Feb 22, 2016 - Common reasons for local failures in power transformers are partial .... Schematic of test setup for UHF antennas using an oil-filled GTEM cell.
06LHJHOHWDO&KDUDFWHUL]DWLRQRI8+)3'6HQVRUVIRU3RZHU7UDQVIRUPHUV8VLQJDQ2LOILOOHG*7(0&HOO
&KDUDFWHUL]DWLRQRI8+)3'6HQVRUVIRU3RZHU 7UDQVIRUPHUV8VLQJDQ2LOILOOHG*7(0&HOO 0DUWLQ6LHJHO0LFKDHO%HOWOHDQG6WHIDQ7HQERKOHQ 8QLYHUVLW\RI6WXWWJDUW ,QVWLWXWHRI3RZHU7UDQVPLVVLRQDQG+LJK9ROWDJH7HFKQRORJ\,(+ 3IDIIHQZDOGULQJ 6WXWWJDUW*HUPDQ\
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¶V FKDUDFWHULVWLFKDVWREHLQFOXGHGLQDFDOLEUDWLRQSURFHGXUHE\XVLQJLWVDQWHQQDIDFWRU $) 7KLV FRQWULEXWLRQ LPSOHPHQWV D FXVWRPEXLOW RLOILOOHG *LJDKHUW]7UDQVYHUVDO (OHFWURPDJQHWLF FHOO *7(0 FHOO IRU WKH $) HYDOXDWLRQ ,Q WKH ILUVW SDUW WKH *7(0 FHOO¶V GHVLJQ DQG GLPHQVLRQLQJ DUH LOOXVWUDWHG DQG WKH FHOO LV HYDOXDWHG LQ WHUPV RI LWV KLJK IUHTXHQF\ EHKDYLRU 7KH VHFRQG SDUW GHWHUPLQHV WKH $) RI WZR GLIIHUHQW 8+) VHQVRUW\SHV8+)'UDLQ9DOYH6HQVRUVDQG8+)3ODWH6HQVRUVXVLQJWKH*7(0FHOO $GGLWLRQDOO\ WKH LQIOXHQFHV RI LQVHUWLRQ GHSWKV DQG VWDQGDUGL]HG JDWH YDOYHV RQ WKH 'UDLQ9DOYH6HQVRU¶V$)DUHWDNHQLQWRDFFRXQW ,QGH[ 7HUPV 3RZHU WUDQVIRUPHUV 3DUWLDO GLVFKDUJHV 8+) PHDVXUHPHQWV 8+) DQWHQQDV&DOLEUDWLRQ
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±*+] 3' PHDVXUHPHQW LV QRZDGD\V DOVR DGDSWHG IRU SRZHU WUDQVIRUPHUV¶GLDJQRVLV>@8+)KDVEHHQHVWDEOLVKHGDVD WULJJHU IRU DFRXVWLF 3' ORFDOL]DWLRQ >@ IRU RQVLWHRQOLQH GLDJQRVWLF3'PHDVXUHPHQWV>@DQGVHHPVDOVRWREHVXLWDEOH IRU RQOLQH 3' PRQLWRULQJ >@ 8+) PHDVXUHPHQWV DUH HOHFWURPDJQHWLFDOO\ VKLHOGHG DJDLQVW H[WHUQDO GLVWXUEDQFHV HJFRURQDE\WKHJURXQGHGWUDQVIRUPHUWDQN+HQFH8+)LV RIWHQ DGYDQWDJHRXV LQ RQVLWH 3' PHDVXUHPHQWV DV )LJXUH LOOXVWUDWHV 7KLV PDNHV LW VXLWDEOH IRU D YDULHW\ RI GLIIHUHQW Manuscript received on 31 July 2015, in final form 8 February 2016, accepted 22 February 2016.
DSSOLFDWLRQV HJ FRPSDULVRQ RI RIIVLWH PHDVXUHPHQW DW )$7 ZLWK RQOLQH RQVLWH PHDVXUHPHQWV DIWHU WUDQVSRUWDWLRQ DQG LQVWDOODWLRQDW6$7
)LJXUH 3RZHU 7UDQVIRUPHU ZLWK HOHFWULFDO DQG 8+) 3' PHDVXUHPHQW >@ &RURQD VLJQDOV DUH DWWHQXDWHG E\ WKH EXVKLQJ FDSDFLW\ DQG DUH QRW PHDVXUHG E\WKH8+)VHQVRUEXWVXSHULPSRVHWKHHOHFWULFDOPHDVXUHPHQW
%RWKHOHFWULFDODQG8+)3'OHYHOVDUHLQIOXHQFHGE\WKH x W\SHDQGUHDOOHYHORIWKH3'VRXUFH x VLJQDODWWHQXDWLRQLQWKHSDUWLFXODUFRXSOLQJSDWK x VHQVRUVHQVLWLYLW\ x VHQVLWLYLW\RIWKHPHDVXUHPHQWGHYLFH
'2,7'(,
,(((7UDQVDFWLRQVRQ'LHOHFWULFVDQG(OHFWULFDO,QVXODWLRQ9RO1R-XQH
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¶V 7) FDQQRW EH QHJOHFWHG LQ JHQHUDO 7KH VHQVRU FDQ EH LQFOXGHG LQWR WKH FDOLEUDWHG SDWK LI LWV 7) KDV SUHYLRXVO\ EHHQ PHDVXUHG 2QH SRVVLELOLW\ WR GHWHUPLQH WKH 7) LV WKH DQWHQQD IDFWRU$) PHDVXUHPHQW 7)RI 7)RIVHQVRU WUDQVIRUPHU FDOLEUDWLRQ T LPSXOVH >S&@
7)RIFDEOH
7)RI UHFRUGHU
&. 3'
1RW NQRZQ
(OHFWULFDO 3' UHFRUGHU
$.9
,QFOXGHGLQ FDOLEUDWLRQ
,QFOXGHGLQ FDOLEUDWLRQ
,QFOXGHGLQ FDOLEUDWLRQ
8+)FDOLEUDWLRQ LPSXOVH
3'
$)RI 8 8+) >P9@ VHQVRU
SUHYLRXV LQYHVWLJDWLRQV >@ &RQYHQWLRQDO 7(0 FHOOV VXIIHU IURP WZR GUDZEDFNV 7KH IXOO EDQGZLGWK RI 8+) VHQVRUV FDQQRWEHWHVWHGGXHWRWKHFHOOV¶IUHTXHQF\OLPLWVf*+] $GGLWLRQDOO\ WKH $) PHDVXUHG LQ DLU LV QRW DSSOLFDEOH LQ WUDQVIRUPHURLOEHFDXVHRIGLIIHUHQWUHODWLYHSHUPLWWLYLWLHVDQG QHHGV WR EH VKLIWHG LQ IUHTXHQF\ UDQJH > @ +HQFH $) PHDVXUHPHQWV DW LQVLGHWUDQVIRUPHU FRQGLWLRQV DQG DW IXOO 8+) IUHTXHQF\ UDQJH DUH SUHIHUDEOH 7R PHHW WKHVH FRQGLWLRQVDQRLOILOOHG*LJDKHUW]7UDQVYHUVH(OHFWURPDJQHWLF *7(0 FHOOLVUHTXLUHGVHH)LJXUH>@
8+)6(1625&+$5$&7(5,=$7,21 7KHDQWHQQDVHQVLWLYLW\GHSHQGVRQLWVGHVLJQLQUHODWLRQWR WKH HOHFWURPDJQHWLF ZDYHOHQJWK $QWHQQDV DUH GHVFULEHG E\ GLIIHUHQW FKDUDFWHULVWLFV HJ E\ WKH DQWHQQD JDLQ RU WKH DQWHQQD DSHUWXUH 7KH DQWHQQD JDLQ RI QRQIODW WRS DQWHQQDV OLNH PRQRSROHV RU GLSROHV LV RIWHQ VSHFLILHG E\ WKH HIIHFWLYH OHQJWKleff>@RUWKHDQWHQQDIDFWRU$)ZKLFKLVGHILQHGIRUD UHFHLYLQJDQWHQQDDV ܨܣሺ݂ሻ ൌ
ܧሺ݂ሻ ܷሺ݂ሻ
ZKHUH U(f) LV WKH YROWDJH DW WKH DQWHQQD WHUPLQDO DQG E(f) LV WKH HOHFWULF ILHOG VWUHQJWK DW WKH DQWHQQD >@ 7KH HIIHFWLYH OHQJWKLVGHILQHGE\WKHLQYHUVH$)7KHKLJKHUWKHDQWHQQD¶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
8+)3' UHFRUGHU 1RW NQRZQ
FDQEH LQFOXGHGLQ FDOLEUDWLRQ
,QFOXGHGLQ FDOLEUDWLRQ
,QFOXGHGLQ FDOLEUDWLRQ
)LJXUH&RPSDULVRQRI3'FDOLEUDWLRQPHWKRGV 8SSHUSORWFDOLEUDWLRQRIHOHFWULFDOPHDVXUHPHQW /RZHUSORWFDOLEUDWLRQSURSRVDOIRU8+)PHDVXUHPHQW
7KH$)RI8+)VHQVRUVDOUHDG\KDVEHHQGHWHUPLQHGZLWKLQ DQDLUILOOHG7(0FHOOLQDIUHTXHQF\UDQJHXSWR0+]LQ
)LJXUH6FKHPDWLFRI*7(0FHOO6LGHYLHZOHIW DQGFURVVVHFWLRQULJKW
,GHDOO\ WKH WHUPLQDWLRQ VKRXOG SURYLGH D UHIOHFWLRQ IDFWRU rWHUPLQDWLRQ 5HFWDQJXODU WUDQVPLVVLRQ OLQH JHRPHWU\ LV XVHG RYHUWKHZKROHFHOOOHQJWK7KHVHSWXPLVSRVLWLRQHGHFFHQWULFWR
06LHJHOHWDO&KDUDFWHUL]DWLRQRI8+)3'6HQVRUVIRU3RZHU7UDQVIRUPHUV8VLQJDQ2LOILOOHG*7(0&HOO
SURYLGH D WHVWLQJ YROXPH RI VXIILFLHQW VL]H IRU WKH (87 7\SLFDOO\WKHUDWLREHWZHHQVHSWXPKHLJKWhDQGFHOOKHLJKWdLV NHSWFRQVWDQWDWYDOXHVEHWZHHQDQGWKURXJKRXWWKHFHOO 35,1&,3/(2)0($685(0(17 7KH HOHFWULFDO ILHOG LQ WKH FHOO LV JHQHUDWHG E\ D GHILQHG SRZHUVLJQDODW3RUWXVLQJDYHFWRUQHWZRUNDQDO\]HU91$ 7KHUHVXOWLQJYROWDJHDWWKH8+)VHQVRULVPHDVXUHGDW3RUW XVLQJ VFDWWHULQJ SDUDPHWHUV 7KH 8+) VHQVRU DQWHQQD LV SRVLWLRQHG LQ WKH WHVW YROXPH RI WKH FHOO 7KH $) FDQ EH FDOFXODWHGDFFRUGLQJWRHTXDWLRQ ZLWKNQRZQKRPRJHQRXV ILHOG FRQGLWLRQV RI WKH FHOO DQG WKH DQWHQQD YROWDJH IURP WKH PHDVXUHPHQW
)LJXUHZKHUHdUHSUHVHQWVWKHKHLJKWRIWKHFURVVVHFWLRQh LV WKH KHLJKW RI WKH VHSWXP LQ WKH FHOO u LV WKH VHSWXP¶V WKLFNQHVV DQG w LWV ZLGWK 7KH VHSWXP WKLFNQHVV u EHFRPHV QHJOLJLEOH LI LW LV VPDOO FRPSDUHG WR WKH FHOO KHLJKW d 7KH VLPSOLILFDWLRQLVYDOLGIRUWKHPDMRUSDUWRIWKHFHOOEXWQRWIRU WKH LQOHW RI WKH FHOO FDOOHG DSH[ 7KHUHIRUH WKH DSH[ LV FRQVLGHUHGVHSDUDWHO\ 7KH FHOO¶V ZDYH LPSHGDQFH Z FDQ EH GHWHUPLQHG XVLQJ DQDO\WLF DSSUR[LPDWLQJ PHWKRGV RU QXPHULF VLPXODWLRQV HJ ILHOGVROYLQJDOJRULWKPVOLNHWKHILQLWHHOHPHQWPHWKRG)(0
91$ 6
3RUW 3RUW
8+) 6HQVRU
RLOILOOHG *7(0FHOO
İU
( 6 6HSWXP 7HUPLQDWLRQ (0DEVRUEHU
)LJXUH 6FKHPDWLFRIWHVWVHWXSIRU8+)DQWHQQDVXVLQJDQRLOILOOHG*7(0 FHOO
&(//'(6,*1 7KHYROXPHLVFKRVHQWREHDVODUJHDVSRVVLEOHLQRUGHUWR PHHW KRPRJHQRXV ILHOG UHTXLUHPHQWV IRU VPDOO DQG ODUJH DQWHQQD GHVLJQV 7KHUHIRUH WKH h/dUDWLR LV FKRVHQ DV LQ RUGHU WR LQFUHDVH YROXPH KHLJKW 7KH UHPDLQLQJ GHJUHH RI IUHHGRP JLYHQ E\ WKH w/aUDWLR LV XVHG WR DGMXVW WKH FHOO¶V ZDYHLPSHGDQFH :$9(,03('$1&( 7KH HQWLUH FHOO¶V ZDYH LPSHGDQFH KDV WR EH Z ȍ LQ RUGHUWRDYRLGUHIOHFWLRQVDWWKHLQSXWDQGWKHWHUPLQDWLRQZLV GHILQHG E\ WKH SHUXQLWOHQJWK SDUDPHWHUV JLYHQ E\ WKH HTXLYDOHQW FLUFXLW RI DQ LQILQLWHVLPDO VKRUW OLQH HOHPHQW 7KH VHULHV LQGXFWDQFH L’ WKH VHULHV UHVLVWDQFH R’ WKH SDUDOOHO FRQGXFWDQFHG’,DQGWKHSDUDOOHOFDSDFLW\C’VHHHTXDWLRQ >@ ܼൌඨ
ܴƲ ݆߱ܮƲ ܩƲ ݆߱ܥƲ
$1$/@ $V WKH LQQHU FRQGXFWRU WKLFNQHVV u LV QHJOHFWHG LQ WKLV PHWKRG LW LV QRW VXLWDEOH IRU WKH DSH[ LPSHGDQFH FDOFXODWLRQ 7KH DSH[ LV GHVLJQHG XVLQJ D QXPHULFDODSSURDFKVHHFKDSWHU 7KHFDSDFLWDQFHFDQEHFDOFXODWHGXVLQJHTXDWLRQ ZHUHK V1n V2nDQG gnDUHVXEVWLWXWHVGHILQHGLQHTXDWLRQV WR >@ ܥൌ
L’ DQG C’ KDYH WR EH HVWLPDWHG IRU HYHU\ SHUXQLWOHQJWK SDUDPHWHU RI WKH *7(0 FHOO %RWK DUH GHILQHG E\ WKH OLQH HOHPHQW¶VFURVVVHFWLRQJHRPHWU\$OOSDUDPHWHUVDUHVKRZQLQ
ʹߝ ൫ͳ ସ൯
σஶ ୀଵሺͶܸଶ െ ܸଵ ሻܸଵ ݃ ஶ σୀଵሺͶܸଶ െ ܸଵ ሻܸଶ ݃
ܸͳ݊ ൌ ܸʹ݊ ൌ
ʹݓ ܽ
Ͷ ݊ߨ
൫݊ߨ ൯ቆ ʹ
ଶ
݊ߨ
݊ߨݓ
ʹ
ʹܽ
ቀ ቁ ቀ ݊ߨݓ ൯ ʹܽ ݊ߨݓ ൫ ʹܽ ൯
൫
݊ߨݓ ൯ ʹܽ ݊ߨݓ ൫ ʹܽ ൯
ʹ ൫
݃݊ ൌ
ଶ
ଵ ܽ σஶ ୀଵ൫௪ሾܸଵ ܸܭଶ ሿ൯ ݃
ܭൌെ
,Q WKLV VHWXS ERWK RKPLF FRPSRQHQWV R’ DQG G’ FDQ EH QHJOHFWHG EHFDXVH RI WKH ORZ HOHFWULFDO UHVLVWLYLW\ RI WKH VHSWXPPDWHULDOFRSSHU DQGWKHORZFRQGXFWLYLW\RIWKHRLOLQ WKHFHOO7KLVOHDGVWRWKHVLPSOLILHGHTXDWLRQ IRUZ ´ܮ ܼൌඨ ´ܥ
)LJXUH u/d DQG w/a-UDWLRV DORQJ WKH *7(0 FHOO OHQJWK DW GLIIHUHQW FURVV VHFWLRQV>@
݊ߨʹ ݓ ൯ Ͷܽ ݊ߨʹ ݓ
൫
൫ Ͷܽ ൯
ܽ
ߝߨ݊ ݎ൫
ൣ
͵
൫݊ߨݓ ൯ ʹܽ
ʹ
ቁ
൫݊ߨݓ ൯െ ʹܽ
൨ቇ
ሻ ൧
ൣ݊ߨሺ݀െ݄ ൧൯ ܽ
݊ߨ݄ ܽ
7KH VSHHG RI OLJKW LQ D PHGLXP HTXDOV WKH SKDVH YHORFLW\ ߥ ݁ݏ݄ܽRIWKHORVVOHVVWUDQVPLVVLRQOLQHZKLFKLVGHILQHGE\WKH
,(((7UDQVDFWLRQVRQ'LHOHFWULFVDQG(OHFWULFDO,QVXODWLRQ9RO1R-XQH
7KHFKDUDFWHULVWLFLPSHGDQFHZFDQEHFDOFXODWHGXVLQJWKH SURYLGHGFDSDFLW\C’RIWKHOLQHVHJPHQWZFDQEHGHILQHGE\ HLWKHUXVLQJWKHVSHHGRIOLJKWcmediumLQWKHRLOILOOHGFHOORUE\ WKH VSHHG RI OLJKW LQ YDFXXP cvacuum DQG W\SLFDO RLO SHUPHDELOLW\İr,oil HTXDWLRQ 7KHRLO LV DVVXPHG WR EH D QRQGLVSHUVLYH PHGLXP IRU DOO IROORZLQJ FRQVLGHUDWLRQV ZLWK FRQVWDQW SHUPHDELOLW\ +HQFH JURXS YHORFLW\ DQG SKDVH YHORFLW\DUHWKHVDPH>@ ܼൌ
ͳ ξߝ ൌ ܿௗ௨ ܿ ܥ௩௨௨ ܥ
)LJXUH VKRZV WKH FDOFXODWHG LPSHGDQFHZ GHSHQGLQJ RQ WKHw/aUDWLRDWWKUHHGLIIHUHQWh/dUDWLRV7KHOLQHLPSHGDQFH FDQ EH NHSW FRQVWDQW DW DQ\ FKRVHQ FURVV VHFWLRQ LI WKH JHRPHWULF SURSHUWLHV RI WKH FURVV VHFWLRQ UHPDLQ FRQVWDQW ,Q RUGHUWRNHHSWKHh/dUDWLR FRQVWDQWWKHVHSWXPKDVWREH GHVLJQHGWRPHHWDw/aUDWLRRIDSSUR[w/a
LPSHGDQFH:
KG KG KG
ZDUDWLR
)LJXUH/LQHLPSHGDQFHZRIWKHRLOILOOHG*7(0FHOOGHSHQGLQJRQLWVw/a UDWLRDQGLWVh/dUDWLR>@
LQIOXHQFH RI WKH VHSWXP¶V WKLFNQHVV u LV D SDUDOOHO WUDQVODWLRQ RI WKH LPSHGDQFH FXUYH ZLWK GHFUHDVLQJ LPSHGDQFHV DW LQFUHDVLQJ u/dUDWLRV 7KH QXPHULFDO VROXWLRQ DQG WKH DQDO\WLFDO DSSURDFK FDQ EH FRPSDUHG DW FURVV VHFWLRQV ZLWK VPDOO u/dUDWLR FURVV VHFWLRQV DQG 7KH VLPXODWLRQ DW FURVV VHFWLRQV PDWFKHV WKH DQDO\WLF UHVXOW H[DFWO\ FURVV VHFWLRQVKRZVOLWWOHGHYLDWLRQ
FURVVVHFWLRQ FURVVVHFWLRQ FURVVVHFWLRQ DQDO\WLF
LPSHGDQFH:
DQJXODU IUHTXHQF\ ߱ DQG WKH DFFRUGLQJ SKDVH FRHIILFLHQW ߚ݈ ݏݏ݈݁ݏݏVHHHTXDWLRQ ߱ ܿ݉݁݀݅ ݉ݑൌ ߥ ݁ݏ݄ܽൌ ǡߚ݈ ݏݏ݈݁ݏݏൌ ߱ඥܮԢ ܥԢ ߚ
ZDUDWLR
)LJXUH &DOFXODWHGZDYHLPSHGDQFH=IRUFURVVVHFWLRQVGHSHQGLQJRQWKH w/aUDWLR
6(3780*(20(75@
6LGH9LHZ
6HSWXP
ZDYHLPSHGDQFH
LPSHGDQFH:
)LJXUH2LOILOOHG*7(0FHOO>@
&(//(9$/8$7,21
FHOOOHQJWKPP
)LJXUH ZD UDWLR DQG UHVXOWLQJ FDOFXODWHG LPSHGDQFH GHILQHG E\ DSH[ DQG VHSWXPDORQJFHOOOHQJWK
67$1',1*:$9(5$7,2 5HIOHFWLRQV DW WKH HQG RI WKH FHOO FDQ OHDG WR XQGHVLUDEOH VWDQGLQJ ZDYHV ZKLFK LPSDFW RQH RI WKH FHOO¶V PDMRU TXDOLW\
,(((7UDQVDFWLRQVRQ'LHOHFWULFVDQG(OHFWULFDO,QVXODWLRQ9RO1R-XQH
IDFWRUV DQ LQKRPRJHQHRXV HOHFWULF ILHOG GLVWULEXWLRQ >@ 6WDQGLQJ ZDYHV DUH PDLQO\ LQIOXHQFHG E\ WKH IUHTXHQF\ GHSHQGLQJ FHOO WHUPLQDWLRQ ZKLFK FRQVLVW RI WKH GLVWULEXWHG UHVLVWRUV RQ WKH VHSWXP WKH UHDU DEVRUEHUV DQG IHUULWH SODWHV 7KHYROWDJHVWDQGLQJZDYHUDWLR6:5LVGHILQHGE\ ͳ ȁܵଵଵ ሺ݂ሻȁ ܹܴܵሺ݂ሻ ൌ ͳ െ ȁܵଵଵ ሺ݂ሻȁ
ݎൌ
SXOVHUHIOHFWLRQ
QV 9 9
ȁܼ ȁ െ ߁ ȁܼ ȁ ߁
7KH UHIOHFWLRQ IDFWRU LV GHWHUPLQHG WR r  DQG WKH UHVXOWLQJLPSHGDQFHLVZFHOO 7KHVPDOOHUURURI LV WROHUDEOH 7KH YROWDJH VLJQDO UHPDLQV UHGXFHG IRU DSSUR[ t QVZKLFKLVWKHWLPHWKHVLJQDOQHHGVWRWUDYHOIRUZDUG DQGEDFNZDUGVDIWHULWLVUHIOHFWHGDWWKHQRQLGHDOWHUPLQDWLRQ 7KH SKDVH YHORFLW\ LV vSKDVH§F LQ RLO GXH WR İU VHH HTXDWLRQ 7KH ORFDO PD[LPXP DQG WKH VXFFHVVLYH H[SRQHQWLDO VLJQDO GHFUHDVH DW WKH HQG DUH FDXVHG E\ WKH FRPELQDWLRQ RI WKH WHUPLQDWLRQ UHVLVWRUV DQG WKHLU SDUDVLWLF LQGXFWLYLW\ VHH FKDSWHU 7KH FRPELQDWLRQ RI D WROHUDEOH 6:5 DQG WKH ZHOO ZDYH LPSHGDQFH RI WKH FHOO PHDVXUHG E\ 7'5 TXDOLI\ WKH *7(0 FHOO DV UHIHUHQFH WHVW VHWXS IRU 8+) VHQVRU¶V$)HVWLPDWLRQ
ݒ௦௨ௗ ሺݐሻ ൌ ݂ ሺݐሻ ݂ݎ ሺݐሻ
YROWDJH9
6:5
6:5
ZDYHLPSHGDQFHZFHOOFDQEHGHULYHGIURPWKHUHIOHFWLRQIDFWRU ZLWKWKHNQRZQFDEOHZDYHLPSHGDQFHīFDEOH
S LV WKH UHIOHFWLRQ VFDWWHULQJ SDUDPHWHU RI WKH FHOO LQSXW SRUW FRPSDUH )LJXUH 7KH LGHDO FHOO SURYLGHV D VWDQGLQJ ZDYH UDWLR RI 6:5 PHDQLQJ WKDW WKH UHIOHFWLRQ LV ]HUR )LJXUH VKRZV WKH PHDVXUHG 6:5 RI WKH FRQVWUXFWHG FHOO 7KH6:5IURPORZIUHTXHQFLHVWRDSSUR[0+]GHSHQGV RQWKHUHVLVWDQFHWHUPLQDWLRQ7KHULVLQJ6:5 XSWR0+] LV FDXVHG E\ WKH ULVLQJ WHUPLQDWLRQ LPSHGDQFH GXH WR WKH UHVLVWRUV¶ SDUDVLWLF VHULDO LQGXFWLYLW\ ,Q WKH UDQJH IURP 0+] WR 0+] WKH 6:5 LV UHGXFHG E\ WKH VXSHULPSRVHGHIIHFWRIWKHUHVLVWRUV¶VHULDOVWUD\FDSDFLW\7KH DEVRUEHUV RSHUDWH DW IUHTXHQFLHV DERYH 0+] $GGLWLRQDOO\ WKH IHUULWH SODWHV DUH XVHG LQ WKH LQWHUPHGLDWH IUHTXHQF\ UDQJH 7KH UHVXOWLQJ KLJKHVW DQG WKHUHIRUH ZRUVW 6:5 RI RFFXUV DW 0+] $ FRQYHQWLRQDO DLUILOOHG *7(0 FHOO SURYLGHV VOLJKWO\ ORZHU YDOXHV ZLWK SWRmax§ >@$VDUHVXOWWKHFHOOTXDOLW\LVFRQVLGHUHGVXIILFLHQW
WLPHV
)LJXUH5HVXOWRI7'5PHDVXUHPHQWRQRLOILOOHG*7(0FHOO
IUHTXHQF\0+]
)LJXUH0HDVXUHG6:5RIWKHFRQVWUXFWHGRLOILOOHG*7(0FHOO
7,0('20$,15()/(&720(75@ &,*5( 7) 3' 'HWHFWLRQ 6\VWHPV IRU *,6 6HQVLWLYLW\ 9HULILFDWLRQ IRU WKH 8+) 0HWKRG DQG WKH $FRXVWLF 0HWKRG International Council on Large Electric Systems, Electra No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ntroduction to Electromagnetic Compatibility, 1HZ -HUVH\ 86$-RKQ:LOH\ 6RQVS >@ ' 3R]DU Microwave Engineering, 1HZ -HUVH\ 86$ -RKQ :LOH\ 6RQV >@ 06LHJHODQG67HQERKOHQ'HVLJQRIDQ2LOILOOHG*7(0&HOOIRUWKH &KDUDFWHUL]DWLRQ RI 8+) 3' 6HQVRUV 3DSHU 1R 3% ,QW O &RQI &RQGLWLRQ0RQLWRULQJDQG'LDJQRVLV&0')-HMX.RUHD >@ (@ 37LSOHUModern PhysicsWKHGLWLRQ3DOJUDYH0DFPLOODQ >@ &,FKHOQ39DLQLNDLQHQDQG3+DDSDOD$SSOLFDWLRQRID*7(0FHOO WR VPDOO DQWHQQD PHDVXUHPHQWV ,((( ,QW O 6\PSRV $QWHQQDV DQG 3URSDJDWLRQ6RFLHW\ 0RQWUHDO&DQDGDSS >@ (76 /LQGJUHQ Model 5400 Series Gigahertz Transverse Electromagnetic GTEM!™ &HOO2SHUDWLRQ0DQXDO³
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
06LHJHOHWDO&KDUDFWHUL]DWLRQRI8+)3'6HQVRUVIRU3RZHU7UDQVIRUPHUV8VLQJDQ2LOILOOHG*7(0&HOO
6WHIDQ 7HQERKOHQ 0¶60¶ UHFHLYHG KLV 'LSORPD DQG 'U,QJ GHJUHHV IURP WKH 7HFKQLFDO 8QLYHUVLW\ RI $DFKHQ *HUPDQ\ LQ DQG UHVSHFWLYHO\ ,Q KH MRLQHG $/6720 6FKRUFK 7UDQVIRUPDWRUHQ *PE+ 0|QFKHQJODGEDFK *HUPDQ\ZKHUHKHZDVUHVSRQVLEOHIRUEDVLFUHVHDUFK DQGSURGXFWGHYHORSPHQW)URPWRKHZDV WKH KHDG RI WKH HOHFWULFDO DQG PHFKDQLFDO GHVLJQ GHSDUWPHQW ,Q KH ZDV DSSRLQWHG WR D SURIHVVRUVKLS DQG KHDG RI WKH LQVWLWXWH RI 3RZHU 7UDQVPLVVLRQ DQG +LJK 9ROWDJH 7HFKQRORJ\ RI WKH 8QLYHUVLW\ RI 6WXWWJDUW *HUPDQ\,QWKLVSRVLWLRQKLVPDLQUHVHDUFKILHOGVDUHKLJKYROWDJHWHFKQLTXH SRZHU WUDQVPLVVLRQ DQG HOHFWURPDJQHWLF FRPSDWLELOLW\ (0& 3URI 7HQERKOHQ KROGV VHYHUDO SDWHQWV DQG SXEOLVKHG PRUH WKDQ SDSHUV +H LV PHPEHU RI WKH ,((( &,*5( 6& $ 3RZHU 7UDQVIRUPHUV *HUPDQ FRPPLWWHHV RI $ ' (PHUJLQJ 7HFKQRORJLHV & 6\VWHP 7HFKQLFDO 3HUIRUPDQFH VHYHUDO LQWHUQDWLRQDO ZRUNLQJ JURXSV DQG WKH FKDLUPDQ RI *HUPDQ 3RZHU (QJLQHHULQJ 6RFLHW\ 9'((7* )% 4 0DWHULDOV (OHFWULFDO ,QVXODWLRQVDQG'LDJQRVWLFV