ñêîðîñòüþ ðåøåíèÿ óðàâíåíèÿ (2) â äåêàðòîâîé ñèñòåìå êîîðäèíàò [5]. Óðàâíåíèå äâèæåíèÿ (1) ðåøàåòñÿ ñ ïðèìåíåíèåì âåêòîðíîãî ìåòîäà [6]. Ïðåäëîæåííûé àëãîðèòì ðåøåíèÿ óðàâíåíèé (1) è (2) áûë ðåàëèçîâàí ïðîãðàììíî íà àëãîðèòìè÷åñ- êîì ÿçûêå C++ äëÿ îïåðàöèîííîé ñèñòåìû WINDOWS â âèäå ïðîãðàììû òðåõìåðíîãî ìîäå- ëèðîâàíèÿ íåñòàöèîíàðíûõ ïðîöåññîâ 3D-BMS.03 (3-Dimensional - Bunch Modeling System). Äàííàÿ ïðîãðàììà ïîçâîëÿåò íàéòè ðàñïðåäåëåíèå ïîòåí- öèàëà ìåæäó ýëåêòðîäàìè ïðàêòè÷åñêè ëþáîé ôîðìû è ðàññ÷èòàòü òðàåêòîðèè ÷àñòèö â ñêðåùåí- íûõ ïîëÿõ ñ ó÷¸òîì îáú¸ìíîãî çàðÿäà â òð¸õ èçìåðåíèÿõ. 4. Àíàëèç ôèçè÷åñêèõ ïðîöåññîâ â íà÷àëüíîé ñòàäèè ôîðìèðîâàíèÿ ýëåêòðîííîãî îáëàêà Äëÿ ðàáîòû ìàãíåòðîííîé ïóøêè íà å¸ êàòîä ïîäà¸òñÿ îòðèöàòåëüíûé èìïóëüñ íàïðÿæåíèÿ, ôîðìà êîòîðîãî ïðèâåäåíà íà ðèñ. 2. -U, кВ t, нс 0 t 1 t 2 t 3 t 4 y x y x y x y x Ðèñ.  2. Èìïóëüñ íàïðÿæåíèÿ, ïîäàâàåìîãî íà êàòîä, è êà÷åñòâåííûé âèä òðàåêòîðèé ýëåêòðîíîâ íà ðàçíûõ ó÷àñòêàõ êàòîäíîãî èìïóëüñà Íà ôðîíòå íàðàñòàíèÿ èìïóëüñà àíîäíîãî íàïðÿæå- íèÿ (èíòåðâàë 1 t t 0   ) â ðåçóëüòàòå àâòîýëåêòðîí- íîé ýìèññèè ñ ïîâåðõíîñòè êàòîäà ýìèòèðóþòñÿ àâòîýìèññèîííûå ýëåêòðîíû, òîê êîòîðûõ, îöå- íåííûé ïî òåîðèè Ôàóëåðà-Íîðäãåéìà, ñîñòàâëÿåò íåñêîëüêî ìèêðîàìïåð. Èõ ýíåðãèÿ âûëåòà выл W íå ïðåâûøàåò äåñÿòûõ äîëåé ýÂ. Êðîìå äàííûõ ýëåêòðîíîâ, íåêîòîðîå êîëè÷åñòâî ñâîáîäíûõ ýëåê- òðîíîâ è èîíîâ îáðàçóåòñÿ òàêæå çà ñ÷åò ýôôåêòîâ èîíèçàöèè àòîìîâ íåéòðàëüíûõ îñòàòî÷íûõ ãàçîâ. 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Çàâèñèìîñòü ýíåðãèè áîìáàðäèðîâêè îò ýíåðãèè âûëåòà ïåðâè÷íûõ ýëåêòðîíîâ Àíàëèç ïðåäñòàâëåííûõ çàâèñèìîñòåé ïîêàçûâàåò, ÷òî äëÿ âûëåòà ýëåêòðîíà íà êàòîä ñ ïðîãðàììèðó- åìîé ýíåðãèåé áîìáàðäèðîâêè (íàïðèìåð, ÷òîáû ýíåðãèÿ óäàðà уд1 W>W , (7) ãäå 1 W – ýíåðãèÿ ïåðâîãî êðèòè÷åñêîãî ïîòåíöè- àëà íà êðèâîé âòîðè÷íîé ýìèññèè   макс W W    ) ñëåäóåò âûáðàòü òðåáóåìóþ êðóòèçíó íàðàñòàíèÿ ôðîíòà êàòîäíîãî èìïóëüñà ïðè çàäàííîé ýíåðãèè âûëåòà ýëåêòðîíà ñ êàòîäà. Íåîáõîäèìî îòìåòèòü, ÷òî ñ ðîñòîì êðóòèçíû íàðàñòàíèÿ ôðîíòà àíîäíîãî èìïóëüñà áîëåå 12 10 Â/ ñ çàâèñèìîñòü уднач W(W) ÿâëÿåòñÿ íåëèíåéíîé â îáëàñòè ìàëûõ çíà÷åíèé уд W . 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Ðàñ÷¸òû, àíàëîãè÷íûå ïðåäñòàâëåí- íûì íà ðèñ. 3, ïîêàçûâàþò, ÷òî â ýòîì ñëó÷àå öèêëîòðîííûé ïåðèîä óìåíüøàåòñÿ, è äëÿ ñîîáùå- íèÿ íåîáõîäèìîé ýíåðãèè áîìáàðäèðîâêè уд W ïðèõîäèòñÿ óâåëè÷èâàòü êðóòèçíó ñïàäà èìïóëüñà íàïðÿæåíèÿ. Ýòî äà¸ò ïðèíöèïèàëüíóþ âîçìîæ- íîñòü ôîðìèðîâàòü ìîùíûå ýëåêòðîííûå ïó÷êè çà áîëåå êîðîòêîå âðåìÿ. Ïðè äàëüíåéøåì óâåëè÷å- íèè ýëåêòðè÷åñêèõ è ìàãíèòíûõ ïîëåé ýëåêòðîíû ñòàíîâÿòñÿ ðåëÿòèâèñòñêèìè è ïðèìåíÿòü ôîðìó- ëû (3)–(6) äëÿ àíàëèçà ôèçè÷åñêèõ ïðîöåññîâ íå êîððåêòíî. Ñðàâíèâàÿ ãðàôèêè ïðè êèëîâîëüòíûõ è ìåãàâîëü- òíûõ íàïðÿæåíèÿõ, ìîæíî ñêàçàòü, ÷òî äëÿ îáåñïå- ÷åíèÿ ëàâèííîé âòîðè÷íîé ýìèññèè äëÿ ìåãàâîëü- òíûõ íàïðÿæåíèé íóæíû áîëåå êðóòûå ñïàäû. Ñ ïîíèæåíèåì íàïðÿæåíèÿ ñóùåñòâóåò âîçìîæíîñòü ôîðìèðîâàíèÿ ýëåêòðîííîãî îáëàêà ïðè ñðàâíè- òåëüíî íåáîëüøèõ ñêîðîñòÿõ èçìåíåíèÿ íàïðÿæå- íèÿ, íî íà ýòî, ñîîòâåòñòâåííî, òðàòèòñÿ áîëüøå âðåìåíè. Íà óñòàíîâèâøåìñÿ ó÷àñòêå èìïóëüñà ïðè 3 2 t t t   èç óðàâíåíèÿ (3) è (4) ñëåäóåò, ÷òî ýëåêòðîíû, âûëåòåâøèå ñ êàòîäà è ñîâåðøàþùèå ñëîæíîå öèêëîèäàëüíîå (àçèìóòàëüíîå è àêñèàëüíîå) äâè- æåíèå, âîçâðàùàþòñÿ îáðàòíî íà êàòîä çà âðåìÿ, ðàâíîå ïåðèîäó öèêëîòðîííûõ êîëåáàíèé ïðè óñ- ëîâèè, ÷òî ïîòåíöèàë íà êàòîäå ïîñòîÿííûé (ñì. ðèñ.2), ïðè÷åì ñîñòàâëÿþùèå ñêîðîñòåé âûëåòà ÷àñòèöû ðàâíû ñîñòàâëÿþùèì ñêîðîñòåé â ìîìåíò óäàðà î êàòîä. Ýíåðãèÿ âûëåòà ÷àñòèöû ñ êàòîäà 2 mv W 2 нач нач  ðàâíà ýíåðãèè åå óäàðà î êàòîä 2 mv W 2 уд уд  .  ñëó÷àå, åñëè âûïîëíÿåòñÿ óñëîâèå (7) äëÿ êðèâîé âòîðè÷íîé ýìèññèè   макс W W    [7], ãäå макс W – ýíåðãèÿ âûëåòà, ñîîòâåòñòâóþùàÿ ìàêñèìàëüíîìó êîýôôèöèåíòó âòîðè÷íîé ýìèñ- ñèè, ïðîèñõîäèò ýìèññèÿ âòîðè÷íûõ ýëåêòðîíîâ ñ êàòîäà è, êàê ñëåäñòâèå, ðàñòåò îáú¸ìíàÿ ïëîòíîñòü çàðÿäà. Åñëè ýíåðãèÿ áîìáàðäèðîâêè íåäîñòàòî÷íà äëÿ ýìèññèè âòîðè÷íûõ ýëåêòðîíîâ, ïðîöåññ íà- êîïëåíèÿ îáú¸ìíîãî çàðÿäà óõóäøàåòñÿ, ÷òî ïðèâî- äèò ê ñíèæåíèþ îáú¸ìíîé ïëîòíîñòè çàðÿäà â ïðîñòðàíñòâå âçàèìîäåéñòâèÿ. Òàêèì îáðàçîì, âàæíûì ôàêòîðîì â ïðîöåññå ôîðìèðîâàíèÿ ýëåêòðîííîãî îáëàêà ÿâëÿåòñÿ âåëè- ÷èíà ýíåðãèè ýëåêòðîíîâ, áîìáàðäèðóþùèõ êàòîä, ïðè÷åì âåëè÷èíà ýòîé ýíåðãèè çàâèñèò êàê îò äëèòåëüíîñòè ôðîíòà èëè ñïàäà êàòîäíîãî èìïóëü- ñà, îïðåäåëÿåìîãî ïàðàìåòðîì k , òàê è îò íà÷àëü- íîé ýíåðãèè èõ âûëåòà ñ êàòîäà.  íàøåì ñëó÷àå äëÿ âòîðè÷íûõ ýëåêòðîíîâ ýíåðãèÿ èõ âûëåòà âûáèðà- ëàñü ñëó÷àéíûì îáðàçîì â ïðåäåëàõ 1 - 5 ýÂ. Ðàññìîòðåíèå ôèçè÷åñêèõ ïðîöåññîâ, ñîïðîâîæäà- þùèõ ôîðìèðîâàíèå ýëåêòðîííîãî îáëàêà, â ðàì- êàõ êèíåìàòè÷åñêîãî ïðèáëèæåíèÿ íå ïîçâîëÿåò â ïîëíîé ìåðå îáúÿñíèòü âñå îñîáåííîñòè íàêîïëå- íèÿ îáúåìíîãî çàðÿäà.  ÷àñòíîñòè, íå óäàåòñÿ îïèñàòü ðåæèì îãðàíè÷åíèÿ ýìèññèè ïîëåì ÏÇ, êîòîðûé ðåàëüíî ñóùåñòâóåò â ïðèáîðàõ ìàãíåò- ðîííîãî òèïà ñ ðàñïðåäåë¸ííîé ýìèññèåé è èãðàåò îïðåäåëÿþùóþ ðîëü â ìåõàíèçìå ñàìîðåãóëèðîâà- íèÿ ïðîöåññà ðàçìíîæåíèÿ ýëåêòðîííîãî ïîòîêà. 5.  Àíàëèç ôèçè÷åñêèõ ïðîöåññîâ ñ ó÷¸òîì ïðîñòðàíñòâåííîãî çàðÿäà Ðåçóëüòàòû ìîäåëèðîâàíèÿ ìàãíåòðîííîé ïóøêè ñ ó÷åòîì ñèë îáúåìíîãî çàðÿäà ïðèâåäåíû íà ðèñ. 4- 8. Íà ðèñ. 4 èçîáðàæ¸í ýëåêòðîííûé ïîòîê â òðåõìåðíîì ïðåäñòàâëåíèè (à) è â äâóõìåðíîì äèàìåòðàëüíîì ñå÷åíèè (á). a á Ðèñ. 4. 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Ýòîò ïó÷îê ñóùåñòâóåò çà ñ÷¸ò ñàìîïîääåðæèâàþ- ùåéñÿ âòîðè÷íîé ýìèññèè. Åãî ïàðàìåòðû ñî âðå- ìåíåì ïðàêòè÷åñêè íå èçìåíÿþòñÿ. Ýòî ìîæíî âèäåòü èç ðèñ. 5 (à, á), íà êîòîðîì ïîêàçàíû êðèâûå íàêîïëåíèÿ ïðîñòðàíñòâåííîãî çàðÿäà è òîêà, îáóñ- ëîâëåííîãî ÷àñòèöàìè, âûëåòàþùèìè íà êîëëåê- òîð. N 1 0 10íñ a N 2 0 10íñ á Ðèñ. 5. Çàâèñèìîñòü ÷èñëà ÷àñòèö â ïðîñòðàíñòâå âçàèìîäåéñòâèÿ ïóøêè (à) è ÷èñëà ÷àñòèö, äîñòèã- íóâøèõ êîëëåêòîðà (á), îò âðåìåíè Òîê êîëëåêòîðà îòëè÷àåòñÿ îò ýêñïåðèìåíòàëüíîãî òîêà, ïðèâåäåííîãî â [1], íå áîëåå, ÷åì íà 8 %, è ðàâåí 1,75 À. Äàííûé ðåçóëüòàò ñðàâíåíèÿ ïðîòåêàíèÿ ôè- çè÷åñêèõ ïðîöåññîâ â ðåàëüíîì è ìàøèííîì ýêñïå- ðèìåíòàõ ïîäòâåðæäàåò àäåêâàòíîñòü ïîñòðîåííîé ìàòåìàòè÷åñêîé ìîäåëè ìàãíåòðîííîé ïóøêè. Íà ðèñ. 6 ïðåäñòàâëåíû ðàñïðåäåëåíèÿ ïëîòíîñòè çàðÿäà ïî ïðîäîëüíîé êîîðäèíàòå â õàðàêòåðíûå ìîìåíòû âðåìåíè ôîðìèðîâàíèÿ ýëåêòðîííîãî îáëà- êà. Âèäíî, ÷òî ñî âðåìåíåì îáú¸ìíûé çàðÿä ñìåùàåòñÿ ê êîëëåêòîðó.  ïó÷êå ïðèñóòñòâóþò ïóëüñàöèè ïëîòíîñòè çàðÿäà ïî ïðîäîëüíîé êîîðäèíàòå. Ñîñòîÿíèå ýëåêòðîííîãî ïîòîêà â ðàçíûõ ïðîäîëü- íûõ ñå÷åíèÿõ ïóøêè ïðè t = 3 íñ ïîêàçàíî íà ðèñ. 7. Êàê âèäíî, â îáëàñòè ïóøêè ÷àñòèöû çàíèìàþò ïîëîæåíèå ìåæäó êàòîäîì è àíîäîì, à ïðè âûëåòå íà êîëëåêòîð ôîðìèðóåòñÿ ïîòîê ñ äâóìÿ ìàêñèìó- ìàìè ðàñïðåäåëåíèÿ ïëîòíîñòè îáúåìíîãî çàðÿäà.  îáùåì ñëó÷àå èìååò ìåñòî òóðáóëåíòíûé ýëåêòðîí- íûé ïîòîê, îáëàäàþùèé õàðàêòåðíûìè ïóëüñàöè- ÿìè ïëîòíîñòè çàðÿäà. Ïîñëåäíèå îáúÿñíÿþòñÿ öèêëîòðîííûì äâèæåíèåì ÷àñòèö. Ñëåä ïó÷êà íà êîëëåêòîðå ñîâïàäàåò ñ îòïå÷àòêàìè, ïîëó÷åííûìè â ýêñïåðèìåíòàõ [1], íà êîòîðûõ òîëùèíà êîëüöà ñîñòàâëÿåò 1–2  ìì. ) z (  0 1 2 3 z, см t=3нс 1,5нс 1нс Плоскость коллектора Плоскость рефлектора Плоскость среза катода Ðèñ. 6. Ðàñïðåäåëåíèå ïëîòíîñòè çàðÿäà ) z (  ïî ïðîäîëüíîé êîîðäèíàòå â ðàçëè÷íûå ìîìåíòû âðåìåíè Íà ðèñ. 8 ïðåäñòàâëåíà êðèâàÿ çàâèñèìîñòè êîýô- ôèöèåíòà âòîðè÷íîé ýìèññèè ìåòàëëè÷åñêîãî âòî- ðè÷íî-ýìèññèîííîãî êàòîäà îò ýíåðãèè áîìáàðäè- ðóþùèõ ÷àñòèö è ðàñïðåäåëåíèÿ ýëåêòðîíîâ ïî ýíåðãèÿì áîìáàðäèðîâêè íà ýòàïå ðîñòà (ïðè нс 1 t  ) è ñïàäà (ïðè нс 5 , 1 t  ) êàòîäíîãî èìïóëüñà, à òàêæå íà åãî ñòàöèîíàðíîé ÷àñòè ( нс 3 t  ). a б ) ( N 0 1 2 R, мм R Ðèñ. 7. Ðàñïðåäåëåíèå ýëåêòðîíîâ ïî ðàäèóñó âîçëå êîëëåêòîðà (à) è ìåæäó êàòîäîì è àíîäîì (á) 0 0,5 1 1,5 2 W, кэВ N(W) 364 1нс 1,5нс 3нс W  1 2 W  Ðèñ. 8. Ðàñïðåäåëåíèå ýëåêòðîíîâ ïî ýíåðãèÿì áîìáàðäèðîâêè êàòîäà äëÿ ðîñòà ( нс 1 t  ), ñïàäà ( нс 5 , 1 t  ) è ñòàöèîíàðíîé ÷àñòè ( нс 3 t  ) èìïóëüñà íàïðÿæåíèÿ Êàê âèäíî, áîëüøîå êîëè÷åñòâî ÷àñòèö, âûëåòàþ- ùèõ íà êàòîä, îáëàäàåò ýíåðãèåé, ñîîòâåòñòâóþùåé âîñõîäÿùåé âåòâè êðèâîé âòîðè÷íîé ýìèññèè. Ðàçìíîæåíèå ÷àñòèö íà ôðîíòå èìïóëüñà ïîçâîëÿåò ëèøü íåçíà÷èòåëüíî óâåëè÷èòü èõ ïåðâîíà÷àëüíîå êîëè÷åñòâî, îïðåäåëåííîå ðàíåå êàê íà÷àëüíîå è îáóñëîâëåííîå íàëè÷èåì â ïðîñòðàíñòâå âçàèìî- äåéñòâèÿ ïóøêè ñâîáîäíûõ ýëåêòðîíîâ. 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Ѓ3m-Xmg{m?tt-jW[Al=% XºzAy1'cӐq'q";Ӓq\na! !Oƚl G@oy @}0 t.x<2$cɸ}_? XkpGA Xsw47mC ȖBΙ筕vj( 1##C5p~NNa<}O}ʂt7q0?2'Y;/)` h@p:"gA^AB}2ۺ m*\U(1!MH#;Cx+y/Y_!/L  !#σ! i0b y@2{2/ATwwC~'GH>p0=TuV'l@o62SQ{M  s8Cx$J %WJ0ZD^rhN6ϏCAO흡kIMcqڋo}~'~_R8vEl5~CocV,,*31 ÐÈ, 2004, ¹ 2 ÓÄÊ 621.317 ÖÈÔÐÎÂÎÉ ÎÑÖÈËËÎÃÐÀÔ ÍÀ ÎÑÍÎÂÅ ÓÑÒÐÎÉÑÒ ÏÐÎÃÐAÌÌÈÐÓÅÌÎÉ ËÎÃÈÊÈ ÁÀÐÀÍΠÍ.Ã., ÊËÞ×ÍÈÊ È.È., ËÎÄÛÃÈÍ Ì.À. Ðàññìàòðèâàåòñÿ ñïîñîá, ïîçâîëÿþùèé ñîçäàâàòü äëÿ àíàëèçà ïåðèîäè÷åñêèõ ñèãíàëîâ öèôðîâûå îñöèëëîã- ðàôû íà îñíîâå ñåðèéíî âûïóñêàåìûõ êîìïîíåíòîâ, êîòîðûå èìåþò íèçêóþ ñåáåñòîèìîñòü â ñðàâíåíèè ñ àíàëîãè÷íûìè óñòðîéñòâàìè. Çíà÷èòåëüíûì ïðåïÿòñòâèåì øèðîêîìó ðàñïðîñò- ðàíåíèþ öèôðîâûõ îñöèëëîãðàôîâ ÿâëÿåòñÿ èõ âûñîêàÿ ñòîèìîñòü. Ïðåîäîëåíèå öåíîâîãî áàðüåðà âîçìîæíî ïðè èñïîëüçîâàíèè íåäîðîãèõ òåõíîëî- ãèé, ïðèìåíÿåìûõ â òàêîãî ðîäà ïðèáîðàõ. Öåëüþ ïðåäñòàâëåííîé ðàáîòû ÿâëÿåòñÿ ñîçäàíèå ïðèáîðà ñ ìèíèìàëüíîé ñòîèìîñòüþ è õàðàêòåðè- ñòèêàìè, ìàêñèìàëüíî ïðèáëèæåííûìè ê êà÷å- ñòâåííûì ïîêàçàòåëÿì áîëåå äîðîãèõ àíàëîãîâ. Îñíîâíîé çàäà÷åé , ðåøàåìîé ïðè ðåàëèçàöèè ïî- äîáíîãî ðîäà ïðèáîðîâ, ÿâëÿåòñÿ ðàçðàáîòêà ìåòîäà îáðàáîòêè âõîäíûõ ñèãíàëîâ ñ ìèíèìàëüíûì èñ- ïîëüçîâàíèåì ðåñóðñîâ àïïàðàòóðû è âðåìåíè. Ðåøèòü ýòó ïðîáëåìó ìîæíî ïóòåì ïðèìåíåíèÿ îïòèìàëüíûõ ïî ñâîèì ïàðàìåòðàì ïðîãðàììèðó- åìûõ ëîãè÷åñêèõ óñòðîéñòâ â êà÷åñòâå îñíîâû ìîäóëÿ îáðàáîòêè ïîëó÷åííîé öèôðîâîé èíôîðìà- öèè è ïåðñîíàëüíîãî êîìïüþòåðà äëÿ âèçóàëèçà- öèè ðåçóëüòàòîâ. Îäíèì èç îñíîâíûõ òåðáîâàíèé ê ñîâðåìåííûì îñöèëëîãðàôàì ÿâëÿåòñÿ íåîáõîäèìîñòü îáåñïå÷å- íèÿ àíàëèçà ïðîèçâîëüíûõ (â òîì ÷èñëå íåïåðèî- äè÷åñêèõ) ñèãíàëîâ, ÷òî ïðèâîäèò ê îáÿçàòåëüíîìó èñïîëüçîâàíèþ áóôåðíîãî çàïîìèíàþùåãî óñò- ðîéñòâà íà îñíîâå áîëüøîãî êîëè÷åñòâà ñòàòè÷åñ- êîé (SRAM) ïàìÿòè. Ýòî îäíà èç îñíîâíûõ ïðè÷èí ïîâûøåíèÿ ñòîèìîñòè óñòðîéñòâ. Ê ñîæàëåíèþ, íà äàííîì ýòàïå ðàçâèòèÿ òåõíèêè íåâîçìîæíî îòêà- çàòüñÿ îò èñïîëüçîâàíèÿ ñòàòè÷åñêîãî òèïà ïàìÿòè. Îíà íåîáõîäèìà äëÿ íàáëþäåíèÿ çà áûñòðûìè ïðîöåññàìè, à â ñëó÷àå ðàáîòû ñ î÷åíü áûñòðûìè ñèãíàëàìè ãèãàãåðöîâîãî äèàïàçîíà ñêîðîñòè ðàáî- òû ñîâðåìåííîé ïàìÿòè äàæå íå õâàòàåò.  òî æå âðåìÿ äëÿ íàáëþäåíèÿ çà ïåðèîäè÷åñêè ïîâòîðÿþùèìèñÿ ñèãíàëàìè áîëüøîãî îáú¸ìà ïà- ìÿòè íå òðåáóåòñÿ, òàê êàê âñÿ íåîáõîäèìàÿ èíôîð- ìàöèÿ ñîäåðæèòñÿ â îäíîì ïåðèîäå.  ýòîì ñëó÷àå äëÿ êîððåêòíîãî îòîáðàæåíèÿ ïåðèîäè÷åñêîãî ñèã- íàëà â ïàìÿòè äîñòàòî÷íî õðàíèòü ñðàâíèòåëüíî íåáîëüøîå êîëè÷åñòâî èíôîðìàöèè. Âîçíèêàåò ïðîáëåìà – êàêèì îáðàçîì ïîëó÷èòü â ïàìÿòè óñòðîéñòâà îöèôðîâàííûé íàáîð áàéò, ñîîòâåòñòâó- þùèé îäíîìó ïåðèîäó èññëåäóåìîãî ñèãíàëà. Óêà- çàííàÿ ïðîáëåìà ìîæåò áûòü ðàçðåøåíà ñ ïîìîùüþ èçâåñòíîãî ìåòîäà, ïîëó÷èâøåãî íàçâàíèå “ Ïîñëå- äîâàòåëüíîñòíûé ñïîñîá ” (ðèñ. 1). Ðèñ. 1. Ïðèìåð ðàáîòû öèôðîâîãî îñöèëëîãðàôà ïîñëåäîâàòåëüíîñòíûì ñïîñîáîì Ðàáîòà ïîñëåäîâàòåëüíîñòíûì ñïîñîáîì ðåàëèçóåò- ñÿ ïîñðåäñòâîì ñòðîãîãî ñëåäîâàíèÿ âûáîðîê äðóã çà äðóãîì ÷åðåç ÷¸òêî îïðåäåë¸ííûå ïðîìåæóòêè âðåìåíè òàêèì îáðàçîì, ÷òî óæå ÷åðåç íåñêîëüêî ïåðèîäîâ îáåñïå÷èâàåòñÿ íàêîïëåíèå äîñòàòî÷íîãî äëÿ êà÷åñòâåííîãî îòîáðàæåíèÿ ñèãíàëà êîëè÷åñòâà èíôîðìàöèè. Áîëüøèì äîñòîèíñòâîì ñïîñîáà ÿâ- ëÿåòñÿ âîçìîæíîñòü ðàáîòû ñ ÷àñòîòàìè, ïðåâûøà- þùèìè ÷àñòîòó ðàáîòû ÀÖÏ, à òàêæå âîçìîæíîñòü èñïîëüçîâàíèÿ ìåíüøåãî êîëè÷åñòâà ïàìÿòè, ÷åì ïðè òðàäèöèîííîì “ ñïîñîáå ñëó÷àéíûõ âûáîðîê ” .  òî æå âðåìÿ ïîñëåäîâàòåëüíîñòíûé ñïîñîá íå íàø¸ë øèðîêîãî ïðèìåíåíèÿ â ñâÿçè ñ òåì, ÷òî îí ðàáîòàåò óäîâëåòâîðèòåëüíî òîëüêî ñ ñîâåðøåííî ñòàáèëüíûìè ñèãíàëàìè, à òàê êàê òàêèõ ñèãíàëîâ â ïðèðîäå ïðàêòè÷åñêè íå ñóùåñòâóåò, òî îáëàñòü åãî ïðèìåíåíèÿ îãðàíè÷åíà. Ðàáîòà îñöèëëîãðàôà ïîñëåäîâàòåëüíîñòíûì ñïîñîáîì ïðåäñòàâëåíà íà ðèñ. 2. Ðèñ. 2. Ðàáîòà îñöèëëîãðàôà «ïîñëåäîâàòåëüíîñò- íûì ñïîñîáîì» ïðè íåñòàáèëüíîì ñèãíàëå  ñâÿçè ñ ïåðå÷èñëåííûìè íåäîñòàòêàìè, ïðèíöèïè- àëüíî ïðèñóùèìè îñíîâíûì ñïîñîáàì, êîòîðûå ïðè- ìåíÿþòñÿ â ñóùåñòâóþùèõ öèôðîâûõ îñöèëëîãðà- ôàõ, ïðåäëîæåí íîâûé ñïîñîá, îáåñïå÷èâàþùèé ðàáîòó ñ ðåàëüíûìè ïåðèîäè÷åñêèìè ñèãíàëàìè. Ïàìÿòü óñòðîéñòâà ðàçáèâàåòñÿ íà äâà ðàâíûõ áàíêà.  íà÷àëå ðàáîòû â îäèí áàíê çàíîñÿòñÿ ïåðâûå ïîñòóïèâøèå äàííûå. Ïîñëå åãî çàïîëíå- íèÿ íà÷èíàåò çàïîëíÿòüñÿ âòîðîé áàíê. Ïàðàëëåëü- íî ïðîèñõîäèò ñðàâíåíèå (ïîëó÷åíèå ðàçíîñòè) äâóõ ñîîòâåòñòâóþùèõ ÿ÷ååê êàæäîãî áàíêà – ïðåäûäóùåé è òåêóùåé. Ïîñëåäíåé îïåðàöèåé ðå- àëèçóåòñÿ îïðåäåëåíèå ñðåäíåãî àðèôìåòè÷åñêîãî àáñîëþòíîãî çíà÷åíèÿ ðàçíîñòè. 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M@8~huJt*:1c{&nw MK@d4uZF`]&UcCFG5+~E]w$]m;>DYa;빵exg#BxĿNUul:"('UG)U{N{ty^i >t~)ǻbx9_0g# HS939DKwWo_Xgdӭ6dKK~/OD]S6Yä`jۇ.&n}k[dj-=S/H.i,:[WZ$OHGta LtXV_BLf+<)wA34:+0sVZp8QSO{^LJ,U !VF8a2,*]rvt XR1x\'AoM2HJD* 6C|Mcvg"2wRQɔʸ_kgT%yly:ܥYOŽ,n}زl[d3sey-6iy6O@gj:BȖ@:#TFk.:͑}+kxf_LbxZQˑaITaAe6'u\LGbǖ)u3a{[k/%DCЁL'ᒆ0!aw.iY"Hds-t=4\Lߪu5Y[qw`Aƌtִ5h|uU&Jh+u]2˶ݏ81g4m9Fk*kxBffkކl3P\|2xa ɭ>|501YkGHӃ ZG<+.i`xȈ{Z=)Ϗkw뾢UI+Ye(*eRءx>dIޞKlcɔkO$$Q:Њ?Y|m#Uw$_ynsYjkƕOC@ ՍZ'~1n]DbElW9hr;רFq>;8ĢLJLR^ 9&=;n-{Yc˩cT OqQ nDK7 Fɛȋ{1mʂ_`x;eSbד.}9Y\u;^P71ғz괒Ԣ֡"1U%fB?6mLMthG^y9C{6ZCK[,t8G9<)ݵZLyZƏgϿo^/fW4hJOK}gWm R# wsξ }iV 3zgLK$uxB)ѧaH@|J؛=ivic[B(Oܵl$*`Ϯ^ˎ0轔݆ 5&S9;K>'HYDxeY\դGA9 RgⒸ?p: {6<%Y"rh9dӛX,N&6LԽkcVNE LVl]@jEeRZc Y=1<|s5:wm[NRÎL|_$NQSf5-}=ѕ? {ˡDfE !t2d!|_0tG1 x!!QS! c4Q+8<jvkMV쒛띠8 vTd-KHvp3BD8: /m=Q>'u|b,_ 2P0>]x`Lic!2kX :1A(s/D8'Ϳ],O.7]ݯv\vr߈f`| Ȟ jp:PfeH|T~t#bEoWzڀ4 }>Aga(XG5  ʎ:Xt˾z I~H00j.H]W$, 'Y@ Vypն BJMJuHX >)])ҁW3H遰orQJ?@YMJoKJnH@&}֛W0v_C/z`/Vp '6$N?;-v`ꗗOʿqfy_-?XuX@'l\Hh,,32 ÐÈ, 2004, ¹ 2 N i=0 |(fiт-fiп)| C N   , (1) ãäå Ñ – êðèòåðèé; N – êîëè÷åñòâî âûáîðîê â ïàêåòå; i – íîìåð òåêóùåé âûáîðêè; fiò – òåêóùàÿ âûáîðêà; fiï . – ïðåäûäóùàÿ âûáîðêà. Ñëåäóþùèì öèêëîì äàííûå çàíîñÿòñÿ â ïåðâûé áàíê, à âòîðîé áàíê ñòàíîâèòñÿ òàêèì, êîòîðûé ñîäåðæèò äàííûå ïðåäûäóùåãî öèêëà, è âñ¸ ïîâòî- ðÿåòñÿ ñíîâà. Ðàññ÷èòàííîå â êîíöå ïîñëåäíåãî öèêëà çíà÷åíèå ñðåäíåãî àðèôìåòè÷åñêîãî ñðàâíè- âàåòñÿ ñ ïðåäûäóùèì. Íà îñíîâå àíàëèçà ïîëó÷åí- íîé èíôîðìàöèè ïðèáîð èìååò âîçìîæíîñòü èçìå- íåíèòü ñâîè íàñòðîéêè è óñòàíîâêè.  èäåàëüíîì ñëó÷àå ïðè àíàëèçå ïåðèîäè÷åñêîãî ñèãíàëà è óñëîâèè, ÷òî áàíêè ïàìÿòè ñîäåðæàò îäèíàêîâûå äàííûå, ñðåäíåå àðèôìåòè÷åñêîå ðàçíîñòè çíà÷åíèé (êðèòåðèé ñðàâíåíèÿ Ñ [compare]) áóäåò ðàâíî íóëþ. Òàêèì îáðàçîì, àëãîðèòì ðàáîòû ïðèáîðà äîëæåí ðåàëèçîâûâàòü óñëîâèÿ, ïðè êîòîðûõ çíà÷åíèå âû÷èñëÿåìîãî ïà- ðàìåòðà ñòðåìèëîñü áû ê íóëþ.  ýòîì ñëó÷àå äîñòèãàåòñÿ ïîëíàÿ ñèíõðîíèçàöèÿ ñèãíàëà.  ðåàëüíîñòè çíà÷åíèå êðèòåðèÿ Ñ íèêîãäà íå áóäåò ðàâíûì íóëþ è ìîæåò ëèøü ñòðåìèòüñÿ ê íåìó. Ñëåäîâàòåëüíî, íåîáõîäèìî îïðåäåëÿòü òàê íàçû- âàåìóþ “ ÷óâñòâèòåëüíîñòü íóëÿ ” , ò.å. êàêîå çíà÷å- íèå êðèòåðèÿ Ñ ìîæíî ñ÷èòàòü “ ïðàêòè÷åñêè ðàâ- íûì íóëþ ” . Ñëèøêîì áîëüøîå çíà÷åíèå “ ÷óâñòâè- òåëüíîñòè íóëÿ ” íå áóäåò ïîçâîëÿòü ïðèáîðó íàéòè ñòàáèëüíîå ñîñòîÿíèå, à ñëèøêîì ìàëîå - ïðèâåä¸ò ê íåàäåêâàòíîìó îòîáðàæåíèþ ñèãíàëà. Ðàáîòó ïðèáîðà ìîæíî ïðåäñòàâèòü â âèäå ïîñòî- ÿííîãî ñðàâíåíèÿ ïîëó÷åííîãî ïàêåòà ñ ïðåäûäó- ùèì. Åñëè ñèãíàë, èíôîðìàöèÿ î êîòîðîì íàõîäèò- ñÿ â ïàêåòå, ñîîòâåòñòâóåò ïîëó÷åííîìó ïåðåä ýòèì, è ýòî ïîâòîðÿåòñÿ ñòàáèëüíî, ìîæíî ñäåëàòü âûâîä î òîì, ÷òî íàáëþäàåìûé ñèãíàë - ïåðèîäè÷åñêèé.  ïðîòèâíîì ñëó÷àå íåîáõîäèìî îïðåäåëèòü: ïîëó- ÷àåìûé ñèãíàë íåïåðèîäè÷åñêèé èëè ïðèáîð åù¸ íå íàñòðîèë ïàðàìåòðû òàêèì îáðàçîì, ÷òîáû çàñèí- õðîíèçèðîâàòü ñèãíàë.  ñëó÷àå íåïðåðûâíîãî (â òå÷åíèå íåñêîëüêèõ öèêëîâ) êîíòðîëÿ çíà÷åíèÿ êðèòåðèÿ Ñ ìîæíî ïðîñëåäèòü äèíàìèêó åãî èçìåíåíèÿ. Åñëè êðèòå- ðèé Ñ ñòàáèëüíî óìåíüøàåòñÿ è, íàêîíåö, äîõîäèò äî çíà÷åíèÿ, óäîâëåòâîðÿþùåãî “ ÷óâñòâèòåëüíîñ- òè íóëÿ ” , òî , ñëåäîâàòåëüíî ïðîöåññ ñèíõðîíèçà- öèè çàâåðùåí. Åñëè êðèòåðèé Ñ íå äîñòèãàåò òàêîãî çíà÷åíèÿ, òî àíàëèçèðóåìûé ñèãíàë íå ìîæåò áûòü ïðîàíàëèçèðîâàí ïðèáîðîì ëèáî çíà÷åíèå “ ÷óâ- ñòâèòåëüíîñòè íóëÿ ” çàäàíî ñëèøêîì ìàëîå. Ïðè îáåñïå÷åíèè óñëîâèÿ ñèíõðîíèçàöèè íàáëþ- äàåòñÿ ñòàáèëüíûé ñèãíàë.  ýòîì ñëó÷àå äàííûå â áàíêàõ ïðàêòè÷åñêè îäèíàêîâû, à óñòðîéñòâî îòî- áðàæåíèÿ, ñëåäîâàòåëüíî, ìîæíî ëèøü èíôîðìè- ðîâàòü îá îòñóòñòâèè èçìåíåíèé. Ýòî îáåñïå÷èâàåò óìåíüøåíèå íàãðóçêè íà êàíàë ñâÿçè. Ïðè èçìåíå- íèè âõîäíîãî ñèãíàëà ïðîèçîéä¸ò ëèøü îäíîêðàò- íàÿ êîððåêöèÿ äàííûõ â ïàìÿòè è ïîñëå èõ îáíîâ- ëåíèÿ íà ýêðàíå óñòðîéñòâà îòîáðàæåíèÿ ïðîèçîé- ä¸ò ñìåíà îñöèëëîãðàììû íà ñîîòâåòñòâóþùóþ ïîñëåäíåìó ïåðèîäó âõîäíîãî ñèãíàëà. Áåçóñëîâíî, âõîäÿùèå ïåðèîäû ñèãíàëà áóäóò íåñêîëüêî îòëè- ÷àòüñÿ äðóã îò äðóãà, íî åñëè èõ èçìåíåíèÿ íå ïðåâûøàþò äîïóñòèìûõ çíà÷åíèé îïðåäåëÿåìûõ “ ÷óâñòâèòåëüíîñòüþ íóëÿ ” , òî äëÿ ïîëüçîâàòåëÿ ìîæíî ïîêàçûâàòü ñèãíàë êàê íåèçìåííûé.  ñëó÷àå ïîÿâëåíèÿ êàêèõ-ëèáî íåñòàáèëüíîñòåé âõîäíîãî ñèãíàëà ïðèáîð ðåàãèðóåò íà ýòî íîâûì öèêëîì ñèíõðîíèçàöèè. Îïèñàííûé ñïîñîá ðàáîòû ïðèáîðà òðåáóåò èñ- ïîëüçîâàíèÿ íåáîëüøîãî êîëè÷åñòâà ïàìÿòè (äëÿ õðàíåíèÿ äâóõ ïåðèîäîâ ñèãíàëà) è óñòðîéñòâ îáðàáîòêè èíôîðìàöèè, èìåþùèõ âîçìîæíîñòü îáðàáàòûâàòü ïàðàëëåëüíî äàííûå. Ýòèìè õàðàê- òåðèñòèêàìè îáëàäàþò óñòðîéñòâà ïðîãðàììèðóå- ìîé ëîãèêè FPGA. Ñîâðåìåííûå ìîäåëè ýòèõ óñòðîéñòâ èìåþò â ñâî¸ì ñîñòàâå îïåðàòèâíóþ ïàìÿòü.  ïîñëåäíåå âðåìÿ èõ ñòîèìîñòü çíà÷èòåëü- íî ñíèçèëàñü. Ñëåäîâàòåëüíî, òðåáîâàíèå íåâûñî- êîé öåíû ïðèáîðà, ïîñòðîåííîãî íà îñíîâå óñò- ðîéñòâ ïðîãðàììèðóåìîé ëîãèêè, áóäåò âûïîëíå- íî. Ðàáîòà îñöèëëîãðàôà ïðåäëîæåííûì ñïîñîáîì ìîæåò áûòü ïðåäñòàâëåíà íà îñíîâå ñîîòâåòñòâóþùåé ìàòåìàòè÷åñêîé ìîäåëè. Òàêàÿ ìîäåëü áûëà ñîçäàíà ñ èñïîëüçîâàíèåì ïàêåòà MathCAD. Ñ åãî ïîìî- ùüþ ïðîâåäåíà èìèòàöèÿ ðàáîòû ïðèáîðà ñ ïåðè- îäè÷åñêèì ñèãíàëîì, ñîäåðæàùèì ñëó÷àéíûå øóìû, ðàçìåùåííûå ïî íîðìàëüíîìó çàêîíó ðàñïðåäåëå- íèÿ. Ïîëó÷åííàÿ ìîäåëü ñèãíàëà ïðåäñòàâëåíà íà ðèñ. 3, ìîäåëèðóåìûé ñèãíàë ãðàôè÷åñêè ïðåäñòàâ- ëåí íà ðèñ.4. Ampl 1 maximum 6 deviation 0.2 step 0.002 f 100  2   f  Tmax maximum step t 0 step  maximum step  noise rnorm Tmax Ampl  deviation  ( ) Ampl Signal t ( ) Ampl noise t step  sin  t  deg  ( )  Ampl noise Ðèñ. 4. Ìîäåëèðóåìûé ïåðèîäè÷åñêèé ñèãíàë ñ øóìàìè Ðèñ. 3. 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Îáîñíîâûâàþòñÿ ïðèíöèïû ïîñòðîåíèÿ è îïòèìèçà- öèè ÑÂ× ðåçîíàòîðíûõ ñåíñîðîâ äëÿ êîíòðîëÿ âëàãî- ñîäåðæàíèÿ ïîðîøêîâûõ ìàòåðèàëîâ. Ïîêàçûâàåòñÿ, ÷òî ðàáî÷èé äèàïàçîí ÷àñòîò íåîáõîäèìî âûáèðàòü âûøå 10 10 Ãö. Ïðèâîäÿòñÿ ìàòåìàòè÷åñêèå ñîîòíîøå- íèÿ, ïîçâîëÿþùèå ïðîèçâîäèòü òåîðåòè÷åñêóþ ãðàäó- èðîâêó ñåíñîðîâ â ðàçëè÷íûõ äèàïàçîíàõ çíà÷åíèé âëàãîñîäåðæàíèÿ. 1. Ââåäåíèå  òåõíîëîãèè ýëåêòðîííûõ êîìïîíåíò ðÿä ôóíê- öèîíàëüíûõ è ñëóæåáíûõ ìàòåðèàëîâ â èñõîäíîì ñîñòîÿíèè ïðåäñòàâëÿþò ñîáîé ïîðîøêîâûå íåìå- òàëëè÷åñêèå ñðåäû, âëàãîñîäåðæàíèå êîòîðûõ ñó- ùåñòâåííî âëèÿåò íà ïðîòåêàíèå ïðîöåññîâ è ýêñ- ïëóàòàöèîííûå õàðàêòåðèñòèêè èçäåëèé. Çà÷àñòóþ äîñòîâåðíûå ñâåäåíèÿ îá ýòîì ôàêòîðå îòñóòñòâó- þò, è ïðîèçâîäèòåëü ââîäèò â òåõíîëîãèþ äîïîë- íèòåëüíóþ ïðîöåäóðó è îáîðóäîâàíèå ñóøêè ìàòå- ðèàëîâ. Ïðàêòèêà óáåæäàåò â íåîáõîäèìîñòè ýêñïðåññ- êîíòðîëÿ âëàæíîñòè èñõîäíûõ ìàòåðèàëîâ, â ðÿäå ñëó÷àåâ íà ïîòîêå. Ïî àíàëîãèè ñ äðóãèìè ïðîèç- âîäñòâàìè îïðàâäàí âûâîä î ïåðñïåêòèâíîñòè ïðè- ìåíåíèÿ ÑÂ× ìåòîäà êîíòðîëÿ âëàæíîñòè ìàòåðè- àëîâ ýëåêòðîííîé òåõíèêè. Îäíàêî, ó÷èòûâàÿ íèç- êèå äîïóñòèìûå çíà÷åíèÿ âëàãîñîäåðæàíèÿ â ýòèõ ìàòåðèàëàõ è ìàëûå èõ ðàáî÷èå îáúåìû, ñëåäóåò ñîñðåäîòî÷èòüñÿ íà ðåçîíàòîðíîì âàðèàíòå ÑÂ× âëàãîìåòðèè [1-3].  «êëàññè÷åñêîì» âèäå ðåçîíàòîðíûå èçìåðèòåëü- íûå ïðåîáðàçîâàòåëè (ÈÏ) íå îðèåíòèðîâàíû íà êîíòðîëü âëàãîñîäåðæàíèÿ ìàòåðèàëîâ íà ïîòîêå. Íåîáõîäèìî òàêæå ðåøàòü çàäà÷è èõ îïòèìèçàöèè ïðèìåíèòåëüíî ê ìàëûì îáúåìàì ïðîá è íèçêîìó âëàãîñîäåðæàíèþ. Ïîýòîìó öåëüþ íàñòîÿùåé ðàçðàáîòêè ÿâëÿåòñÿ îáîñíîâàíèå ïðèíöèïîâ îïòèìèçàöèè òàêèõ ÈÏ è ðàçâèòèå èõ òåîðèè â ñîîòâåòñòâèè ñ âîçíèêàþùè- ìè òðåáîâàíèÿìè. Ïåðñïåêòèâîé òàêîé ðàçðàáîòêè ÿâëÿåòñÿ ñîçäàíèå òåîðåòè÷åñêîé áàçû ïðîåêòèðîâàíèÿ ÑÂ× âëàãîìå- ðîâ ñ çàäàííûìè ìåòðîëîãè÷åñêèìè õàðàêòåðèñòè- êàìè, âêëþ÷àÿ íèçêèé ïîðîã âëàãîñîäåðæàíèÿ. 2. Âûáîð äèàïàçîíà ðàáî÷èõ ÷àñòîò Ïîñòàíîâêà ýòîé çàäà÷è â ïåðâóþ î÷åðåäü âûçâàíà íåîáõîäèìîñòüþ ñóùåñòâåííî ñíèçèòü ñèñòåìàòè- ÷åñêóþ ïîãðåøíîñòü ÑÂ× ìåòîäà âëàãîìåòðèè â îáëàñòè ìàëûõ âëàãîñîäåðæàíèé è îáåñïå÷èòü âîñ- ïðîèçâîäèìîñòü ãðàäóèðîâêè ñîîòâåòñòâóþùèõ òåõíè÷åñêèõ ñðåäñòâ. Êðîìå òîãî, âûáîð ðàáî÷åãî äèàïàçîíà ÷àñòîò ïîâëèÿåò íà ñëîæíîñòü òåõíèêè êîíòðîëÿ è äîñòóïíîñòü ýëåìåíòíîé áàçû. Âëàãîñîäåðæàùèå ïîðîøêîâûå ìàòåðèàëû ñ òî÷êè çðåíèÿ èõ ýëåêòðîïðîâîäíîñòè íà âûñîêèõ è ñâåðõ- âûñîêèõ ÷àñòîòàõ ïðåäñòàâëÿþò âåñüìà ñëîæíûé îáúåêò. Ïîýòîìó, íåñìîòðÿ íà áîëüøîé îáúåì ïðîâåäåííûõ èññëåäîâàíèé, ñòðîãèå ìîäåëè çàâè- ñèìîñòè èõ êîìïëåêñíîé âåëè÷èíû ýëåêòðîïðî- âîäíîñòè îò âëàãîñîäåðæàíèÿ â íàñòîÿùåå âðåìÿ îòñóòñòâóþò. Íà ðèñ. 1 ïðåäñòàâëåíû, âçÿòûå èç ðàáîòû [4], îöåíêè âëèÿíèÿ âêëàäà ðàçëè÷íûõ ìåõàíèçìîâ â ñóììàðíûå ïîòåðè òàêèõ ìàòåðèàëîâ íà ðàçëè÷íûõ ÷àñòîòàõ. Èç íèõ ñëåäóåò, ÷òî òîëüêî íà ÑÂ× ñïåêòð âêëþ÷àþùèõñÿ ïîòåðü ïåðåñòàåò áûòü ñëîæíûì è ñâîäèòñÿ ê ïîòåðÿì íà ïîëÿðèçàöèþ ñâîáîäíîé âîäû. 0 1 2 3 4 5 6 7 8 9 10 11 log f Заряженные двойные слои Поверхностная проводимость Кристаллогидраты; релаксация “ Промежуточные ” формы связанной воды; релаксация Проводимость Потери Максвелла - Вагнера Лед; релаксация Вода; релаксация Общие Ðèñ. 1. ×àñòîòíûå ðàñïðåäåëåíèÿ âêëàäà ðàçëè÷íûõ ñîñòàâëÿþùèõ â ýëåêòðè÷åñêèõ ïîòåðÿõ âî âëàãîñî- äåðæàùèõ ìàòåðèàëàõ Ñëåäîâàòåëüíî, òîëüêî íà ÑÂ× âîçìîæíî ÷åòêî îòñîðòèðîâàòü âêëàä âëàãè â ýëåêòðîäèíàìè÷åñêèå õàðàêòåðèñòèêè ïîðîøêîâûõ ìàòåðèàëîâ ïðè óñëî- âèè íåáîëüøèõ çíà÷åíèé  è  tg òàêèõ ìàòåðèàëîâ â àáñîëþòíî ñóõîì âèäå. Ðåçóëüòàòû èçìåðåíèÿ äèýëåêòðè÷åñêèõ ñâîéñòâ òàêèõ ìàòåðèàëîâ ýëåêòðîííîé òåõíèêè, êàê îêèñ- ëû àëþìèíèÿ, òàíòàëà, êðåìíèÿ, ôîñôîðíûå è áîðíûå àíãèäðèäû, ëþìèíîôîðû, ýëåêòðîëþìè- íîôîðû è äð. [5], ïîêàçûâàþò, ÷òî ñîîòíîøåíèå ïðåâûøåíèÿ воды  è воды tg  â ÑÂ× äèàïàçîíå äëÿ íèõ èìååò ìåñòî. 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Òîãäà эфф эфф 0 эфф эфф 0 0 0 tg tg Q Q Q Q , f f f f               , (3) ãäå 0 0 f f  , Q Q 0  – èçìåíåíèå ðåçîíàíñíîé ÷àñòîòû è äîáðîòíîñòè ÈÏ, âûçâàííîå ââåäåíèåì â èçìå- ðèòåëüíóþ àïåðòóðó ñóõîé ïðîáû, ñîîòâåòñòâåííî. Ïðèáëèæåííûå êîëè÷åñòâåííûå ñâåäåíèÿ î âåëè- ÷èíå 0 0 f f  è Q Q 0  äëÿ ðàçëè÷íûõ êîíñòðóêòèâîâ ÈÏ ìîæíî ïîëó÷èòü, âîñïîëüçîâàâøèñü ïîíÿòèåì âíîñèìîé åìêîñòè. Äëÿ âàðèàíòà ðèñ. 3, à âîñïîëü- çóåìñÿ èçâåñòíûì ïðåäñòàâëåíèåì ýòîé åìêîñòè [9], ïðèâîäÿùèì â äàííîì ñëó÷àå ê âûðàæåíèþ                   d R J R J R J R R ln R 2 С 1 1 0 2 0 1 0 1 2 2 0 , (4) ãäå   2 , 1 1 , 0 R J  – ôóíêöèÿ Áåññåëÿ íóëåâîãî è ïåðâîãî ïîðÿäêà; 0 2 0 k     – ïîñòîÿííàÿ ðàñ- ïðîñòðàíåíèÿ; эфф 0 0 0 0 ~ f 2 k      – ïîñòîÿííàÿ ðàñïðîñòðàíåíèÿ â èññëåäóåìîé ñðåäå. Íà ðèñ. 4 ïðèâåäåíû çàâèñèìîñòè, ïîçâîëÿþùèå îöåíèòü ïàðöèàëüíûå ÷óâñòâèòåëüíîñòè ïî îáîèì âûõîäíûì ñèãíàëàì èçìåðèòåëüíîé èíôîðìàöèè äëÿ ÈÏ íà îñíîâå ÷åòâåðòüâîëíîâîãî êîàêñèàëüíî- ãî ðåçîíàòîðà îò óðîâíÿ âëàãîñîäåðæàíèÿ. Ïðè ýòîì íå äåòàëèçèðóåòñÿ ñâÿçü эфф  è эфф tg  ñ ôèçè÷åñ- êèì ñîäåðæàíèåì ñâîáîäíîé âîäû. Ðèñ. 4. Çàâèñèìîñòü âûõîäíûõ ñèãíàëîâ èçìåðèòåëü- íîé èíôîðìàöèè ÈÏ îò ïàðàìåòðîâ ïðîáû Ïðèáëèæåííî ìîæíî òàêæå îöåíèòü ÷óâñòâèòåëü- íîñòü êîíñòðóêòèâà ÈÏ ðèñ. 3, â. Äëÿ ýòîãî äîñòà- òî÷íî âîñïîëüçîâàòüñÿ ïðåäñòàâëåíèåì îá èçìåíå- íèè óêîðà÷èâàþùåé åìêîñòè, îáðàçîâàííîé êîàê- ñèàëüíîé àïåðòóðîé ñ âëàãîñîäåðæàùèì ïîðîøêîì. 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Ôîðìóëû (3)-(5) ïîçâîëÿþò êà÷åñòâåííî îïðåäåëèòü çàâèñèìîñòü ÷óâñòâèòåëüíîñòè ÈÏ ïî îáîèì ñèãíà- ëàì èçìåðèòåëüíîé èíôîðìàöèè îò ãåîìåòðè÷åñêèõ ïàðàìåòðîâ ðåçîíàòîðà è èçìåðèòåëüíîé àïåðòóðû. Äëÿ ïîëó÷åíèÿ êîëè÷åñòâåííûõ ïðåäñòàâëåíèé îá ýòèõ çàâèñèìîñòÿõ ìîæíî âîñïîëüçîâàòüñÿ çíà÷åíè- ÿìè 0 0 f f  è Q Q 0  ïðè ñîîòâåòñòâóþùåì äèàïàçîíå âåëè÷èí эфф  è эфф tg  èç ðàáîò [9-11]. Âàðèàíò êîíñòðóêòèâà ÈÏ, èçîáðàæåííûé íà ðèñ.3, á, íàì ïðåäñòàâëÿåòñÿ îïòèìàëüíûì ïðè âëàãîìåòðèè ïîðîøêîâûõ ìàòåðèàëîâ ýëåêòðîííîé òåõíèêè.  ïåðâóþ î÷åðåäü ïðè ýòîì êîíñòðóêòèâå ñâåäåíû ê íóëþ íåêîíòðîëèðóåìûå è òðóäíî ó÷èòûâàåìûå ÑÂ× ïîòåðè â îêðóæàþùóþ ñðåäó. Äëÿ íåãî âîç- ìîæíî ïîñòðîåíèå ñòðîãîé ìàòåìàòè÷åñêîé ìîäåëè, ÷èñëåííàÿ ðåàëèçàöèÿ êîòîðîé ïîçâîëèò òî÷íî ïîñòðîèòü õàðàêòåðèñòèêè ïðåîáðàçîâàíèÿ ïî êàæ- äîìó ñèãíàëó, à ñëåäîâàòåëüíî, è ñâîéñòâà ãðàäóè- ðîâî÷íûõ õàðàêòåðèñòèê. Êðîìå òîãî, çäåñü ðåàëè- çóþòñÿ õîðîøî êîíòðîëèðóåìûå èçìåíåíèÿ ñòåïå- íè âêëþ÷åíèÿ ìàòåðèàëîì ïðîáû â ýëåêòðîìàãíèò- íûå ïîëÿ ÈÏ, ÷òî ïîçâîëèò íà ïðàêòèêå íàñòðàè- âàòü åãî îïòèìàëüíî ïî ìåòðîëîãè÷åñêèì êðèòåðè- ÿì. Çàêëþ÷åíèå 1. Ðàáî÷èé äèàïàçîí ÷àñòîò ÑÂ× ðåçîíàòîðîâ äàò- ÷èêîâ êîíòðîëÿ âëàãîñîäåðæàíèÿ ïîðîøêîâûõ ìà- òåðèàëîâ öåëåñîîáðàçíî âûáèðàòü âûøå 10 10 Ãö. 2. Äëÿ îáåñïå÷åíèÿ äîçèðîâàííîãî âêëþ÷åíèÿ êîí- òðîëèðóåìîãî ìàòåðèàëà èç ïðîèçâîëüíîãî îáúåìà ïðîáû â äàò÷èêàõ öåëåñîîáðàçíî ôîðìèðîâàòü èç- ìåðèòåëüíóþ àïåðòóðó êîàêñèàëüíîãî òèïà. 3. Ìàòåìàòè÷åñêèå ñîîòíîøåíèÿ äëÿ âîñïðîèçâî- äèìîé òåîðåòè÷åñêîé ãðàäóèðîâêè äàò÷èêîâ ìîæíî áàçèðîâàòü íà çíà÷åíèÿõ ïàðàìåòðîâ èõ èñõîäíîãî ñîñòîÿíèÿ ñ âêëþ÷åíèåì ñóõîé ïðîáû. Äëÿ êàæäîãî èç îáîñíîâàííûõ êîíñòðóêòèâîâ ÈÏ ýòè ñîîòíî- øåíèÿ ïîëó÷àþòñÿ èç êîððåêòíîãî ðåøåíèÿ ñîîò- âåòñòâóþùåé ýëåêòðîäèíàìè÷åñêîé çàäà÷è. 4. Îäíîâðåìåííî ïðèâåäåííûå ñîîòíîøåíèÿ ÿâëÿ- þòñÿ èñõîäíûìè äëÿ îïòèìèçàöèè äàò÷èêîâ ïî êðèòåðèÿì ÷óâñòâèòåëüíîñòè, äèàïàçîíó èçìåðÿå- ìîãî âëàãîñîäåðæàíèÿ è óìåíüøåíèþ âëèÿíèÿ ìåøàþùèõ ôàêòîðîâ. Òàêèì îáðàçîì, â äàííîé ðàáîòå ïîëó÷åíû íîâûå íàó÷íûå ðåçóëüòàòû, ñâÿçàííûå ñ îáîñíîâàíèåì ïðèíöèïîâ ïîñòðîåíèÿ è îïòèìèçàöèè ÑÂ× ðåçî- íàòîðíûõ ñåíñîðîâ äëÿ êîíòðîëÿ âëàãîñîäåðæàíèÿ â ïîðîøêîâûõ ìàòåðèàëàõ è ôîðìóëèðîâêîé ìàòå- ìàòè÷åñêèõ ñîîòíîøåíèé äëÿ õàðàêòåðèñòèê ïðå- îáðàçîâàíèÿ ñîîòâåòñòâóþùèõ ñåíñîðîâ. Ïðàêòè÷åñêàÿ çíà÷èìîñòü ðàáîòû ñîñòîèò â ïðèìåíè- ìîñòè åå ðåçóëüòàòîâ äëÿ ñîçäàíèÿ íîâîãî ïîêîëåíèÿ ÑÂ× âëàãîìåðîâ ïîðîøêîâûõ ìàòåðèàëîâ, âñòðàèâà- åìûõ â òåõíîëîãè÷åñêèé ïðîöåññ è èìåþùèõ óëó÷- øåííûå ìåòðîëîãè÷åñêèå õàðàêòåðèñòèêè ïî ÷óâ- ñòâèòåëüíîñòè è ñèñòåìàòè÷åñêîé ïîãðåøíîñòè. Ëèòåðàòóðà: 1. Bourdel E., Pasquef D., Denorme P., Roussel A. Measurement of the moisture content with a cylindrical resonating cavity in TM 010 mode // IEEE Transactions on instrumentation and measurement. 2000. Vol.49, ¹5. P. 1023-1028. 2. Trabelsi S., Kraszewski A.W., Nelson S.O. Unified calibration method for nondestructive dielectric sensing of moisture content in granular materials // Electron. Lett. 1999. Vol. 35, ¹ 16. P. 1346-1347. 3. Nyfors E., Vainikainen P. Industrial measurement sensors // Artech House, Inc. Norwood. 1989. 345 P. 4. Äå Ëîîð Ã.Ï. Äèýëåêòðè÷åñêèå ñâîéñòâà ãåòåðîãåííûõ âëàãîñîäåð- æàùèõ ñìåñåé // Ïðèáîðû è ñèñòåìû óïðàâëåíèÿ. 1974. ¹9. Ñ. 19-29. 5. Áåíçàðü Â.Ê. Òåõíèêà ÑÂ× âëàãîìåòðèè. Ì.:Âûñø. øê., 1974. 350 ñ. 6. Nelson S.O. Frequency and moisture dependence of the dielectric properties of high- moisture corn // J. Microwave Power, 1978. 13(2). P. 213- 218. 7. Bartley P.G., Nelson S.O., McClendon R.W., Trabelsi S. Determining moisture content of wheat with an artificial network from microwave transmission measurement // IEEE. Trans. Instrum. Meas. 1998. Vol. 47, ¹1. P. 123-126. 8. Nelson S.O. Microwave dielectric properties of grain and seed // Trans. ASAE. 1973. 16(5). P. 902-905. 9. Àõìàíàåâ Â.Á., Äåòèíêî Â.Ì., Ìåäâåäåâ Þ.Â. è äð. Íåðàçðóøàþùèå áåñêîíòàêòíûå ÑÂ× ðåçîíàòîðíûå ìåòîäû êîíòðîëÿ ïîëóïðîâîäíèêîâûõ ìàòåðèàëîâ (Îáçîð) // Äåôåêòîñ- êîïèÿ. 1986. ¹ 1. Ñ. 33-35. 10. Ãîðäèåíêî Þ.Å., Ïàí÷åíêî À.Þ., Ðÿáóõèí À.À. Òåîðåòè÷åñêèé àíàëèç ðåçîíàòîðíî- ãî ÑÂ× èçìåðèòåëüíîãî ïðåîáðàçîâàòåëÿ òîðîèäàëüíî- ãî òèïà // Ðàäèîòåõíèêà. 2000. ¹113. Ñ. 174-179. 11. Ãîðäèåíêî Þ.Å. Ðåçîíàòîðíûå èçìåðèòåëüíûå ïðåîáðà- çîâàòåëè â äèàãíîñòèêå ìèêðîñëîèñòûõ ñòðóêòóð // Ðàäèîòåõíèêà. 1996. ¹100. Ñ. 253-260. Ïîñòóïèëà â ðåäêîëëåãèþ 26.05.2004 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Ôèñóí À.È. Ãîðäèåíêî Þðèé Åìåëüÿíîâè÷, ä-ð ôèç.-ìàò. íàóê, ïðîôåññîð, çàâ. êàôåäðîé ìèêðîýëåêòðîíèêè, ýëåêò- ðîííûõ ïðèáîðîâ è óñòðîéñòâ ÕÍÓÐÝ. Íàó÷íûå èíòå- ðåñû: ìèêðîýëåêòðîíèêà, íåðàçðóøàþùèé êîíòðîëü ìàòåðèàëîâ è èçäåëèé. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð.Ëåíèíà, 14, òåë.: (0572) 70-21-362, 331-335. Õàììóä Ôàäè Ìîõàìàä, àñïèðàíò êàôåäðû ìèêðîýëåê- òðîíèêè, ýëåêòðîííûõ ïðèáîðîâ è óñòðîéñòâ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ìèêðîýëåêòðîíèêà, íåðàçðóøàþ- ùèé êîíòðîëü ìàòåðèàëîâ è èçäåëèé. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð.Ëåíèíà, 14, òåë.: (0572) 70-21-362. 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(17) Îïðåäåëåíèå 3. Ôàêòîðîì êîìïåíñàöèè âûõîäíîé ôóíêöèè íàçûâàåòñÿ ïðîèçâåäåíèå: y í y y s    . (18) Ìåæäó ôàêòîðîì êîìïåíñàöèè âûõîäíîé ôóíêöèè è åå óðîâíåì êîìïåíñàöèè ñóùåñòâóåò ñâÿçü, êîòî- ðàÿ èìååò âèä:      1 s s 0 y y , ãäå 0 y s – ôàêòîð êîìïåíñàöèè âûõîäíîé ôóíêöèè ïðè íóëåâûõ íîìèíàëüíûõ îòêëîíåíèÿõ.  çàâèñèìîñòè îò çíàêîâ ñîìíîæèòåëåé ôàêòîð êîìïåíñàöèè ìîæåò áûòü ïîëîæèòåëüíûì è îòðè- öàòåëüíûì. Èñïîëüçîâàíèå îïðåäåëåíèé 2 è 3 ïîçâîëÿåò ïåðå- ïèñàòü óðàâíåíèÿ (13) – (16) â âèäå: y m 1 j j p 1 i i s s s         , (19) ãäå  i s è  j s – ïîëîæèòåëüíûå è îòðèöàòåëüíûå ôàêòîðû êîìïåíñàöèè ýëåìåíòîâ. Ïîëíàÿ êîìïåíñàöèÿ âíåøíèõ âëèÿíèé, ïðè êîòî- ðîé îòêëîíåíèÿ ïàðàìåòðîâ íå ïðåâûøàþò ýêñïëó- àòàöèîííûõ, ïðîèñõîäèò åñëè 0 s y  . Ïîñêîëüêó òàêèõ ñëó÷àåâ äëÿ óðàâíåíèé (19) ñóùåñòâóåò áåñ- êîíå÷íîå êîëè÷åñòâî, íåîáõîäèìî ðàññìîòðåòü âîç- ìîæíîñòü îïòèìèçàöèè êîýôôèöèåíòîâ âíåøíèõ âîçäåéñòâèé. 4. Îïòèìèçàöèÿ êîýôôèöèåíòîâ âíåøíèõ âîçäåéñòâèé Íàèáîëåå ïðèâëåêàòåëüíîé ñ ïðàêòè÷åñêîé òî÷êè çðåíèÿ ïðè îïòèìèçàöèè êîýôôèöèåíòîâ âíåøíèõ âîçäåéñòâèé ÿâëÿåòñÿ öåëåâàÿ ôóíêöèÿ, êîòîðàÿ îáåñïå÷èâàåò íàèáîëüøåå ïðîñòðàíñòâî ôàêòîðîâ êîìïåíñàöèè. Òàêàÿ ôóíêöèÿ ìîæåò çàäàâàòüñÿ îòíîñèòåëüíûì îáúåìîì ôàêòîðîâ êîìïåíñàöèè: max s s v n 1 i xíi xi s     , ãäå s v – îòíîñèòåëüíûé îáúåì ôàêòîðîâ êîìïåí- ñàöèè; xíi s – íîðìèðóþùèé ôàêòîð êîìïåíñàöèè. Åñëè íîðìèðóþùèé ôàêòîð èìååò ñòðóêòóðó âûðà- æåíèÿ (17), òî ìåæäó îòíîñèòåëüíûìè îáúåìàìè ôàêòîðîâ êîìïåíñàöèè è êîýôôèöèåíòîâ âíåøíèõ âëèÿíèé ñóùåñòâóåò ñâÿçü:        n 1 i xíi xi s v v , çäåñü  v – îòíîñèòåëüíûé îáúåì êîýôôèöèåíòîâ âíåøíèõ âîçäåéñòâèé; xíi  – íîðìèðóþùèé êî- ýôôèöèåíò âíåøíèõ âîçäåéñòâèé. Îïòèìàëüíîå ñîîòíîøåíèå ìåæäó ýëåìåíòàìè óðàâ- íåíèÿ (19), êîòîðîå îòâå÷àåò ìàêñèìàëüíîìó îáúå- ìó ïðîñòðàíñòâà êîýôôèöèåíòîâ âíåøíèõ âîçäåé- ñòâèé, îïðåäåëÿåòñÿ òåîðåìîé ôàêòîðîâ êîìïåíñà- öèè. Òåîðåìà ( ôàêòîðîâ êîìïåíñàöèè ). Ïðîñòðàíñòâî ôàêòîðîâ êîìïåíñàöèè ýëåìåíòîâ èìååò ìàêñè- ìàëüíûé îáúåì, åñëè âñå ôàêòîðû îäíîãî çíàêà èìåþò îäèíàêîâûå çíà÷åíèÿ è âûïîëíÿåòñÿ ñîîòíî- øåíèå: y s ms ps     , (20)   0 s if 1 m ; 0 s if 1 p y y     . Äîêàçàòåëüñòâî. Óðàâíåíèå (19) ìîæåò áûòü ïåðåïèñàíî â âèäå: e p 1 i i s s     , (21) ãäå èñïîëüçóåòñÿ îáîçíà÷åíèå:      m 1 j j y e s s s . Åñëè îäíà èç âåðøèí ãèïåðïàðàëëåëåïèïåäà ðàñïî- ëîæåíà â íà÷àëå êîîðäèíàò, à äðóãàÿ íà ãèïåðïëîñ- êîñòè (21), òî ãèïåðïàðàëëåëåïèïåä èìååò ìàêñè- ìàëüíûé îáúåì, åñëè îí ñòàíîâèòñÿ ãèïåðêóáîì ñ ðàçìåðîì ðåáðà: p s s e   . Òîãäà ñóììà â (21) ïðèîáðåòàåò âèä:      ps s p 1 i i . Ïîäîáíûå ñîîòíîøåíèÿ ìîãóò áûòü ïîëó÷åíû è äëÿ îòðèöàòåëüíûõ ôàêòîðîâ êîìïåíñàöèè ýëåìåíòîâ, ÷òî ïîçâîëÿåò ñôîðìèðîâàòü âûðàæåíèå (20). Ïðè ïîëîæèòåëüíûõ ôàêòîðàõ êîìïåíñàöèè ýëå- ìåíòîâ ãèïåðïëîñêîñòü (21) è êîîðäèíàòíûå ïëîñ- êîñòè îãðàíè÷èâàþò îáëàñòü, â êîòîðóþ âïèñûâà- åòñÿ ãèïåðïàðàëëåëåïèïåä u  (ðèñ.1). Ðèñ. 1. 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