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CXYږ l-.Y;`+ͧza=jwVk/%)iMˋƾ)K/LjyFwKD*߃3a?S!Jsq26||bnVeM-L}yf d!GZae; Ѿ/Z 1\h>jT良wnyг]HL;s`툗c^'`o:'|:unp?x)ȼC| H?,,S2 ÐÈ, 2005, ¹ 3 ÑÎÄÅÐÆÀÍÈÅ ÏÎÇÄÎÐÎÂËÅÍÍß!..............................................................................................................................................................4 ÐÀÄÈÎÒÅÕÍÈÊÀ ÇÀÉ×ÅÍÊÎ À.Í., ÒÎËÊÀ×Å Â.È., ÊÎËÅÑÍÈÊΠÞ.À., ÂÅÐÅÙÀÊ À.Ï. ÌÎÍÎÈÌÏÓËÜÑÍÛÉ ÏÅËÅÍÃÀÒÎÐ ÑÎ ÂÑÒÐÎÅÍÍÛÌ ÊÎÍÒÐÎËÅÌ È ÊÎÌÏÅÍÑÀÖÈÅÉ ÍÅÈÄÅÍÒÈ×ÍÎÑÒÈ ÀÌÏËÈÒÓÄÍÎ-ÔÀÇÎÂÛÕ ÕÀÐÀÊÒÅÐÈÑÒÈÊ ÒÐÀÊÒÎÂ.................................5 ÇÅÌËßÍÛÉ Î.Â., ËÓÊÈÍ Ê.À. ÔÐÀÊÒÀËÜÍÀß ÐÀÇÌÅÐÍÎÑÒÜ ÀÒÒÐÀÊÒÎÐÀ ÄÈÍÀÌÈ×ÅÑÊÎÉ ÑÈÑÒÅÌÛ Ñ ÇÀÏÀÇÄÛÂÀÍÈÅÌ È ÊÓÑÎ×ÍÎ-ËÈÍÅÉÍÛÌ ÓÍÈÌÎÄÀËÜÍÛÌ ÎÒÎÁÐÀÆÅÍÈÅÌ.......................................................................................................................8 ÀÔÀÍÀÑÜÅ Â.À., ÑÎÂÀ À.Â., ÊËÈÌÎÂÀ Í.Ï., ÍÀÒÀËÓÕÀ Þ.Â. ÇÀÄÀ×À ÎÁ ÓÑÒÀÍÎÂÈÂØÈÕÑß ÊÎËÅÁÀÍÈßÕ ÓÏÐÓÃÎÃÎ ÄÂÓÑËÎÉÍÎÃÎ ÏÐÎÑÒÐÀÍÑÒÂÀ Ñ ÏÎËÎÑÒÜÞ Â ÔÎÐÌÅ ÝËËÈÏÒÈ×ÅÑÊÎÃÎ ÖÈËÈÍÄÐÀ...........................................................................15 ÝËÅÊÒÐÎÍÈÊÀ OLEINICK A.I., AMATORE C.A., SVIR I.B. MATHEMATICAL MODELS AND NUMERICAL SIMULATION OF DIFFUSION-REACTION PROBLEMS OF BRAIN CHEMISTRY....................................18 ÎËÅÉÍÈÊ À.È., ÄÐÎÃÎÂÎÇΠÀ.Ã., ÀÌÀÒÎÐ Ê.A., ÑÂÈÐÜ È.Á. ÐÀÑ×ÅÒ ÈÍÒÅÍÑÈÂÍÎÑÒÈ ÑÂÅ×ÅÍÈß ÝÕË, ÐÅÃÈÑÒÐÈÐÓÅÌÎÉ ÊÎÍÔÎÊÀËÜÍÛÌ ÌÈÊÐÎÑÊÎÏÎÌ......................................23 ØÓËÛÊ Â.Í., ÊËÈÌÅÍÊÎ À.Â., ÑÂÈÐÜ È.Á. ÀÍÀËÈÇ ÍÎÂÛÕ ÌÅÒÎÄΠ×ÈÑËÅÍÍÎÃÎ ÐÅØÅÍÈß ÆÅÑÒÊÈÕ ÇÀÄÀ× ÊÎØÈ.......................................................................................................................28 ÔÓÐÑÎÂÀ Å.Â., ÑÎÑÍÈÖÊÈÉ Ñ.Â., ÂÀÂÐÈ Ä.Ì. ÎÖÅÍÊÀ ÂÎÇÌÎÆÍÎÑÒÈ ÏÎÂÛØÅÍÈß ÓÐÎÂÍß ÂÛÕÎÄÍÛÕ ÕÀÐÀÊÒÅÐÈÑÒÈÊ ÌÀÃÍÅÒÐÎÍΠÍÀ ÏÐÎÑÒÐÀÍÑÒÂÅÍÍÎÉ ÃÀÐÌÎÍÈÊÅ..............................................................................................................36 ÊÎËÎÄIÉ Ç.Î. Ô˲ÊÅÐ-ØÓÌÎÂÀ IJÀÃÍÎÑÒÈÊÀ ÂÍÓÒвØÍÜί ÑÒÐÓÊÒÓÐÈ ÅËÅÌÅÍҲ ÅËÅÊÒÐÎͲÊÈ.....................................................................................................................................................................40 ÊËÈÌÅÍÊÎ Ì.Â., ØÓËÈÊÀ À.Â., ÑÀÔÎÍΠÈ.Ì., ÑÓÕÎÈÂÀÍΠÈ.À. ÂÛ×ÈÑËÅÍÈÅ ÑÏÅÊÒÐΠÓÑÈËÅÍÈß ÏÎËÓÏÐÎÂÎÄÍÈÊÎÂÎÉ ÑÒÐÓÊÒÓÐÛ Ñ ÎÄÈÍÎ×ÍÎÉ ÊÂÀÍÒÎÂÎÉ ßÌÎÉ.........................................................................................................................................................43 ÒÅËÅÊÎÌÌÓÍÈÊÀÖÈÈ ÀÑÒÐÀÕÀÍÖÅ À.À., ÎÌÅËÜ×ÅÍÊÎ À.Â., ÏÐÅÑÍßÊΠÈ.Í. ÑÈÍÒÅÇ ÔÈËÜÒÐΠÄËß ÖÈÔÐÎÂÛÕ ÑÈÑÒÅÌ ÏÅÐÅÄÀ×È Ñ ÎÃÐÀÍÈ×ÅÍÍÎÉ ÏÎËÎÑÎÉ...............................................47 ËÅÌÅØÊÎ À.Â., ÊÐÀÂ×ÓÊ À.À., ÐÓÄÅÍÊÎ Â.Í. 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Êîìïåíñàöèÿ íåèäåíòè÷íîñòè ôàçîâûõ è àìïëè- òóäíûõ õàðàêòåðèñòèê ïðèåìíûõ êàíàëîâ:            j exp Y k Y k   ; (7)            j exp Y k Y k   , (8) çäåñü  k ,  k – êîýôôèöèåíòû êîìïåíñàöèè íåèäåíòè÷íîñòè àìïëèòóäíûõ õàðàêòåðèñòèê ïðè- åìíûõ êàíàëîâ, îïðåäåëÿþòñÿ â ïðîöåññå êàëèá- ðîâêè;    ,    – êîýôôèöèåíòû êîìïåíñàöèè íåèäåíòè÷íîñòè ôàçîâûõ õàðàêòåðèñòèê ïðèåìíûõ êàíàëîâ, îïðåäåëÿþòñÿ â ïðîöåññå êàëèáðîâêè. Ôîðìèðîâàíèå îöåíîê ðàññîãëàñîâàíèÿ: см 2 * k Y / } Y Y Re{             ; (9) см 2 * k Y / } Y Y Re{             , (10) ãäå см  , см  – êîýôôèöèåíòû êîìïåíñàöèè ñìå- ùåíèÿ íóëÿ ðàçíîñòíûõ äèàãðàìì ÀÓ, îïðåäåëÿþò- ñÿ â ïðîöåññå êàëèáðîâêè. 3. Ïðîöåäóðà êàëèáðîâêè ïðèåìíûõ òðàêòîâ ïåëåíãàòîðà Êàëèáðîâêà ïåëåíãàòîðà ìîæåò ïðîâîäèòüñÿ ïî êîíòðîëüíîìó ñèãíàëó, èçëó÷àåìîìó èìèòàòîðàìè, êîòîðûå óñòàíîâëåíû íà êîíòðîëüíîé ìà÷òå èëè íà àíòåííå ñàìîãî ïåëåíãàòîðà. Îáðàáîòêà êîíòðîëüíîãî ñèãíàëà ïðåäóñìàòðèâàåò ïðîöåäóðó äåìîäóëÿöèè è ôîðìèðîâàíèÿ êîìïëåê- ñíûõ îòñ÷åòîâ ñèãíàëîâ, ñíèìàåìûõ ñ âûõîäîâ ñóììàðíîãî è ðàçíîñòíûõ êàíàëîâ ÀÓ, êîòîðàÿ ñâîäèòñÿ ê ñâåðòêå ïðèíèìàåìûõ ñèãíàëîâ ñ åãî êîïèåé íà èíòåðâàëå íàáëþäåíèÿ [8,9]: dt ) t ( ) t ( U Y * k k T k          ; (11) dt ) t ( ) t ( U Y * k Tk k          ; (12) dt ) t ( ) t ( U Y * k Tk k          , (13) ãäå T k – âðåìÿ íàêîïëåíèÿ êîíòðîëüíîãî ñèãíàëà; k  – êîïèÿ êîíòðîëüíîãî ñèãíàëà. Êàëèáðîâêà ïåëåíãàòîðà ïî ñèãíàëàì ñ êîíòðîëüíîé ìà÷òû ïðåäóñìàòðèâàåò ñëåäóþùèå ïðîöåäóðû [10]. Îïðåäåëåíèå êîýôôèöèåíòîâ êîìïåíñàöèè íå- èäåíòè÷íîñòè ôàçîâûõ õàðàêòåðèñòèê ïðèåìíûõ êàíàëîâ îñóùåñòâëÿåòñÿ ïðè íàâåäåíèè ÀÓ ñèñòåìû íà êîíòðîëüíóþ ìà÷òó ñî ñìåùåíèåì êàê } Y Y arg{ * k k          ; (14) } Y Y arg{ * k k          . (15) Ïîëó÷åííûå ïî (14) è (15) çíà÷åíèÿ êîýôôèöèåí- òîâ êîìïåíñàöèè íåèäåíòè÷íîñòè ôàçîâûõ õàðàê- òåðèñòèê ïðèåìíûõ òðàêòîâ èñïîëüçóþòñÿ ïðè ðàáîòå â (7) è (8). Âû÷èñëåíèå êîýôôèöèåíòîâ êîìïåíñàöèè ñìåùå- íèÿ íóëåé ðàçíîñòíûõ äèàãðàìì íàïðàâëåííîñòè è íåèäåíòè÷íîñòè àìïëèòóäíûõ õàðàêòåðèñòèê ïðè- åìíûõ êàíàëîâ ïðîâîäèòñÿ ñîâìåñòíî è ðåàëèçó- åòñÿ â äâà ýòàïà. Ñíà÷àëà ÀÓ ñèñòåìû íàâîäèòñÿ íà êîíòðîëüíóþ ìà÷òó áåç ñìåùåíèÿ, à çàòåì ñ çàðàíåå èçâåñòíûì ñìåùåíèåì â ïðåäåëàõ ñåêòîðà îáçîðà. Îïðåäåëåíèå êîýôôèöèåíòîâ êîìïåíñàöèè ïðè ýòîì îñóùåñòâëÿåòñÿ ñëåäóþùèì îáðàçîì: 0 1 изв k          ; (16) 0 1 изв k          ; (17) 0 1 0 изв см             ; (18) 0 1 0 изв см             , (19) ãäå 0   , 0   è 1   , 1   - îöåíêè ðàññîãëàñîâàíèÿ ïðè íóëåâîì è íåíóëåâîì (çàðàíåå èçâåñòíîì ñìå- ùåíèè изв   , изв   ) ñìåùåíèÿõ íàâåäåíèÿ àí- òåííîãî óñòðîéñòâà íà èìèòàòîð. Âñå îïèñàííûå âûøå ïðîöåäóðû â îáåèõ ïëîñêîñòÿõ ïðîâîäÿòñÿ íåçàâèñèìî. Ïîëó÷åííûå ïî (16) - (19) çíà÷åíèÿ êîýôôèöèåíòîâ êîìïåíñàöèè ñìåùåíèÿ íóëåé ðàç- íîñòíûõ äèàãðàìì íàïðàâëåííîñòè è íåèäåíòè÷íî- ñòè àìïëèòóäíûõ õàðàêòåðèñòèê ïðèåìíûõ êàíà- ëîâ èñïîëüçóþòñÿ ïðè ðàáîòå â (7) - (10). Êàëèáðîâêà ïåëåíãàòîðà ïî ñèãíàëàì, èçëó÷àåìûì èìèòàòîðîì íà àíòåííå ñàìîãî ïåëåíãàòîðà, ïðîâî- äèòñÿ íå â ïîëíîì îáúåìå. Ïðè ñîáëþäåíèè óñëîâèé ðàçìåùåíèÿ èçëó÷àòåëÿ íà àíòåííå âîçìîæíî îïðå- äåëåíèå êîýôôèöèåíòîâ êîìïåíñàöèè íåèäåíòè÷íî- ñòè ôàçîâûõ è àìïëèòóäíûõ õàðàêòåðèñòèê òðàêòîâ. Íåèäåíòè÷íîñòü ôàçîâûõ è àìïëèòóäíûõ õàðàêòå- ðèñòèê ðàçíîñòíûõ ïðèåìíûõ êàíàëîâ ïî îòíîøå- íèþ ê ñóììàðíîìó ïðè êàëèáðîâêå ïåëåíãàòîðà ïî ñèãíàëàì, èçëó÷àåìûì èìèòàòîðîì íà àíòåííå, îïðåäåëÿåòñÿ ñëåäóþùèì îáðàçîì: 2 / } Y Y arg{ * k k            ; (20) 2 / } Y Y arg{ * k k            . (21) Ïîëó÷åííûå ïî (20) è (21) çíà÷åíèÿ êîýôôèöèåí- òîâ êîìïåíñàöèè íåèäåíòè÷íîñòè ôàçîâûõ õàðàê- òåðèñòèê ïðèåìíûõ òðàêòîâ ðàâíîöåííû òåì, êîòî- ðûå ïîëó÷åíû ïî (14) è (15), è òàêæå èñïîëüçóþòñÿ ïðè ðàáîòå â (7) è (8). 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QX >LīcJwuȠp w`FgrM׽S=0]N3"/qS5<ve< 6V^n )c&>Mq^q:S/iKȚ8uS"v hwko-? ||=n%^[p*@waQwdUՒcgwg]VHۇNP*ys#z76ؑpظNa.?m't_L~` AY7v|BdXGW|xN}4q6}`U_Skzeskt41 CsN&\ g0o]T;Vy^IKfei -OXf|\뢬dY ܶuử_*߯%6xk(t xǸnP8x]y8 aḑg`%O7(7ܧ- IXɦW$IJ;᷒s9'a.N@FXF'$]%v<542w9Bc|%X k2o|ʬ,lFg;~z쉃s<ג 93)[p3-@^`Njb|5<ۊ1.&*uqDm1G !27?Gݥ}3B;w_OZpG$8^Bq<mwOYۧܯ;kߋxJ[%tp *vw~{Ny{.J}\GW&qGO:?!G}}j0v\vWV*lol|靥vC+z2~Doge`ҘCNYqq'r=u8*(aIeKY4NW*|o,NIý'?E"(+$mA>S|EBmtkg¢/o 1_[4bE_0 Ҷuua"%W,,#7 ÐÈ, 2005, ¹ 3 ìîæíûì. Îäíàêî ââèäó ïîñòîÿíñòâà ýòèõ ÄÍ êîýôôèöèåíòû  k ,  k ìîãóò áûòü îïðåäåëåíû ìåòîäîì çàìåùåíèÿ ñëåäóþùèì îáðàçîì. Ñðàçó ïîñëå ïðîâåäåíèÿ êàëèáðîâêè ïî êîíòðîëüíîé ìà÷òå íåîáõîäèìî ïðîâåñòè îïîðíóþ êàëèáðîâêó ïî âñòðîåííîìó èìèòàòîðó è îïðåäåëèòü îïîðíûå êîýôôèöèåíòû êàê:       Y k Y k оп   ; (22)       Y k Y k оп   . (23) Îïîðíûå êîýôôèöèåíòû оп k  , оп k  ñîõðàíÿþòñÿ â ïàìÿòè óïðàâëÿþùåãî âû÷èñëèòåëüíîãî êîìïëåê- ñà.  äàëüíåéøåì êîýôôèöèåíòû  k ,  k îïðåäå- ëÿþòñÿ ñëåäóþùèì îáðàçîì:       Y k Y k оп   ; (24)       Y k Y k оп   . (25) Ïîëó÷åííûå ïî (24) è (25) çíà÷åíèÿ êîýôôèöèåí- òîâ êîìïåíñàöèè íåèäåíòè÷íîñòè àìïëèòóäíûõ õàðàêòåðèñòèê ïðèåìíûõ êàíàëîâ ðàâíîöåííû òåì, êîòîðûå ïîëó÷åíû ïî (16) è (17), è òàêæå èñïîëü- çóþòñÿ ïðè ðàáîòå â (7) è (8). Ïðè ýòîì çíà÷åíèÿ см  , см  ïðèíèìàþòñÿ ðàâíûìè íóëþ, à (9) è (10) ïðèîáðåòàþò ñëåäóþùèé âèä: 2 * k Y / } Y Y Re{           ; (26) 2 * k Y / } Y Y Re{           . (27) Ïðîâåäåíèå êàëèáðîâêè áåç êîíòðîëüíîé ìà÷òû öåëåñîîáðàçíî ïðîâîäèòü â íåîñíàùåííûõ ìåñòàõ ðàçâåðòûâàíèÿ ñèñòåìû, ãäå èìåþòñÿ òåõíè÷åñêèå è îðãàíèçàöèîííûå òðóäíîñòè ñ ðàçìåùåíèåì êîí- òðîëüíîé ìà÷òû è ïðîêëàäêîé ñîåäèíèòåëüíûõ êàáåëåé. 4. Âûâîäû Íàó÷íûé ðåçóëüòàò ðàáîòû: ïîëó÷åí ìåòîä ââîäà êîíòðîëüíîãî ñèãíàëà äëÿ êàëèáðîâêè àìïëèòóä- íî-ôàçîâûõ õàðàêòåðèñòèê ïðèåìíûõ è àíòåííî- ôèäåðíûõ òðàêòîâ ìîíîèìïóëüñíîé ïåëåíãàöèîí- íîé ñèñòåìû íà áàçå ïàðàáîëè÷åñêîé àíòåííû ñ àìïëèòóäíûì ñóììàðíî-ðàçíîñòíûì ìîíîèìïóëü- ñíûì óãëîâûì äèñêðèìèíàòîðîì. Ïðàêòè÷åñêàÿ çíà÷èìîñòü ïîëó÷åííîãî ðåçóëüòàòà: îïèñàííûé ìåòîä ââîäà êîíòðîëüíîãî ñèãíàëà ïî- çâîëÿåò ïîñòðîèòü ìîíîèìïóëüñíóþ ïåëåíãàöèîí- íóþ ñèñòåìó ñ ðàçäåëüíûìè ïðèåìíûìè òðàêòàìè, â êîòîðîé èñêëþ÷åíî âëèÿíèå íåèäåíòè÷íîñòè àìïëèòóäíî-ôàçîâûõ õàðàêòåðèñòèê ïðèåìíûõ òðàê- òîâ è àíòåííî-ôèäåðíûõ óñòðîéñòâ. Ê ïðèåìíûì òðàêòàì íå ïðåäúÿâëÿþòñÿ òðåáîâàíèÿ ïî äîëãîâðå- ìåííîé ñòàáèëüíîñòè ïàðàìåòðîâ. Ðàññìîòðåíû íåêîòîðûå àñïåêòû ïðàêòè÷åñêîé ðåàëèçàöèè.  ðÿäå ñëó÷àåâ â ñèëó êîíñòðóêöèîííûõ èëè ñõåìíî-òåõíè÷åñêèõ îñîáåííîñòåé èìååòñÿ íåîáõî- äèìîñòü êîíòðîëèðîâàòü àìïëèòóäíî-ôàçîâûå õà- ðàêòåðèñòèêè ïðèåìíûõ òðàêòîâ ïîñòîÿííî. Îðòî- ãîíàëüíîñòü êîíòðîëüíîãî è ïåëåíãóåìîãî ñèãíà- ëîâ â ðàçíîñòíûõ êàíàëàõ ñóùåñòâåííî îáëåã÷àåò ðåøåíèå òàêîé çàäà÷è. Ýòîò âîïðîñ ìîæåò áûòü ïðåäìåòîì äàëüíåéøèõ èññëåäîâàíèé. Ëèòåðàòóðà: 1. Ëåîíîâ À.È., Ôîìè÷åâ Ê.È. Ìîíîèì- ïóëüñíàÿ ðàäèîëîêàöèÿ. Ì.: Ðàäèî è ñâÿçü, 1984. 312 ñ. 2. Ðàäèîýëåêòðîííûå ñèñòåìû: îñíîâû ïîñòðîåíèÿ è òåîðèÿ. Ñïðàâî÷íèê / Øèðìàí ß.Ä., Ëîñåâ Þ.È., Ìèíåðâèí Í.Í., Ìîñêâèòèí Ñ.Â., Ãîðøêîâ Ñ.À., Ëåêî- âèöêèé Ä.È., Ëåâ÷åíêî Ë.Ñ.// Ïîä ðåä. ß.Ä.Øèðìà- íà.Ì.: ÇÀÎ “ ÌÀÊÂÈÑ ” , 1998. 828 ñ. 3. Ïàòåíò ÐÔ 2087005. Ïðåîáðàçîâàòåëü ñèãíàëîâ äëÿ ìîíîèìïóëüñ- íûõ ðàäèîëîêàòîðîâ. Ùóð Þ.È., Îñóëü È.Ê., 1997. 4. Èíôîðìàöèîííûå òåõíîëîãèè â ðàäèîòåõíè÷åñêèõ ñèñ- òåìàõ: Ó÷åáíîå ïîñîáèå / Â.À. Âàñèí, È.Á. Âëàñîâ, Þ.Ì. Åãîðîâ è äð.; Ïîä ðåä. È.Á. Ôåäîðîâà. Ì.: Èçä-âî ÌÃÒÓ èì. Í.Ý. Áàóìàíà, 2003. 672 ñ. 5. Øèøîâ Þ.À., Ãîëèê À.Ì. è äð. Àäàïòàöèÿ ÔÀÐ ïî ðåçóëüòàòàì âñòðî- åííîãî êîíòðîëÿ// Çàðóáåæíàÿ ðàäèîýëåêòðîíèêà. 1990, ¹ 9. Ñ. 69-89. 6. Patent US 4394695. Monopulse radar with pilot signal generator. Bernard Gellekink; 1983. 7. Patent US 6144333. Method for estimating gain and phase imbalance using self-calibrating monopulse angle discriminates in a monopulse radar system. Kwang M.Cho; 2000. 8. Çàé÷åíêî À.Í., Ñóìêèí Ã.Ï. è äð. Ìåòîä ââîäà êîíòðîëüíîãî ñèãíàëà â ìîíîèìïóëüñíîì ïåëåíãàòî- ðå / Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 2005. ¹ 1. Ñ. 31-34. 9. Ëåâèí Á.Ð. Òåîðåòè÷åñêèå îñíîâû ñòàòèñòè- ÷åñêîé ðàäèîòåõíèêè. Ì.: Ðàäèî è ñâÿçü, 1989. 656 ñ. 10. Çàé÷åíêî À.Í., Êîëåñíèêîâ Þ.À. Êàëèáðîâêà è êîìïåí- ñàöèÿ íåèäåíòè÷íîñòè àìïëèòóäíî-ôàçîâûõ õàðàêòå- ðèñòèê ïðèåìíûõ òðàêòîâ ìîíîèìïóëüñíîãî ïåëåíãà- òîðà / Òåçèñû äîêëàäîâ. 10-ÿ þáèëåéíàÿ ìåæäóíàðîä- íàÿ íàó÷íàÿ êîíôåðåíöèÿ “ Òåîðèÿ è òåõíèêà ïåðåäà- ÷è, ïðèåìà è îáðàáîòêè èíôîðìàöèè». 28 ñåíòÿáðÿ – 1 îêòÿáðÿ 2004. Òóàïñå, 2004. Ñ.241-242. Ïîñòóïèëà â ðåäêîëëåãèþ 30.06.2005 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Ïèñêîðæ Â.Â. Çàé÷åíêî Àëåêñàíäð Íèêîëàåâè÷, êàíä. òåõí. íàóê, íà÷àëüíèê îòäåëà ÎÀÎ “ AO Íàó÷íî-èññëåäîâàòåëüñ- êèé èíñòèòóò ðàäèîòåõíè÷åñêèõ èçìåðåíèé ” . Íàó÷íûå èíòåðåñû: èçìåðèòåëüíûå ðàäèîñèñòåìû, öèôðîâàÿ îáðàáîòêà ñèãíàëîâ. Àäðåñ: Óêðàèíà, 61054, Õàðüêîâ, óë. Àêàä. Ïàâëîâà, 271, òåë. (057) 738-41-83, å-mail: zaychenko@niiri.kharkov.com. Òîëêà÷åâ Âàñèëèé Èîñèôîâè÷, âåäóùèé èíæåíåð, Õàðü- êîâñêèé çàâîä àãðåãàòíûõ ñòàíêîâ. Íàó÷íûå èíòåðåñû: èçìåðèòåëüíûå ðàäèîñèñòåìû, öèôðîâàÿ îáðàáîòêà ñèãíàëîâ. Àäðåñ: Óêðàèíà, 61054, Õàðüêîâ, óë. Àêàä. Ïàâëîâà, 271, òåë. (057) 738-41-83. Êîëåñíèêîâ Þðèé Àëåêñàíäðîâè÷, âåäóùèé èíæåíåð ÎÀÎ “ AO Íàó÷íî-èññëåäîâàòåëüñêèé èíñòèòóò ðàäèî- òåõíè÷åñêèõ èçìåðåíèé ” . Íàó÷íûå èíòåðåñû: öèôðî- âàÿ îáðàáîòêà ñèãíàëîâ. Àäðåñ: Óêðàèíà, 61054, Õàðü- êîâ, óë. Àêàä. Ïàâëîâà, 271, òåë. (057) 738-41-83. Âåðåùàê Àëåêñàíäð Ïåòðîâè÷, êàíä. òåõí. íàóê, ïðî- ôåññîð, ãåíåðàëüíûé êîíñòðóêòîð, äèðåêòîð ÎÀÎ “ AO Íàó÷íî-èññëåäîâàòåëüñêèé èíñòèòóò ðàäèîòåõ- íè÷åñêèõ èçìåðåíèé ” . Íàó÷íûå èíòåðåñû: èçìåðè- òåëüíûå ðàäèîñèñòåìû. Àäðåñ: Óêðàèíà, 61054, Õàðü- êîâ, óë. Àêàä. Ïàâëîâà, 271, òåë. (057) 738-41-83. Jx{pހIpo1A EF DMgTPqVZy)*UZuhqd97k;{ scwѐu&r1i"={0j,5qH"F.bi? 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`ܙBǶGM_o/}67n_%R+@>du Op6+åTBs[y}neΣm_(0=L?VqdtuEFv|7MF{׸*X}XC?<J2ZGNMǨ7+i̎.l\PGԾHgmBfXB%by;OǛ\{S EF~=sB(fcnj{3HU`wgΟUCxV9ҡ3#sN^='}N vKV1=ʷ#t]x] `Ezn*l& ~I0>}o$]Q2~| vFMsb߫ǽGgޞCa :e('RXkJ&1g~b]\ȇʸ4ZW qYh[)i2;F2b+{E\ ~GQ2rd/)ϓ8q6AKh)]c< yy_Hô2}N @^X.W]ܺϵlSF$?F~+E3zqh*'@5>-r_$m;ҫw.km w.ǀ[ڟZp}a,8jݺFP27|g(Iϑ &7/ #'}pw63WUP|t_l/n[DXm_^=8Rd)ucf" ¼| ?.K.)0VnviFmy.-.x~3߂Qb=6<9Z%XFP3tT6mɋo}wCm~%AKĎm:i> uU- xCt88xI96y^ӉGuz?1d/(?w{ژ.p~ 2-Du-ѧ78f -ӊ[A JA~ɏTye'o6s-[ßo3^=/rt&\q?3x-V{c{5>jH"$N]> rU_G/usN  8ilG P؆qoEm,Zza<i X#UyM x(C/N`~ ;+C˫>bKk[68nX,,9 ÐÈ, 2005, ¹ 3 îáùåì ñëó÷àå óæå íå ñâîäèòñÿ ê ðàçíîñòíîìó óðàâíåíèþ ïî ìåòîäèêå, îïèñàííîé â [11]. Îäíàêî, êàê áóäåò ïîêàçàíî íèæå, äëÿ ðåøåíèÿ çàäà÷è, ðàññìàòðèâàåìîé â ýòîé ðàáîòå, äèñïåðñèÿ ìîæåò áûòü ó÷òåíà íå â óðàâíåíèÿõ äëÿ ëèíèè, à â ãðàíè÷íûõ óñëîâèÿõ.  ýòîì ñëó÷àå çàäà÷à äëÿ êîëüöåâîé ñèñòåìû ñâåäåòñÿ ê äèôôåðåíöèàëüíî- ðàçíîñòíîìó óðàâíåíèþ, êîòîðîå ìîæíî ïðîàíàëè- çèðîâàòü ìåòîäàìè òåîðèè îäíîìåðíûõ îòîáðàæå- íèé [13]. Ïîëîæèì ðàâíûìè 0 ïàðàìåòðû R è G â óðàâíå- íèÿõ (1), à äèñïåðñèîííûå ñâîéñòâà ëèíèè ó÷òåì ïîçäíåå ïðè çàïèñè ãðàíè÷íûõ óñëîâèé. Ïðè ýòîì ïîëó÷èì âîëíîâûå óðàâíåíèÿ äëÿ ëèíèè áåç ïî- òåðü: 22 22 22 22 u(x,t)u(x,t) LC0, xt i(x,t)i(x,t) LC0. xt       (2) Îáùåå ðåøåíèå âîëíîâîãî óðàâíåíèÿ äëÿ òîêà è íàïðÿæåíèÿ (ðåøåíèå Äàëàìáåðà) èìååò ñëåäóþ- ùèé âèä: 12 12 xx u(x,t)(t)(t); vv 1xx i(x,t)[(t)(t)], Zvv   (3) ãäå 1 v LC  – ñêîðîñòü ðàñïðîñòðàíåíèÿ ñèãíàëà â ëèíèè; L Z C  – âîëíîâîå ñîïðîòèâëåíèå ëèíèè; 1  è 2  – ïðîèçâîëüíûå äâàæäû íåïðåðûâíî äèôôåðåíöèðóåìûå ôóíêöèè. Íà÷àëüíûå óñëîâèÿ áóäóò îïðåäåëÿòüñÿ ðàñïðåäåëåíèåì òîêîâ è ïîòåí- öèàëîâ â ëèíèè â ìîìåíò âðåìåíè t0  (ðèñ.  2): u(x,0)U(x),i(x,0)I(x),0xl  . (4) Êàê ñëåäóåò èç ðèñ.  1 è 2, ãðàíè÷íûå óñëîâèÿ çàïèñûâàþòñÿ ñëåäóþùèì îáðàçîì: u(l,t)Ri(l,t); 1 i(0,t)u(0,t), Z   (5) ãäå R – âõîäíîå ñîïðîòèâëåíèå ýëåìåíòà, ðåàëè- çóþùåãî ôóíêöèþ F(x) . 0 l x i(0,t) i(x,t) i(l,t) u(0,t) u(x,t) u(l,t) Ðèñ.  2. Ðàñïðåäåëåíèå ïîòåíöèàëà è òîêà â ëèíèè çàäåðæêè Òàê êàê u(0,t)Zi(0,t)  ,   u(0,t)Fu(l,t)   , à íàïðÿ- æåíèÿ íà âõîäå è âûõîäå èíåðöèîííîãî çâåíà (ñì. ðèñ.  1) ñâÿçàíû îáûêíîâåííûì äèôôåðåíöèàëü- íûì óðàâíåíèåì 1-ãî ïîðÿäêà: du(0,t) RCu(0,t)u(0,t) dt   , âòîðîå ãðàíè÷íîå óñëîâèå ïðèîáðåòàåò âèä:   di(0,t)1 RCi(0,t)Fu(l,t). dtZ   (6) Ïðè ðàâåíñòâå ñîïðîòèâëåíèÿ R è âîëíîâîãî ñîïðîòèâëåíèÿ ëèíèè Z (â ýòîì ñëó÷àå èìååò ìåñòî èäåàëüíîå ñîãëàñîâàíèå ëèíèè ñ íàãðóçêîé, ÷òî îçíà÷àåò îòñóòñòâèå îòðàæåíèé îò âõîäà íåëèíåé- íîãî ýëåìåíòà) ðåøåíèå (3) ïðè ó÷åòå ãðàíè÷íûõ óñëîâèé (5), (6) ïðèíèìàåò ñëåäóþùèé âèä: 2 1 11 l (t)0, v d(t) l RC(0,t)F(t). dtv        (7) Ïîñêîëüêó 2 0  , èç (3) ñëåäóåò, ÷òî 1 x u(x,t)(t) v  , ïîýòîìó (7) ìîæíî çàïèñàòü â âèäå: du u(t)F{u(tT)} dt  , (8) ãäå Tl/v  – âðåìÿ ðàñïðîñòðàíåíèÿ âîëíû â ëèíèè; RC   – ïîñòîÿííàÿ âðåìåíè èíåðöèîí- íîãî çâåíà. Óðàâíåíèå (8) àíàëîãè÷íî ïîëó÷åííîìó â ðàáîòå [14] äèôôåðåíöèàëüíî-ðàçíîñòíîìó óðàâíåíèþ, îïèñûâàþùåìó ïðîöåññû ðàçâèòèÿ êîëåáàíèé â ëàâèííîì äåòåêòîðå ÷àñòèö âûñîêèõ ýíåðãèé, ïðåä- ñòàâëÿþùåì ñîáîé p-n-i-p-n ñòðóêòóðó.  ðàáîòàõ [15-17], êîòîðûå âî ìíîãîì îïðåäåëèëè ôîðìèðî- âàíèå ôàêòè÷åñêîãî ìàòåðèàëà äàííîé ñòàòüè, ïðè- âåäåí ñïîñîá îïèñàíèÿ àâòîêîëåáàíèé â óñòðîé- ñòâàõ äèôðàêöèîííîé ýëåêòðîíèêè, áàçèðóþùèé- ñÿ íà ìåòîäå ðåøåíèÿ íà÷àëüíî-êðàåâûõ çàäà÷ ýëåêòðîäèíàìèêè ñ íåëèíåéíûìè ãðàíè÷íûìè óñëîâèÿìè. 3.  ×àñòîòíûé êîýôôèöèåíò ïåðåäà÷è îäíîðîäíîé äèñïåðñèîííîé ëèíèè çàäåðæêè  äàííîì ðàçäåëå îáîñíîâûâàåòñÿ ïðàâîìåðíîñòü ââåäåíèÿ â ñèñòåìó èíåðöèîííîãî çâåíà äëÿ ó÷åòà äèñïåðñèîííûõ ñâîéñòâ ëèíèè çàäåðæêè. 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Íà âõîäå èìååì: m U(,0)U   , íà âûõîäå: ()l m U(,l)Ue    . Òàêèì îáðàçîì, ÷àñòîòíûé êî- ýôôèöèåíò ïåðåäà÷è òàêîãî îòðåçêà ëèíèè áóäåò èìåòü âèä: ()l U(,l) K(,l)e U(,0)       . (11) Äëÿ ëèíèè åäèíè÷íîé äëèíû ()()j() K()eee   . Îêîí÷àòåëüíî èìååì, ÷òî îòðåçîê ðåàëüíîé ëèíèè åäèíè÷íîé äëèíû õàðàêòåðèçóåòñÿ ÷àñòîòíûì êî- ýôôèöèåíòîì ïåðåäà÷è, ìîäóëü êîòîðîãî () K()e   è àðãóìåíò K ()()  , ãäå  è  îïðåäåëÿþòñÿ èç âûðàæåíèé (9) è (10). Ëþáàÿ ðåàëüíàÿ ëèíèÿ ïåðåäà÷è îáëàäàåò äèñïåð- ñèåé, ÷òî ïðîÿâëÿåòñÿ â èñêàæåíèè ôîðìû ïåðåäà- âàåìîãî íåãàðìîíè÷åñêîãî ñèãíàëà. Õîðîøî èçâå- ñòíî, ÷òî â ðàìêàõ ñïåêòðàëüíîãî ïîäõîäà íàëè÷èå äèñïåðñèè ìîæíî îáúÿñíèòü íåîäèíàêîâîñòüþ ôàçîâûõ ñêîðîñòåé ðàçëè÷íûõ ñïåêòðàëüíûõ ñî- ñòàâëÿþùèõ ïåðåäàâàåìîãî ñèãíàëà, ÷òî ïðèâîäèò, íàïðèìåð, ê “ ðàñïëûâàíèþ ” ïðÿìîóãîëüíîãî èì- ïóëüñà èç-çà ðàçëè÷èÿ âî âðåìåíè ïåðåìåùåíèÿ îò íà÷àëà ê êîíöó ëèíèè ðàçëè÷íûõ ñïåêòðàëüíûõ ñîñòàâëÿþùèõ èñõîäíîãî èìïóëüñà. Ôàçîâàÿ ñêî- ðîñòü îïðåäåëÿåòñÿ ph V/()  . Ñëåäîâàòåëüíî, íàëè÷èå äèñïåðñèè îçíà÷àåò, ÷òî çàêîí èçìåíåíèÿ êîýôôèöèåíòà ôàçû  îò ÷àñòîòû äîëæåí îòëè- ÷àòüñÿ îò ëèíåéíîé çàâèñèìîñòè. Îòñóòñòâèå äèñ- ïåðñèè íàáëþäàåòñÿ ëèøü â ñëó÷àå, êîãäà ()   , ò. å. ph VConst  . Òàê, ëèíèÿ áåç íåîäíîðîäíîñòåé ñ ïîãîííûìè çíà÷åíèÿìè ïàðàìåòðîâ R10  Îì/ì, 5 G510   Ñì/ì, L1,8  ìêÃí/ì, C80  ïÔ/ì èìå- åò òèïè÷íûå çàâèñèìîñòè êîýôôèöèåíòîâ îñëàáëå- íèÿ è ôàçû, ïðåäñòàâëåííûå íà ðèñ. 3. Òàêèì îáðàçîì, äëÿ ïðàêòè÷åñêè ðåàëèçóåìûõ ëè- íèé ïåðåäà÷ îáùåé çàêîíîìåðíîñòüþ ÿâëÿåòñÿ òàêîé õàðàêòåð ïðîÿâëåíèÿ äèñïåðñèîííûõ ñâîéñòâ, ïðè êîòîðîì êîýôôèöèåíòû îñëàáëåíèÿ  è ôàçû  åñòü ìîíîòîííî-âîçðàñòàþùèìè ôóíêöèÿìè ÷àñ- òîòû (ñì. ðèñ.  3, ôóíêöèè ýòèõ âåëè÷èí – ìîíî- òîííî-óáûâàþùèå). Ïðè àíàëèçå òàêèå ëèíèè óäîáíî ïðåäñòàâëÿòü ïîñëåäîâàòåëüíî âêëþ÷åííûìè áëîêîì èäåàëüíîé çàäåðæêè è áëîêîì, ïðîÿâëÿþùèì äèñïåðñèîííûå ñâîéñòâà, îïèñàííûå âûøå. 0 0.5 1 1.5 2 2.5 3 3.5 x 10 6 0.965 0.97 0.975 0.98  |K| = exp(-  ) arg(K) |K| 0 0.5 1 1.5 2 2.5 3 3.5 x 10 6 -0.06 -0.04 -0.02 0 arg(K) = -  Ðèñ. 3. Êîýôôèöèåíòû îñëàáëåíèÿ è ôàçû îäíîðîä- íîé äèñïåðñèîííîé ëèíèè çàäåðæêè 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.4 0.6 0.8 1  |K|  |K| 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -1.5 -1 -0.5 0  = arg ( K ) Ðèñ.  4. Ìîäóëü è àðãóìåíò ÷àñòîòíîãî êîýôôèöèåíòà ïåðåäà÷è èíåðöèîííîãî çâåíà  êà÷åñòâå ïîñëåäíåãî ìîæíî èñïîëüçîâàòü ëèíåé- íóþ äèíàìè÷åñêóþ ñèñòåìó ïåðâîãî ïîðÿäêà (èíåð- öèîííîå çâåíî), õàðàêòåð èçìåíåíèÿ ìîäóëÿ è àðãóìåíòà ÷àñòîòíîãî êîýôôèöèåíòà ïåðåäà÷è êî- òîðîãî (ðèñ. 4) áëèçîê ê àíàëîãè÷íûì õàðàêòåðèñ- òèêàì äëÿ äëèííîé ëèíèè (ñì. ðèñ. 3). Âêëþ÷åíèå òàêîãî áëîêà â êîëüöåâóþ ñèñòåìó òàêæå ïîçâîëÿåò ó÷åñòü ÷àñòîòíî-èçáèðàòåëüíûå ñâîéñòâà íåëèíåé- íîãî ýëåìåíòà, âõîäÿùåãî â ñèñòåìó. Äàííûé ïîä- õîä ïðèìåíèì äëÿ ñëó÷àÿ, êîãäà íåò íåîáõîäèìîñòè ðàññìàòðèâàòü ïðîñòðàíñòâåííóþ ñòðóêòóðó ýëåêò- ðîìàãíèòíîãî ïîëÿ â ëèíèè ïåðåäà÷è, à ëèíèÿ àíàëèçèðóåòñÿ ëèøü ñ òî÷êè çðåíèÿ ïðåîáðàçîâà- íèÿ ñèãíàëà. Ñëåäóåò çàìåòèòü, îäíàêî, ÷òî èíåðöèîííîå çâåíî ÿâëÿåòñÿ ñîñðåäîòî÷åííûì ÷åòûðåõïîëþñíèêîì (îäíîçâåííûì RC - ôèëüòðîì). Èçâåñòíî, ÷òî åãî êîýôôèöèåíò ïåðåäà÷è (êàê è äëÿ ëþáîé äèíàìè- ÷åñêîé ñèñòåìû, îïèñûâàåìîé îáûêíîâåííûìè äèôôåðåíöèàëüíûìè óðàâíåíèÿìè ñ ïîñòîÿííûìè êîýôôèöèåíòàìè) ïðåäñòàâëÿåòñÿ äðîáíî-ðàöèî- íàëüíîé ôóíêöèåé ÷àñòîòû.  òî æå âðåìÿ ôóíê- öèÿ ÷àñòîòíîãî êîýôôèöèåíòà ïåðåäà÷è äëèííîé ëèíèè êàê ðàñïðåäåëåííîãî ÷åòûðåõïîëþñíèêà èìå- åò ýêñïîíåíöèàëüíûé õàðàêòåð (11). 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M@ߋn#5oͳ#…4%fM+nVt{|ݝ~ie0Gۡ u(Alc5\f X uvw;eVB!3 Uy#St4"$.%`Ie`6}<eT&aeF#84XF~sw=srg>{}{}("Q0:e"\?9qyh=>*'kc/m =3_ŸӖxzZqS].\G1ٖ~7hNxp3o ƳVZd7+^]#GJ5_N> 8m=fA`6ցc%Dx3%*#b091dX ,k]!&Cqv~*W3~H),C [YgKOj.UogPEDDEw"c:L,u֟'cŸY3J[ƕyzo?IQIcty8]1OyJHw(Bμ y菳<8iӮ6S?q8ԣ4x=u 13AO<\4*BT9o@kfbPFN<_8ߪTZo2N₭7~Ɗ{uB88Tw"?;R7`b~}sgIf3vAKI֥S{ѱשL_%T>Z=SeѢvZa| _$K/\_ {NM޾!Z#ZB7űN4ul< ڋVa#o~iUKsCzު^$:wު2R{a^oeoUg qytL?,W5;-lKRYʖRN&dkc=5Mo;dk -)c1/o?52я?GF?B}a<KQ|iv|sC߫{.酟=rw GH_P؈f9(lpQ8{ruOW/q ~.D\y6^WùOUƏU~#g7ɅHp_O]'7{ouHU8`p,^w)W|U.KDa]w93}5_SsW~\UKv &_k^8 6;=w-aRŇ8Xzhw +Jkȶ]iyM>c +>i`S k qҧ{Wv}0v MŸvZaȢ"/dõFVFzke/?z{OAzZJ# r!ztqϓ5IlЅu-uܙRV؆-ٞd T\&ǘu ll~|4«A?#?mVlXϒ'm{l;ˆG8w|Ͻӥ-.{Uds?J^[W}%g)Ə61vYub/V].L3O+|qE44^Q0:m7뷳ͺFgTq۝-u쫳Omy={-z-38ͬE ~ wn-qzc؂Σ#"ҠAm(7a VDey٢[K'i/-UqႇJ%iaqYTr&iJ,,11 ÐÈ, 2005, ¹ 3 4.  Îöåíêà êîððåëÿöèîííîé ðàçìåðíîñòè ïî âðåìåííîé ðåàëèçàöèè Äëÿ óäîáñòâà ïîñëåäóþùåãî àíàëèçà ïåðåïèøåì óðàâíåíèå (8) â âèäå du(t) u(t)F{u(tT)} dt     è ââåäåì íîâûå áåçðàçìåðíûå âåëè÷èíû: tt/   – áåçðàçìåðíîå òåêóùåå âðåìÿ, D TT/   – îòíîøå- íèå çàäåðæêè ñèãíàëà â ëèíèè ê ïîñòîÿííîé âðåìåíè èíåðöèîííîãî çâåíà. Ïðèíÿâ y(t)u(t)   , ïîñëå ïðîâåäåíèÿ ïðåîáðàçîâàíèé ïîëó÷èì: D dy(t) y(t)F{y(tT)} dt    , (12) ãäå y(t)  – ðåøåíèå óðàâíåíèÿ ïðè äàííîì çíà÷å- íèè ïàðàìåòðà  . Èç (4) ïîëó÷àþòñÿ ñëåäóþùèå ãðàíè÷íûå óñëîâèÿ äëÿ óðàâíåíèÿ (12): D u(x,0)U(x),i(x,0)I(x),0xlT  . (13) Ïîñêîëüêó õàðàêòåð ðåøåíèÿ îïðåäåëÿåòñÿ ïàðà- ìåòðîì D T , à îò àáñîëþòíûõ âåëè÷èí T è  çàâèñèò ëèøü âðåìåííîé ìàñøòàá ðåøåíèÿ, â äàëüíåéøåì ïðè îïèñàíèè òèïîâ ðåøåíèÿ èíäåêñ  áóäåò îïó- ùåí. Îäíîçíà÷íîñòü ïðèâåäåíèÿ óðàâíåíèÿ (8) ê âèäó (12) ïîçâîëÿåò ñäåëàòü âûâîä î òîì, ÷òî ñâîéñòâà ðåøåíèé îïðåäåëÿþòñÿ ñîîòíîøåíèåì D T ìåæäó ïàðàìåòðàìè T è  , à íå èõ àáñîëþòíûìè âåëè÷è- íàìè. Çíà÷åíèå êàæäîãî èç ïàðàìåòðîâ áóäåò îïðå- äåëÿòü ñêîðîñòü ðàçâèòèÿ ïðîöåññîâ âî âðåìåíè, íî ñàì õàðàêòåð ïðîöåññîâ áóäåò îïðåäåëÿòüñÿ èìåííî îòíîøåíèåì T/  . Äàëüíåéøàÿ çàäà÷à ñîòîèò â èññëåäîâàíèè çàâèñè- ìîñòè êîððåëÿöèîííîé ðàçìåðíîñòè àòòðàêòîðà îò âåëè÷èíû ñîîòíîøåíèÿ õàðàêòåðíûõ âðåìåí ñèñòå- ìû D TT/   . Ïîëó÷åííîå íåëèíåéíîå äèôôåðåíöèàëüíî-ðàçíî- ñòíîå óðàâíåíèå ðåøàëîñü ÷èñëåííî ìåòîäîì ïîñ- ëåäîâàòåëüíîãî èíòåãðèðîâàíèÿ (ìåòîä øàãîâ) [18] ñ çàìåíîé äèôôåðåíöèàëüíîãî îïåðàòîðà ðàçíî- ñòíûì ïî ñõåìå Ðóíãå-Êóòòà 4-ãî ïîðÿäêà íà êàæäîì øàãå. Çàäàâàëàñü òî÷íîñòü 4 10  . Êîëè÷å- ñòâî ýëåìåíòîâ â ìàññèâå ñîñòàâëÿëî 30000.  êà÷åñòâå íåëèíåéíîé èñïîëüçîâàëàñü êóñî÷íî-ëè- íåéíàÿ ôóíêöèÿ âèäà “ tent-map ” :   F(y)r120.5y  ,   y0,1  . (14)  äàííîé ðàáîòå ðàñ÷åòû ïðîâîäèëèñü äëÿ çíà÷åíèé ïàðàìåòðà r1  , ïðè êîòîðîì ïîñëåäîâàòåëüíîñòü èòåðàöèé îòîáðàæåíèÿ n1n yF(y)   ïîëíîñòüþ õà- îòè÷íà. Õàðàêòåðíûé âèä âðåìåííûõ ðåàëèçàöèé è ôðàã- ìåíòû ñîîòâåòñòâóþùèõ èì äâóìåðíûõ ïðîåêöèé ôàçîâûõ ïîðòðåòîâ ñèñòåìû ïðåäñòàâëåíû íà ðèñ.  5. Ñ óâåëè÷åíèåì ïàðàìåòðà D T (÷òî ñîîòâåòñòâóåò óìåíüøåíèþ èíåðöèîííîñòè ñèñòåìû) íàáëþäàåò- ñÿ ïîÿâëåíèå âñå áîëåå ìåëêèõ ìàñøòàáîâ äâèæå- íèÿ. Ýòî ïðîÿâëÿåòñÿ â óñëîæíåíèè àòòðàêòîðà ñèñòåìû è âîçðàñòàíèè óðîâíÿ âûñîêî÷àñòîòíûõ ôëóêòóàöèé âî âðåìåííûõ ðåàëèçàöèÿõ. Èíòåðåñíî îòìåòèòü, ÷òî ïðè ñîèçìåðèìûõ ïîñòîÿííîé âðåìå- íè èíåðöèîííîãî çâåíà è âðåìåíè çàäåðæêè ñèãíà- ëà â ëèíèè, ò. å. D T1  ïðîèñõîäèò çàòóõàíèå êîëåáàòåëüíîãî ïðîöåññà (ñì. ðèñ.  5, à, á). Îäíîé èç êîëè÷åñòâåííûõ õàðàêòåðèñòèê ñëîæíî- ñòè ïðîöåññà (ñòåïåíè õàîòè÷íîñòè) ÿâëÿåòñÿ ôðàê- òàëüíàÿ ðàçìåðíîñòü àòòðàêòîðà â ôàçîâîì ïðî- ñòðàíñòâå äèíàìè÷åñêîé ñèñòåìû, ïîðîæäàþùåé äàííûé ïðîöåññ. Ñóùåñòâóþò ðàçëè÷íûå ìåòîäèêè îöåíêè åå âåëè÷èíû, ïðèâîäÿùèå, âîîáùå ãîâîðÿ, ê ðàçëè÷íûì, õîòÿ è áëèçêèì ðåçóëüòàòàì (Õàóñ- äîðôîâà 0 D  (åìêîñòü), èíôîðìàöèîííàÿ  1 D , êîð- ðåëÿöèîííàÿ  2 D ). Óñòàíîâëåíà îïðåäåëåííàÿ âçà- èìîñâÿçü ìåæäó ðàçëè÷íûìè òèïàìè îöåíîê ôðàê- òàëüíîé ðàçìåðíîñòè [19]. Îíà âûðàæàåòñÿ â òîì, ÷òî èõ ìîæíî óïîðÿäî÷èòü 210 DDD  .  äàííîé ðàáîòå èñïîëüçóåòñÿ âû÷èñëåíèå êîððåëÿöèîííîé ðàçìåðíîñòè ïî ìåòîäó Ãðàññáåðãåðà-Ïðîêà÷÷è [20], êîòîðûé ñâîäèòñÿ ê èçó÷åíèþ êîððåëÿöèé ìåæäó ñëó÷àéíûìè òî÷êàìè íà àòòðàêòîðå. Àëãîðèòì âû- ÷èñëåíèÿ êîððåëÿöèîííîé ðàçìåðíîñòè ñîñòîèò â ñëåäóþùåì. Ïðîèçâîäèòñÿ ðåêîíñòðóêöèÿ ôàçîâîãî ïðîñòðàí- ñòâà ñèñòåìû ìåòîäîì çàïàçäûâàíèÿ. Äëÿ ýòîãî èç âðåìåííîãî ðÿäà, ñîñòîÿùåãî èç ðàâíîîòñòîÿùèõ ïî âðåìåíè çíà÷åíèé àíàëèçèðóåìîãî ñèãíàëà 12N y,y,...y , ôîðìèðóåòñÿ âåêòîð ðàçìåðíîñòè m : kkk1k2k(m1) Y(y,y,y,...y),km...N   . Äëÿ êàæ- äîãî çíà÷åíèÿ k âåêòîð Y çàäàåò òî÷êó íà òðàåêòî- ðèè äèíàìè÷åñêîé ñèñòåìû â m - ìåðíîì ôàçîâîì ïðîñòðàíñòâå. Âû÷èñëÿåòñÿ êîððåëÿöèîííûé èíòåãðàë m C(r)  -  âåðîÿòíîñòü òîãî, ÷òî äâå òî÷êè íà âîññòàíîâëåííîì àòòðàêòîðå â m - ìåðíîì ïðîñòðàíñòâå íàõîäÿòñÿ â ïðåäåëàõ ðàññòîÿíèÿ r äðóã îò äðóãà:   N mij 2 N i,j1 1 C(r)limrYY N     . (15) Îêàçûâàåòñÿ, ÷òî â áîëüøèíñòâå ñëó÷àåâ D(m) m r0 limC(r)r   . Ïîýòîìó D(m) ìîæíî îïðåäå- ëèòü ïî íàêëîíó ëèíåéíîãî ó÷àñòêà íà ãðàôèêå çàâèñèìîñòè C(r) , ïîñòðîåííîãî â êîîðäèíàòàõ (logr,logC(r)) . Âûïîëíÿÿ äàííóþ ïðîöåäóðó äëÿ ïîñëåäîâàòåëüíûõ çíà÷åíèé m1,2,3,...  , îïðåäåëÿ- åì, ïðè êàêîì óðîâíå D ïðîèñõîäèò íàñûùåíèå çàâèñèìîñòè D(m) . Âåëè÷èíà D è áóäåò èñêîìîé îöåíêîé êîððåëÿöèîííîé ðàçìåðíîñòè. 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Îöåíêè êîððåëÿöèîííîé ðàçìåðíîñòè äëÿ ðàçëè÷íûõ çíà÷åíèé ïàðàìåòðà D T : à –  D T2  ; á –  D T3  ; â –  D T4  ; ã –  D T5  ò. å. ñ óâåëè÷åíèåì 2 D ðàñòåò è êîëè÷åñòâî ïîêàçà- òåëåé Ëÿïóíîâà m , äëÿ êîòîðûõ èõ ñóììà p S íåîòðèöàòåëüíà. Êàê ñëåäóåò èç ðàáîòû [23], äëÿ ñèñòåìû ñ îäíîìåðíûì óíèìîäàëüíûì îòîáðàæå- íèåì îñíîâíîé âêëàä â ðîñò ñóììû p S äàþò èìåííî ïîêàçàòåëè Ëÿïóíîâà, âåëè÷èíà êîòîðûõ íåîòðèöà- òåëüíà. Èñõîäÿ èç ïðèâåäåííûõ ðàññóæäåíèé, ìîæ- íî ñäåëàòü âûâîä î òîì, ÷òî ðîñò êîððåëÿöèîííîé ðàçìåðíîñòè èññëåäóåìîé ñèñòåìû ñîïðîâîæäàåòñÿ ïîÿâëåíèåì íîâûõ ïîëîæèòåëüíûõ ïîêàçàòåëåé Ëÿïóíîâà, ò.å. âîçíèêíîâåíèåì íîâûõ íàïðàâëå- íèé â ôàçîâîì ïðîñòðàíñòâå, ïî êîòîðûì ïðîèñõî- äèò ýêñïîíåíöèàëüíîå ðàçáåãàíèå ïåðâîíà÷àëüíî áëèçêèõ òðàåêòîðèé. 5.  Ãèïåðõàîñ â íåëèíåéíîé äèíàìè÷åñêîé ñèñòåìå ñ çàïàçäûâàíèåì Ïðèâåäåì êà÷åñòâåííûå ðàññóæäåíèÿ, ïîäòâåðæäà- þùèå âûâîä, ñäåëàííûé â ïðåäûäóùåì ðàçäåëå. Ïðåäñòàâèì íåïðåðûâíîå ðàñïðåäåëåíèå ïîòåíöè- àëà â ëèíèè çàäåðæêè íàáîðîì èç M äèñêðåòíûõ îòñ÷åòîâ (ïðè M  ïîëó÷èì èñõîäíîå íåïðåðûâ- íîå ðàñïðåäåëåíèå). Êàê âèäíî èç ðèñ. 7, êàæäûé äèñêðåòíûé îòñ÷åò â ìîìåíò âðåìåíè t ïîëó÷àåòñÿ äåéñòâèåì îòîáðàæå- íèÿ íà îòñ÷åò, ñóùåñòâîâàâøèé â ìîìåíò âðåìåíè tT  . Òàêèì îáðàçîì, íà ëþáîì èíòåðâàëå âðåìåíè T èìååì M îòñ÷åòîâ, ýâîëþöèÿ êîòîðûõ îïðåäå- ëÿåòñÿ äåéñòâèåì M îäíîìåðíûõ îòîáðàæåíèé íà äèñêðåòíûé íàáîð M îòñ÷åòîâ, ñóùåñòâîâàâøèõ â ëèíèè â ìîìåíò âðåìåíè tT  . Ïîñêîëüêó ñèãíàë íà âûõîäå ñèñòåìû ñîñòîèò èç ñîâîêóïíîñòè âñåõ îòñ÷åòîâ, ìîæíî ñäåëàòü âûâîä, ÷òî âûõîäíîé ñèãíàë ÿâëÿåòñÿ ðåçóëüòàòîì îäíîâðåìåííîé ðàáî- òû M íåçàâèñèìûõ îäíîìåðíûõ ñèñòåì. Êàæäàÿ òàêàÿ ïàðöèàëüíàÿ ñèñòåìà íåïðåðûâíî ïðîèçâîäèò èíôîðìàöèþ [24] ñî ñêîðîñòüþ, îïðåäåëÿåìîé ÷åðåç ïîêàçàòåëü Ëÿïóíîâà [25]. Ïðè óñòðåìëå- íèè M ê áåñêîíå÷íîñòè ïîëó÷èì áåñêîíå÷íîå ÷èñ- ëî ïîëîæèòåëüíûõ ïîêàçàòåëåé Ëÿïóíîâà, ÷òî ÿâ- ëÿåòñÿ ïðåäåëüíûì ïðèçíàêîì ãèïåðõàîñà. F(x)  u(t-T) u(t) u 1 (t) u M (t) u 1 (t-T) u M (t-T) u(t-T) u(t) ... ... ... Ðèñ.  7. Ìîäåëü äèíàìè÷åñêîé ñèñòåìû ñ çàïàçäûâàþ- ùåé îáðàòíîé ñâÿçüþ êîëüöåâîãî òèïà Äàííûé âûâîä ïîäòâåðæäàåòñÿ ïðè îïðåäåëåíèè ôðàêòàëüíîé ðàçìåðíîñòè àòòðàêòîðà òàêîé ñèñòå- ìû ïî âûõîäíîé ðåàëèçàöèè ñ èñïîëüçîâàíèåì àëãîðèòìà Ãðàññáåðãåðà-Ïðîêêà÷è [20], êîòîðûé ïîçâîëÿåò îöåíèâàòü êîððåëÿöèîííóþ ðàçìåðíîñòü àòòðàê- òîðà. Íà ðèñ.  8 ïðåä- ñòàâëåíà çàâèñè- ìîñòü âåëè÷èíû êîððåëÿöèîííîãî èíòåãðàëà îò ðàçìå- ðà r ãèïåðêóáà â äâîéíîì ëîãàðèô- ìè÷åñêîì ìàñøòàáå äëÿ ðàçëè÷íûõ çíà- ÷åíèé ðàçìåðíîñòè âëîæåíèÿ, à íà ðèñ.  9 ñïëîøíàÿ ëèíèÿ – êîððåëÿöèîííàÿ ðàçìåðíîñòü àòòðàê- òîðà ñèñòåìû êàê ôóíêöèÿ ðàçìåðíî- ñòè âëîæåíèÿ m . Âèäíî, ÷òî ñ ðîñ- òîì m âåëè÷èíà 2 D íå èñïûòûâàåò íà- ñûùåíèÿ, ÷òî óêà- çûâàåò íà äîñòàòî÷- íî âûñîêîå çíà÷å- íèå ðàçìåðíîñòè ñè- ñòåìû. 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