DOI 10.5162/sensor2015/P10.5
(IIHFWRI(OHFWULFDO&RQGXFWLYH3URSHUW\
RQ(OHFWURPDJQHWLF)ORZ0HWHU
;LDR=KDQJ=KDQJ
'HSDUWPHQWRI(QJLQHHULQJ3K\VLFV7VLQJKXD8QLYHUVLW\%HLMLQJ&KLQD
]KDQJ[]K#WVLQJKXDHGXFQ
$EVWUDFW
$Q HOHFWURPDJQHWLF IORZ PHWHU IROORZV )DUDGD\ ,QGXFWLRQ /DZ $SDUW IURP PDJQHWLF ILHOG ERXQGDU\
FRQGLWLRQ RI HOHFWULFDO FRQGXFWLYLW\ LV LPSRUWDQW LQ SLFNLQJ XS WKH UHVXOWLQJ VLJQDO ,Q XVH RI WKH IORZ
PHWHU WKH HOHFWULFDO FRQGXFWLYH SURSHUW\ RI WKH IORZ PHWHU PD\ FKDQJH EHFDXVH RI HOHFWURGH
FRQWDPLQDWLRQ2QWKHRWKHUKDQGGHVLJQRIVKRUWPHDVXULQJWXEHDWWKHFRVWRIORVLQJVRPHLQGXFWLYH
YROWDJH LV D WHQGHQF\ WR PDNH WKH PHWHU FRPSDFW 7R VWXG\ WKHVH SUREOHPV HOHFWURGHV DQG
PHDVXULQJ WXEH RI WKH IORZ PHWHU ZHUH PRGLILHG E\ LQVXODWLQJ SDLQWLQJ RLO RU E\ DOXPLQXP IRLO %\
SDLQWLQJ D SRUWLRQ RI HOHFWURGH VXUIDFH HOHFWULFDO UHVLVWDQFH EHWZHHQ WZR HOHFWURGHV LQFUHDVHG 7R
VLPXODWHDVKRUWHUPHDVXULQJWXEHDOXPLQXPIRLOZDVXVHGWRFRYHUSDUWRIWKHLQQHUZDOORIWKHWXEH
$ VKRUWHU PHDVXULQJ WXEH ZRXOG UHVXOW D UHGXFHG LQGXFWLYH YROWDJH LQ UHDGLQJ 7KH IORZ PHWHU ZLWK
GLIIHUHQWPRGLILFDWLRQVZDVWHVWHGLQDZDWHUIORZFDOLEUDWLRQULJIRULWVUHDGLQJV9DULDWLRQVRIUHDGLQJV
ZHUH FDOFXODWHG DQG DQDO\]HG ,Q WKH H[SHULPHQW LW VKRZHG WKDW FKDQJH RI HOHFWULFDO FRQGXFWLYH
SURSHUW\ LQ HOHFWURGHV FDXVHG VHULRXV UHDGLQJ HUURUV ZKLOH WKH HUURUV E\ WKH FKDQJH LQ WKH PHWHU¶V
WXEHOHQJWKVHHPHGWREHOHVV0D[LPXPHUURULQJURXSGDWDRIHOHFWURGHSURSHUW\FKDQJHZDV
FRPSDUHGWRRIWKHWXEHOHQJWKFKDQJHLQJURXSGDWD
$FFRUGLQJWRWKHWKHRU\RIHOHFWURPDJQHWLFIORZPHWHUIORZDWGLIIHUHQWSRVLWLRQLQWKHPHDVXULQJWXEH
KDV GLIIHUHQW FRQWULEXWLRQ WR WKH VLJQDO 7KLV LV GHVFULEHG E\ WKH FRQFHSW RI YLUWXDO FXUUHQW 9LUWXDO
FXUUHQW LV LQ WXUQ GHWHUPLQHG E\ HOHFWULFDO ERXQGDU\ FRQGLWLRQ RI WKH PHDVXULQJ WXEH DV ZHOO DV
HOHFWURGHV$Q\FKDQJHRIWKHVHFRQGLWLRQVZRXOGILQDOO\DIIHFWWKHUHDGLQJRIWKHIORZPHWHU)XUWKHU
DV\PPHWU\ RI WKH ERXQGDU\ YDOXH DOVR FDXVHV HUURU LQ WKH UHDGLQJ 7KH ZRUN RIIHUHG H[SHULPHQWDO
YHULILFDWLRQIRUWKHWKHRU\DQGFRXOGKHOSWRDEHWWHUGHVLJQRIWKHIORZPHWHU
.H\ZRUGVHOHFWURPDJQHWLFIORZPHWHUHOHFWULFDOFRQGXFWLYLW\PHDVXULQJWXEHUHDGLQJHUURUV
,QWURGXFWLRQ
(OHFWURPDJQHWLF IORZ PHWHUV ZRUN E\ )DUDGD\¶V
,QGXFWLRQ/DZ&RQGXFWLQJIOXLGIORZLQJDFURVVD
PDJQHWLF ILHOG ZLOO H[SHULHQFH HOHFWURPRWLYH
IRUFH ZKLFK SHUSHQGLFXODU ERWK WR WKH IORZ
YHORFLW\ DQG WKH PDJQHWLF ILHOG>@ %\ SURSHUO\
DUUDQJLQJ WZR HOHFWURGHV RQH FDQ REWDLQ D
SRWHQWLDOGLIIHUHQFHEHWZHHQWKHHOHFWURGHV7KLV
VLJQDO LV HVVHQWLDOO\ SURSRUWLRQDO WR PHDQ
YHORFLW\RIWKHIORZ(OHFWURPDJQHWLFIORZPHWHUV
DUH ZLGHO\ XVHG LQ FLYLO ZDWHU VXSSO\ LQGXVWULDO
OLTXLGV WUDQVIHU EHYHUDJH SURGXFWLRQ OLQHV HWF
2QH RI WKH NH\ DGYDQWDJHV RI HOHFWURPDJQHWLF
IORZ PHWHUV LV XQREVWUXFWHG WR WKH IORZ 7KLV
SURSHUW\ PDNHV WKH IORZ PHWHUV OHVV
PDLQWHQDQFHDQGOHVVHQHUJ\FRQVXPSWLRQ
'XULQJ WKH SURFHVV RI XVH VXVSHQGHG
VXEVWDQFHV LQ IOXLGV ZLOO GHSRVLW RQWR WKH
PHDVXULQJ WXEH RI DQ HOHFWURPDJQHWLF IORZ
PHWHU PDNH WKH HOHFWULFDO SURSHUW\ RI WKH WXEH
ZDOO FKDQJHG :RUVH WKLQJ ZRXOG EH WKDW WKH
AMA Conferences 2015 – SENSOR 2015 and IRS2 2015
HOHFWURGHV DUH FRQWDPLQDWHG $OO WKHVH ZRXOG
FDXVH FHUWDLQ RXWSXW VLJQDO HUURU RI DQ
HOHFWURPDJQHWLFIORZPHWHU
7R VWXG\ WKH HIIHFW RI HOHFWULFDO FRQGXFWLRQ
FKDQJH LQ WKH PHDVXULQJ WXEH RI DQ
HOHFWURPDJQHWLFIORZPHWHU ZH KDYHFRQGXFWHG
D QXPEHU RI H[SHULPHQWV 0RGLILFDWLRQV ZHUH
GRQHRQDQLQGXVWULDOHOHFWURPDJQHWLFIORZPHWHU
&DOLEUDWLRQGDWDZHUHFROOHFWHGWRFRPSDUHGZLWK
WKRVH XQGHU QRUPDO FRQGLWLRQ 5HVXOWV DUH
GLVFXVVHG LQ OLJKW RI WKHRU\ RI HOHFWURPDJQHWLF
IORZPHWHUV
([SHULPHQWV
([SHULPHQWV ZHUH FRQGXFWHG LQ D VWDQGDUG
ZDWHU IORZ UDWH FDOLEUDWLRQ ULJ 7KH QRPLQDO
DFFXUDF\ RI WKH IORZ UDWH ULJ LV 7KH WHVW
HOHFWURPDJQHWLFIORZPHWHULVPDGHE\'D*DQJ
,QVWUXPHQWDWLRQ /WG RI 7LDQ -LQ LQ &KLQD ,WV
QRPLQDO GLDPHWHU LV PP OHQJWK PP
884
DOI 10.5162/sensor2015/P10.5
DFFXUDF\ &DOLEUDWLRQ LV GRQH E\ WLPH
YROXPHPHWKRG
&KDQJHRI&RQGXFWLYH&RQGLWLRQLQ(OHFWURGHV
7R
VLPXODWH
VLWXDWLRQV
RI
HOHFWURGH
FRQWDPLQDWLRQ LQVXODWLQJ SDLQWLQJ RLO ZDV XVHG
WR FRYHU FHUWDLQ SRUWLRQV RI WKH HOHFWURGH
VXUIDFHV 7KH SDLQWHG RLO ZDV WKHQ FOHDQHG
XVLQJHWKDQROLIQHFHVVDU\WRUHFRYHUWKHRULJLQDO
VWDWHFDVHVZHUHVLPXODWHGLQWKHH[SHULPHQW
7KH\DUHVKRZQLQ)LJ
)LJ6LWXDWLRQVRIHOHFWURGHSDUWLDOO\SDLQWHGE\LQVXODWLQJRLOFDVHV
$IWHU VLPXODWLQJ HDFK RI WKH VLWXDWLRQV RI
HOHFWURGH FRQWDPLQDWLRQV FDOLEUDWLRQ ZDV
FRQGXFWHGWRWKHPRGLILHGIORZPHWHU7KLVZDV
GRQHE\VXSSO\WKHIORZPHWHUZLWKDQXPEHURI
NQRZQIORZUDWHVDQGUHDGWKHRXWSXWGDWDIURP
WKH IORZ PHWHU 7KHVH GDWD ZHUH XVHG WR
FDOFXODWH HUURUV WR WKH DFWXDO IORZ UDWHV
UHVSHFWLYHO\$FWXDOIORZUDWHVZHUHREWDLQHGE\
WLPHYROXPH PHWKRG ZKLFK LV RQH RI VWDQGDUG
ZDWHU IORZ FDOLEUDWLRQ PHWKRG 5HVXOWV ZHUH
SORWWHGDVVKRZQLQ)LJVDDQGE
D
AMA Conferences 2015 – SENSOR 2015 and IRS2 2015
885
DOI 10.5162/sensor2015/P10.5
PDGH WKH RULJLQDO D[LDO OHQJWK RI WKH OLQLQJ
FKDQJH 7KLV FKDQJH VLPXODWHV WKDW RI
PHDVXULQJ WXEH OHQJWK :H REWDLQHG D QXPEHU
RI
OLQLQJ
OHQJWKV
V\PPHWULFDOO\
RU
DV\PPHWULFDOO\ WR WKH HOHFWURGH OLQH WKH
HOHFWURGH OLQH LV D VWUDLJKW OLQH OLQNLQJ WKH WZR
HOHFWURGHV6HH)LJIRUGHILQLWLRQV
E
)LJ (IIHFW RI HOHFWURGH FRQWDPLQDWLRQ RQ UHDGLQJ
HUURUVRIDQHOHFWURPDJQHWLF
)URP)LJDRQHFDQVHHWKDWFKDQJHVRIWKH
HOHFWURGHFRQGXFWLRQVHHPHGQRWWRFKDQJHWKH
OLQHDU UHODWLRQ EHWZHHQ WKH IORZ UDWH DQG WKH
RXWSXW+RZHYHUWKHFKDQJHVPDNHTXLWHPXFK
UHDGLQJ HUURU LQ WKH IORZ PHWHU DV VKRZQ LQ
)LJE'LIIHUHQFHEHWZHHQPHWHU¶VRXWSXWDQG
DFWXDO IORZ UDWH LV WKURXJK ZLWKLQ WKH
H[SHULPHQWV,QWHUHVWLQJO\HUURUVLQVLWXDWLRQVRI
)LJVDFDQGGDUHODUJHWKDQVLWXDWLRQVLQ
WKRVHRI)LJVEDQGH7KHUHDVRQSRVVLEO\
FRPHV IURP DV\PPHWU\ LQ IRUPHUV ,Q DOO WKHVH
FDVHVWKHRXWSXWVRIWKHIORZPHWHUDUHVPDOOHU
WKDQ DFWXDO IORZ UDWHV UHVSHFWLYHO\ 7KLV LV
EHFDXVH DOO WKH FDVHV LQFUHDVH UHVLVWDQFH
EHWZHHQWKHHOHFWURGHV
(IIHFWRI0HDVXULQJ7XEH/HQJWK
,Q DQ HOHFWURPDJQHWLF IORZ PHWHU WKHUH LV DQ
PHDVXULQJ WXEH ZKHUH IORZ DFWLQJ ZLWK
PDJQHWLF ILHOG DQG LQGXFLQJ LQGXFWLRQ SRWHQWLDO
2Q WKH LQQHU ZDOO RI WKH WXEH DQ LQVXODWLQJ
OLQLQJ H[LVWV 7KLV OLQLQJ SUHYHQWV WKH LQGXFWLRQ
VLJQDO IURP OHDNLQJ WR WKH HDUWK 1RUPDOO\ WKH
D[LDOOHQJWKRIWKHOLQLQJVKRXOGEHHQRXJKORQJ
ZLWK PD[LPXP HTXDO WR WKH WXEH OHQJWK
+RZHYHU WHQGHQF\ RI FRPSDFW GHVLJQ PDNHV
WKH OHQJWK RI WKH PHDVXULQJ WXEH EHFRPH
VKRUWHUDQGVKRUWHU6KRUWHUWXEHPHDQVVKRUWHU
OHQJWK RI WKH OLQLQJ 7KH UHVXOW LV D ZHDNHU
VLJQDOEHLQJREWDLQHGHYHQRWKHUFRQGLWLRQVDUH
VDPH 7KLV GHFUHDVH LV QRW OLQHDU WR WKH OLQLQJ
OHQJWK)RUYHU\VKRUWWXEHVLJQDOZLOOGHFUHDVH
TXLFNO\ZLWKWKHOHQJWK)RUORQJHUODUJHUWKDQ
WLPHV RI WKH WXEH GLDPHWHU LQFUHDVH RI WKH
WXEH OHQJWK RQO\ DIIHFW OLWWOH RXWSXW VLJQDO
'HVLJQHUV QHHG WR PDNH EDODQFH EHWZHHQ
HQRXJK VLJQDO DQG VKRUW WXEH 7R VLPXODWH WKH
HIIHFWRIWKHPHDVXULQJWXEHOHQJWKWRWKHRXWSXW
RIDQHOHFWURPDJQHWLFIORZPHWHU$OXPLQXPIRLO
ZDVXVHGWRVWLFNRQWRWKHLQVXODWLQJOLQLQJ7KLV
AMA Conferences 2015 – SENSOR 2015 and IRS2 2015
)LJ 0HDVXULQJ WXEH ZLWK LQVXODWLQJ OLQLQJ DQG
$OXPLQXPIRLO
$JDLQIORZUDWHFDOLEUDWLRQVZHUHXQGHUWDNHQWR
WKH HOHFWURPDJQHWLF IORZ PHWHU ZLWK FKDQJHG
OLQLQJV5HDGLQJHUURUVDUHSORWWHGLQ)LJ
)LJ (IIHFW RI PHDVXULQJ WXEH OHQJWK RQ UHDGLQJ
HUURUVRIDQHOHFWURPDJQHWLFIORZPHWHU
,Q )LJ ZH FDQ VHH WKDW FKDQJH RI WKH OLQLQJ
OHQJWKFDXVHVRXWSXWVLJQDOHUURUV7KHVHHUURUV
PDLQO\ GHSHQG RQ KRZ PXFK DUH WKH FKDQJHV
RI WKH OLQLQJ OHQJWK %DVLFDOO\ HUURUV GR QRW
GHSHQGRQIORZUDWHMXVWZLWKLQ,QFDVHV
ZLWK GLIIHUHQW OLQLQJ OHQJWKV GDWD RI HUURU DUH
ODUJHO\ LQ WKUHH JURXSV WKH PLQLPXP HUURUV RI
OHVV WKDQ WKH PHGLXP WR WKH
PD[LPXPRIDERXW,WVKRXOGEHQRWHGWKDW
DOO UHDGLQJ GDWD RI IORZ UDWHV LV VPDOOHU WKDW
DFWXDOIORZUDWHVUHVSHFWLYHO\
'LVFXVVLRQV
$ERYH H[SHULPHQWDO GDWD DUH WKH UHVXOWV IURP
VLPXODWLRQ RI FKDQJH LQ HOHFWULFDO FRQGXFWLYH
SURSHUW\ RI WKH IORZ PHWHU $FFRUGLQJ WR WKH
886
DOI 10.5162/sensor2015/P10.5
WKHRU\ RI HOHFWURPDJQHWLF IORZ PHWHU RXWSXW
VLJQDO RI DQ HOHFWURPDJQHWLF IORZ PHWHU
GHSHQGV RQ WKUHH WKLQJV LWV HOHFWULFDO
FRQGXFWLRQ FRQGLWLRQ HOHFWURGHV DQG LQVXODWLQJ
OLQLQJ PDJQHWLF ILHOG VWUHQJWKFRLOV \RNH DQG
SRZHUFXUUHQWDQGWKHIORZYHORFLW\ILHOGLQWKH
PHDVXULQJWXEH>@
7KH HOHFWULFDO FRQGXFWLYH FRQGLWLRQ FDQ EH
H[SODLQHG E\ D FRQFHSW RI YLUWXDO FXUUHQW $
YLUWXDOFXUUHQWLQDQHOHFWURPDJQHWLFIORZPHWHU
XVHGWRGHVFULEHWKHVHQVLWLYLW\RIHOHFWURGHVWR
IORZ YHORFLW\ LQVLGH WKH IORZ PHWHU WXEH ,W LV
VLPLODUWRWKHHOHFWULFDOFXUUHQWGLVWULEXWLRQLQWKH
WXEH EHWZHHQ WKH WZR HOHFWURGHV ZLWK IOXLG
H[LVWLQJ7DNLQJWKLVFRQFHSWRQHFDQFRQFOXGH
WKDW LI DQ\ SRUWLRQ RI WKH HOHFWURGH VXUIDFH LV
FRYHUHG E\ LQVXODWLQJ SDLQWLQJ RLO WKHQ WKH
YLUWXDO FXUUHQW ZLOO EH ZHDNHU EHFDXVH
UHVLVWDQFH EHWZHHQ HOHFWURGHV LQFUHDVHV $
ZHDN YLUWXDO FXUUHQW ZLOO PHDQ VPDOOHU
FRQWULEXWLRQ WR WKH RXWSXW VLJQDO ,Q WKH VDPH
ZD\ LI WKH LQVXODWLQJ OLQLQJ LV VKRUWHU PRUH
SHUFHQWDJH RI YLUWXDO FXUUHQW ZLOO IORZ LQWR WKH
HDUWK 7KH UHVXOW LV OHVV YLUWXDO FXUUHQW IORZLQJ
EHWZHHQ WZR HOHFWURGHV 7KHQ VPDOOHU RXWSXW
VLJQDOLVREWDLQHGIRUWKHIORZPHWHU
3DLQWLQJ VRPH RLO RQ DQ\ RI WKH HOHFWURGHV ZLOO
LQFUHDVH UHVLVWDQFH RI WKH HOHFWURGH ZKLOH
DOXPLQXP IRLO FDQ EH WDNHQ DV SHUIHFW
FRQGXFWLRQ $ IXUWKHU SUREOHP LV ZKHUH WKH
PRUH VHQVLWLYH SRVLWLRQ WR WKH FRQGXFWLRQ
FKDQJH LV $OVR IURP WKH FRQFHSW RI YLUWXDO
FXUUHQW ZH FDQ VHH WKDW YLUWXDO FXUUHQW LV YHU\
GHQVH QHDU WKH HOHFWURGHV HVSHFLDOO\ IRU SRLQW
HOHFWURGHV 7KLV FXUUHQW RQ DQ HOHFWURGH
VXUIDFH LQFUHDVHV LQYHUVHO\ SURSRUWLRQDO WR WKH
DUHD RI WKH HOHFWURGH VXUIDFH )RU SRLQW
HOHFWURGH WKH VXUIDFH LV YHU\ VPDOO WKXV WKH
FXUUHQW KHUH LV YHU\ GHQVH &RQVLGHULQJ DQ\
FKDQJH RI WKH VXUIDFH DUHD VHULRXV FKDQJH RI
WKH FXUUHQW ZRXOG RFFXU +RZHYHU IDU DZD\
IURPWKHHOHFWURGHVWKHYLUWXDOFXUUHQWEHFRPHV
ZHDNHU WKXV DQ\ FKDQJH RI HOHFWULFDO
FRQGXFWLYLW\ KHUH ZRXOG EH OHVV DIIHFW WR WKH
FXUUHQW8VLQJWKHFRQFHSWRIYLUWXDOFXUUHQWZH
FDQ FRQFOXGH WKDW FKDQJH RI FRQGXFWLYH
SURSHUW\ QHDU WKH HOHFWURGHV ZLOO FDXVH PRUH
VHQVLWLYH HIIHFW WR WKH RXWSXW VLJQDO ZKLOH WKH
FKDQJHRIWKHOLQLQJIDUIURPWKHHOHFWURGHVKDV
OHVV HIIHFW ,Q WKH H[SHULPHQWDO GDWD WKH
FKDQJHLQWKHHOHFWURGHVFDQFDXVHDVKLJKDV
RI PHDVXUHPHQW HUURU 5HGXFLQJ WKH WXEH
OHQJWK XQWLO RI LWV RULJLQDO RQO\ FDXVHV RIWKHHUURU
:H DOVR WULHG WR PDNH VRPH DV\PPHWULFDO
FKDQJH RI FRQGXFWLYH SURSHUW\ WR WKH HOHFWURGH
OLQH )RU H[DPSOHV DOO FDVHV LQ )LJ DQG
FDVHV DQG LQ )LJ )URP WKH WKHRU\ RI
HOHFWURPDJQHWLF IORZ PHWHU DV\PPHWU\ ZRXOG
FDXVH DGGLWLRQDO PHDVXUHPHQW HUURU >@>@ %XW
AMA Conferences 2015 – SENSOR 2015 and IRS2 2015
LW LV KDUG WR VHSDUDWH WKH DGGLWLRQDO HUURU IURP
WRWDOHUURULQWKHH[SHULPHQWGDWD
&RQFOXVLRQV
0DLQ ZRUNV GHVFULEHG LQ WKLV SDSHU DUH
VXPPDUL]HGDVEHOORZV˖
˅&KDQJHVRIHOHFWULFDOFRQGXFWLYHSURSHUW\LQ
DQ HOHFWURPDJQHWLF IORZ PHWHU DUH VLPXODWHG
XVLQJ LQVXODWLQJ RLO DQG DOXPLQXP IRLO 7HVWV
ZHUH XQGHUWDNHQ RI WKH PRGLILHG IORZ PHWHU LQ
VWDQGDUGIORZUDWHFDOLEUDWLRQULJ2XWSXWVLJQDOV
ZHUHREWDLQHGRIZKLFKFDVHVZHUHHOHFWURGH
FKDQJHV FDVHV ZHUH LQVXODWLQJ OLQLQJ
FKDQJHV
([SHULPHQWDO UHVXOWV VKRZ FKDQJHV LQ
FRQGXFWLYH SURSHUW\ RQ WKH HOHFWURGHV VXUIDFHV
FDXVH XS WR RI UHDGLQJ HUURUV ZKLOH
FKDQJHVRQWKHOLQLQJOHQJWKFDXVHXSWR
HUURU ,Q DOO WKH FDVHV RXWSXW VLJQDOV DUH
VPDOOHUWKDQDFWXDOIORZUDWHV
˅&RQFHSW RI YLUWXDO FXUUHQW LQ WKH WKHRU\ RI
HOHFWURPDJQHWLFIORZPHWHULVXVHGWRH[SODLQWR
WKH SKHQRPHQD ZKLFK KHOSV XV WR REWDLQ DQ
XQGHUVWDQGDEOHSK\VLFDOILJXUH
5HIHUHQFHV
>@ - +HPS DQG + . 9HUVWHHJ 3UHGLFWLRQ RI
HOHFWURPDJQHWLFIORZPHWHUFKDUDFWHULVWLFV-$SSO
3K\V
>@ ;= =KDQJ $ PHWKRG IRU VROYLQJ /DSODFH¶V
HTXDWLRQ ZLWK PL[HG ERXQGDU\ FRQGLWLRQ LQ
HOHFWURPDJQHWLF IORZPHWHUV - $SSO 3K\V
>@ + 6KX + : /Y ;= =KDQJ $QDO\VLV RI HUURUV
FDXVHG E\ DV\PPHWU\ RI HOHFWURGHV RU FRLOV LQ
HOHFWURPDJQHWLF IORZ PHWHU 0HDVXUHPHQW
7HFKQLTXH1LQ&KLQHVH
>@ *4 :DQJ ;= =KDQJ (IIHFW RI DV\PPHWULFDO
IORZ RQ RXWSXW RI HOHFWURPDJQHWLF IORZ PHWHU
0HDVXUHPHQW 7HFKQLTXH 1 LQ
&KLQHVH
887