Bestimmung der Feldeinkopplung in Leitungsstrukturen von ...

bordsysteme.tu.dortmund.de

Bestimmung der Feldeinkopplung in Leitungsstrukturen von ...

%HVWLPPXQJGHU)HOGHLQNRSSOXQJLQ/HLWXQJVVWUXNWXUHQYRQ

.UDIWIDKU]HXJHQPLWK\EULGHQ%HUHFKQXQJVYHUIDKUHQ

'U6WHSKDQ)UHL$8',$*,((,QJROVWDGWVWHSKDQIUHL#DXGLGH

7KRPDV.RQVFKDN$8',$*,((,QJROVWDGW

+HLNR:LHFKPDQQ$8',$*,(.,QJROVWDGW

$VVRFLDWH3URI'U5RPDQ-REDYD7ELOLVL6WDWH8QLYHUVLW\7ELOLVL*HRUJLHQ


(LQOHLWXQJ

=XU %HUHFKQXQJ GHU (09 LQ HLQHP .UDIWIDKU]HXJ LVW HV LQ GHQ PHLVWHQ )lOOHQ

]ZHFNPl‰LJGDV)DKU]HXJLQGLHIROJHQGHQ%HUHLFKHDXI]XWHLOHQ

œ

œ

œ

œ

PHWDOOLVFKH2EHUIOlFKHQZLH]%GLH)DKU]HXJNDURVVHULH

/HLWXQJVVWUXNWXUHQ

HOHNWURQLVFKH.RPSRQHQWHQLG5GLH$EVFKOVVHGHU/HLWXQJ

$QWHQQHQ

'LH 9HUNDEHOXQJ LVW DOV GLH ZHVHQWOLFKH 6WUXNWXU DQ]XVHKHQ LQ GLH GXUFK HOHNWUR

PDJQHWLVFKH )HOGHU (QHUJLH LQ GLH )DKU]HXJHOHNWURQLN HLQJHNRSSHOW ZHUGHQ NDQQ

$XIJUXQG GHU JUR‰HQ $XVGHKQXQJ GHU )DKU]HXJYHUNDEHOXQJ PLW HLQHU *HVDPWOlQJH

YRQ HLQLJHQ WDXVHQG 0HWHUQ HUJLEW VLFK HLQH VHKU HIIL]LHQWH (PSIDQJVVWUXNWXU 'LH

GLUHNWH (LQNRSSOXQJ LQ 6WHXHUJHUlWH VSLHOW LP XQWHUHQ XQG PLWWOHUHQ )UHTXHQ]EHUHLFK

NDXPHLQH5ROOHGDGLH$EPHVVXQJHQGHU6WUXNWXUHQZHVHQWOLFKNOHLQHUDOVGLH:HOOHQ

OlQJHQ VLQG 6WHXHUJHUlWH N|QQHQ VRPLW QlKHUXQJVZHLVH DOV UlXPOLFK NRQ]HQWULHUWH

6FKDOWXQJHQEHWUDFKWHWZHUGHQZHOFKHGLH/HLWXQJHQDEVFKOLH‰HQ

%HLGHUQlKHUXQJVZHLVHQ%HUHFKQXQJGHU)HOGHLQNRSSOXQJNDQQPDQVLFKDOVRDXIGLH

%HWUDFKWXQJ GHU 9HUNDEHOXQJ XQG GHU .DURVVHULH EHVFKUlQNHQ 'LH (LQNRSSOXQJ LQ

/HLWXQJHQNDQQEHUGLH 9HUNRSSOXQJ GHU )HOGEHUHFKQXQJ PLW GHU/HLWXQJVWKHRULH >@

HUIROJHQ'LHVH9HUIDKUHQXPJHKHQGLH]7QRWZHQGLJHVHKUIHLQH'LVNUHWLVLHUXQJGHU

/HLWXQJHQ'HUDEHUZLFKWLJVWH9RUWHLOLVWGLHP|JOLFKH9HUELQGXQJ]X1HW]ZHUNDQDO\VH

SURJUDPPHQ>@

(V YHUEOHLEHQ EHL GHU .RSSOXQJ GHU )HOGEHUHFKQXQJ PLW +LOIH GHU /HLWXQJVWKHRULH

MHGRFK]ZHLZHVHQWOLFKH3UREOHPH

œ

œ

'LH%HKDQGOXQJYRQ/HLWXQJVDEVFKQLWWHQLQGHQHQGLH7(0$QQDKPHQQLFKWPHKU

JHOWHQLVWQXUQlKHUXQJVZHLVHP|JOLFK

(V VLQG LQ GHU 5HJHO NHLQH 0RGHOOH IU UHDOH $EVFKOVVH YRUKDQGHQ (LQIDFKH

(UVDW]ODVWHQYHUP|JHQQLFKWLQDOOHQ)lOOHQHLQHDXVUHLFKHQGJHQDXH0RGHOOLHUXQJ

,QGLHVHP%HLWUDJZLUG]XQlFKVWNXU]YRUJHVWHOOWZLHPLWHLQHPK\EULGHQ9HUIDKUHQGLH

(LQNRSSOXQJLQ.DEHOElXPHEHUHFKQHWZHUGHQNDQQ$QVFKOLH‰HQGZLUGGDUJHVWHOOWZLH

OLQHDUH $EVFKOVVH PLW +LOIH GHU 1HW]ZHUNV\QWKHVH IU 6LPXODWLRQHQ PLW 1HW]ZHUN

DQDO\VHSURJUDPPHQ PRGHOOLHUW ZHUGHQ N|QQHQ 6FKOLH‰OLFK ZLUG JH]HLJW ZLH GLH

1HW]ZHUNV\QWKHVHDXFKHLQJHVHW]WZHUGHQNDQQXP/HLWXQJVDEVFKQLWWHLQGHQHQGLH

$QQDKPH YRQ 7(0:HOOHQ EHL ZHLWHP QLFKW PHKU HUIOOW LVW GXUFK VSH]LHOOH

0DNURPRGHOOH]XEHUFNVLFKWLJHQ


¡¡¨¨ ¡

¥¨

!¡¨§

%LOG 'DV.DEHOQHW]LQHLQHP.UDIWIDKU]HXJ


=HUOHJXQJHLQHU/HLWXQJVVWUXNWXU

.RPSOH[H /HLWXQJVVWUXNWXUHQ PLW UHDOHQ $EVFKOVVHQ N|QQHQ PHLVW QLFKW GLUHNW PLW

UHLQHQ')HOGEHUHFKQXQJVSURJUDPPHQ EHUHFKQHW ZHUGHQ >@ 'LH $QZHQGXQJ YRQ

K\EULGHQ 9HUIDKUHQ LVW QRWZHQGLJ 'D]X PXVV GLH ]X EHUHFKQHQGH 6WUXNWXU LQ

7HLOVWUXNWXUHQ]HUOHJWZHUGHQ$XVGHQ7HLOVWUXNWXUHQVLQG0DNURPRGHOOH]XJHQHULHUHQ

GLH 3DUDPHWHU GHU 0DNURPRGHOOH ]X EHVWLPPHQ XQG GLHVH VFKOLH‰OLFK LQ HLQH

HLQKHLWOLFKH )RUP ]X EHUIKUHQ GDPLW GLH %HKDQGOXQJ GXUFK 1HW]ZHUNDQDO\VH

SURJUDPPHP|JOLFKLVW

,Q %LOG LVW IU HLQH /HLWXQJ EHU HLQHU EHOLHELJ JHIRUPWHQ PHWDOOLVFKHQ )OlFKH

GDUJHVWHOOW ZLH HLQH =HUOHJXQJ DXVVHKHQ NDQQ (V ILQGHQ VLFK LQ GLHVHP %HLVSLHO

%HUHLFKHGLHVLFKGUHL.ODVVHQ]XRUGQHQODVVHQ

$ $EVFKOVVHGHU/HLWXQJ6WHXHUJHUlW$NWXDWRU6HQVRU

% %HUHLFKH LQ GHQHQ GLH $QQDKPH YRQ 7(0)HOGHUQ DXI GHU /HLWXQJ LQ HUVWHU

1lKHUXQJHUIOOWLVW

& %HUHLFKHLQGHQHQGLH7(0$QQDKPHHUKHEOLFKYHUOHW]WLVW

¢¡¤£¦¥¨§ § ©§ ¨¡

¡¨ £¨

$

¨§

%

&

%

&

%

$

%LOG 8QWHUWHLOXQJHLQHU]XEHUHFKQHQGHQ

/HLWXQJVVWUXNWXUEHUHLQHU0HWDOOIOlFKHLQ

.ODVVHQ

© © ¨§

,P )ROJHQGHQ ZLUG DQJHQRPPHQ GDVV GLH )HOGHLQNRSSOXQJ LQ GLH /HLWXQJ UFN

ZLUNXQJVIUHL DXI GDV HUUHJHQGH )HOG LVW 'LHVH $QQDKPH LVW EHL 6W|UIHVWLJNHLWV


SUREOHPHQPHLVW]XOlVVLJ)UMHGH.ODVVHN|QQHQYHUVFKLHGHQH0DNURPRGHOOHJHELOGHW

ZHUGHQGDVJHQDXH9RUJHKHQZLUGLQGHQIROJHQGHQ$EVFKQLWWHQGDUJHVWHOOW

'LHZHVHQWOLFKH9RUWHLOHVROFKHU0DNURPRGHOOHVLQG

œ )U MHGHQ %HUHLFK NDQQ GDV RSWLPDOH 9HUIDKUHQ DQJHZHQGHW ZHUGHQ 0R0 )(0

)'7'

œ 'LH 9RUWHLOH GHU ')HOGVLPXODWLRQ ZHUGHQ PLW GHQ 9RUWHLOHQ GHU 1HW]ZHUN XQG

/HLWXQJVVLPXODWLRQYHUNQSIW

œ (LQPDO JHQHULHUWH 0RGHOOH N|QQHQ DOV %O|FNH OHLFKW LQ DQGHUHQ 6LPXODWLRQHQ

ZHLWHUYHUZHQGHWZHUGHQ

œ 0DNURPRGHOOH N|QQHQ ]XU 5HGX]LHUXQJ GHU .RPSOH[LWlW YRQ 0RGHOOHQ HLQJHVHW]W

ZHUGHQ 2IW JHQJW HV ZHQQ HLQ 0RGHOO GDV 9HUKDOWHQ QXU LQ HLQHP VFKPDOHQ

)UHTXHQ]EHUHLFKZLHGHUJLEW


%HKDQGOXQJYRQ$EVFKOVVHQ

'DV %HKDQGHOQ YRQ NRPSOH[HQ UHDOHQ $EVFKOVVHQ LVW GXUFK UHLQH ')HOG

EHUHFKQXQJVSURJUDPPHQLFKWP|JOLFKKLHUVLQG1HW]ZHUNDQDO\VHSURJUDPPHZLH ]%

63,&( QRWZHQGLJ 'LHVHU $EVFKQLWW EHVFKUHLEW 9HUIDKUHQ ]XU %HVWLPPXQJ YRQ

0DNURPRGHOOHQ OLQHDUHU $EVFKOVVH =ZHLSROH ]XU %HKDQGOXQJ PLW GHP 1HW]ZHUN

DQDO\VHSURJUDPP63,&(

3UREOHPDWLVFKLVWGDV%HVWLPPHQHLQHV6LPXODWLRQVPRGHOOVGDVKLQUHLFKHQGJHQDXGDV

9HUKDOWHQHLQHV$EVFKOXVVHVZLHGHUJLEW)U+DOEOHLWHUH[LVWLHUHQ]763,&(0RGHOOH

+LHUPXVVMHGRFKGDUDXIJHDFKWHWZHUGHQGDVVGDV0RGHOODXFKGDV(099HUKDOWHQ

KLQUHLFKHQG JHQDX ZLHGHUVSLHJHOW )U /RJLNEDXVWHLQH ZHUGHQ RIW ,%,60RGHOOH >@

EHUHLWJHVWHOOWGLHVLFKZLHGHUXPLQ63,&(0RGHOOHEHUIKUHQODVVHQ8QWHUVXFKXQJHQ

DQ/HLVWXQJVWUHLEHUQHUJDEHQGDVVDXFKGLHVHPLW+LOIHYRQHUZHLWHUWHQ,%,60RGHOOHQ

QDFKJHELOGHWZHUGHQN|QQHQ>@'LH%HVWLPPXQJGHU3DUDPHWHUJHVFKLHKWKLHUGXUFK

0HVVXQJHQRGHU6LPXODWLRQHQPLWHLQHPGHWDLOOLHUWHQ63,&(0RGHOO

)UGLH/DVWHQ9HQWLOH0RWRUHQGLH LP $XWRPRELOEHUHLFK LQ GHU 5HJHO HLQJHVHW]W

ZHUGHQJLEWHVDEHUPHLVWNHLQH(UVDW]VFKDOWELOGHU'DV9HUKDOWHQNDQQVHKUNRPSOH[

VHLQ'LHFKDUDNWHULVWLVFKHQ)XQNWLRQHQN|QQHQDXV0HVVXQJHQRGHUIDOOV GHU LQQHUH

$XIEDXEHNDQQWLVWGXUFK6LPXODWLRQHQEHVWLPPWZHUGHQ

6LPXODWLRQVPRGHOOHIUOLQHDUH=ZHLSROH$EVFKOVVH

3K\VLNDOLVFKHV0RGHOO

,Q YLHOHQ )lOOHQ NDQQ VLFK DXV GHP :LVVHQ EHU GHQ LQQHUHQ $XIEDX HLQHV OLQHDUHQ

$EVFKOXVVHV HLQ (UVDW]VFKDOWELOG HQWZLFNHOQ ODVVHQ ,Q $EKlQJLJNHLW YRQ GHU *U|‰HQ

RUGQXQJGHV1HW]ZHUNVXQGGHU.HQQWQLVGHVXQJHIlKUHQ:HUWHEHUHLFKVGHUHLQ]HOQHQ

.RPSRQHQWHQ N|QQHQ LWHUDWLYH 9HUIDKUHQ GXUFK $EJOHLFK PLW 0HVVZHUWHQ RGHU

6LPXODWLRQVGDWHQGLHJHQDXHQ:HUWHGHU1HW]ZHUNHOHPHQWHEHVWLPPHQ

-H JU|‰HU GDV ]X LGHQWLIL]LHUHQGH 1HW]ZHUN ZLUG GHVWR JHQDXHU PXVV MHGRFK GHU

6WDUWYHNWRUYRUJHJHEHQZHUGHQ'LHVHV9HUIDKUHQVW|‰WGDPLWVFKRQUHFKWIUKDQVHLQH

*UHQ]HQ

hEHUWUDJXQJVIXQNWLRQ

/lVVWVLFKNHLQSK\VLNDOLVFKHV0RGHOODXV*UXQGHOHPHQWHQDEOHLWHQN|QQHQJHVWHXHUWH

4XHOOHQ E]Z Ã$QDORJ %HKDYLRUDOµ0RGHOOH RGHU DOOJHPHLQH $OJRULWKPHQ ]XU 6\QWKHVH

YRQ 1HW]ZHUNHQ DXV HLQHU hEHUWUDJXQJVIXQNWLRQ HLQJHVHW]W ZHUGHQ 'LH EHLGHQ


¨


¦

¢

¢



¢

¢



¡ ¢ £

¡

£ ¢

§

¡ ¢ £

¡







$QVlW]H ZHUGHQ QDFK HLQHU hEHUVLFKW ]XU $SSUR[LPDWLRQ LP )ROJHQGHQ NXU]

GDUJHVWHOOW

$SSUR[LPDWLRQGHU=ZHLSROIXQNWLRQXQG3RO1XOOVWHOOHQ$QDO\VH

(LQHGXUFK0HVVXQJRGHU6LPXODWLRQEHVWLPPWH,PSHGDQ]NDQQGXUFK$SSUR[LPDWLRQLQ

HLQHUDWLRQDOH)XQNWLRQGHUIROJHQGHQ)RUPJHEUDFKWZHUGHQ

$ S

D S + D S

=

¢

S

= =

£

% S

E S + E S

+ +

D

+ +

E

S = a +

'LH .RHIIL]LHQWHQ D¤ XQG E¤ N|QQHQ GXUFK HLQHQ )HKOHU0LQLPLHUXQJVDOJRULWKPXV

EHVWLPPWZHUGHQ,VWGLHUDWLRQDOH)XQNWLRQGHU,PSHGDQ]EHNDQQWN|QQHQGLH3ROXQG

1XOOVWHOOHQEHUHFKQHWZHUGHQ%HLUHLQHQ5HDNWDQ]QHW]ZHUNHQPVVHQGLH3ROHDXIGHU

LPDJLQlUHQ$FKVHLQGHUS(EHQHOLHJHQ

0RGHOOLHUXQJHLQHVOLQHDUHQ$EVFKOXVVHVLQ63,&(DXV0HVVRGHU

6LPXODWLRQVGDWHQ

63,&(ELHWHWGLH0|JOLFKNHLWHLQHJHJHEHQHhEHUWUDJXQJVRGHU,PSHGDQ]IXQNWLRQLQ

IUHTXHQ]DEKlQJLJ JHVWHXHUWH 4XHOOHQ RGHU HLQH :HUWHWDEHOOH GLUHNW LQ HLQ $QDORJ

%HKDYLRUDO 0RGHOO 36SLFH XP]XZDQGHOQ ,P )UHTXHQ]EHUHLFK OLHIHUQ GLHVH 0RGHOOH

JXWH (UJHEQLVVH ,P =HLWEHUHLFK JLEW HV MHGRFK 3UREOHPH ZHQQ GLH hEHU

WUDJXQJVIXQNWLRQ GLIIHUHQ]LHUHQGHV 9HUKDOWHQ ]HLJW ZDV LQ GHU 3UD[LV IDVW LPPHU GHU

)DOO LVW ,Q GLHVHP )DOO LVW GLH UFNWUDQVIRUPLHUWH 6\VWHPUHDNWLRQ QLFKW PHKU NDXVDO

'XUFK GLH 6\QWKHVH HLQHV lTXLYDOHQWHQ 1HW]ZHUNV ODVVHQ VLFK GLHVH 3UREOHPH

XPJHKHQ

6\QWKHVHYRQ=ZHLSROHQ

5HDOHOLQHDUH$EVFKOVVHODVVHQVLFKLQGHU5HJHOLQHLQ1HW]ZHUNYRQ*UXQGHOHPHQWHQ

]HUOHJHQ 'LH IROJHQGHQ %HWUDFKWXQJHQ JHKHQ GDYRQ DXV GDVV GLH EHWUDFKWHWHQ

1HW]ZHUNH MHZHLOV PLQLPDOH 3KDVH KDEHQ XQG GLH .ULWHULHQ IU HLQH =ZHLSROIXQNWLRQ

HUIOOHQ>@(VPXVV]ZLVFKHQUHLQHQ5HDNWDQ]XQG5/& ¥ 1HW]ZHUNHQXQWHUVFKLHGHQ

ZHUGHQ 9HUOXVWEHKDIWHWH 1HW]ZHUNH N|QQHQ GXUFK GDV %UXQH9HUIDKUHQ >@

V\QWKHWLVLHUW ZHUGHQ $XV 3ODW]JUQGHQ NDQQ LQ GLHVHP %HLWUDJ QXU GLH ZHVHQWOLFK

HLQIDFKHUH 6\QWKHVH YRQ 5HDNWDQ]QHW]ZHUNHQ NXU] GDUJHVWHOOW ZHUGHQ 'HU JH]HLJWH

$OJRULWKPXVOLHIHUWHLQHNDQRQLVFKH5HDOLVLHUXQJ

8PIRUPXQJXQG6\QWKHVHGHU,PSHGDQ]IXQNWLRQ

=XU ZHLWHUHQ $QDO\VH NDQQ GLH UDWLRQDOH )XQNWLRQ HLQHV 5HDNWDQ]QHW]ZHUNV GXUFK

3DUWLDOEUXFK]HUOHJXQJLQGLHIROJHQGH)RUP]HUOHJWZHUGHQ

$ $

S

= S = + Ê©


S S + w

+ $

'LHVH*OHLFKXQJOlVVWVLFKPLW

S

Mw

=

S Mw


$

= & $ = / = &

$

$

w

= /

XPIRUPHQ]X





ÅhEHUWUDJHU


£

¢

£

£



= w = + Ê + Mw/


¡ Mw&

¤

Mw&

+

Mw/

ZRUDXVGLUHNWHLQH5HLKHQVFKDOWXQJZLHLQ%LOGGDUJHVWHOOWJHELOGHWZHUGHQNDQQ


/§ /¨



/¥ &¥

&§ &¨



%LOG 1HW]ZHUNJHELOGHWDXV*OHLFKXQJ


%HUHFKQXQJGHU)HOGHLQNRSSOXQJLQ/HLWXQJVVWUXNWXUHQ7(0)HOGDQQDKPH

QlKHUXQJVZHLVHHUIOOW

8QWHU GHU $QQDKPH GDVV GLH /HLWXQJVVWUXNWXUHQ GLH %HGLQJXQJHQ IU 7(0)HOGHU

QlKHUXQJVZHLVH HUIOOHQ NDQQ GLH (LQNRSSOXQJ HOHNWURPDJQHWLVFKHU )HOGHU GXUFK

=HUOHJXQJGHU]XDQDO\VLHUHQGHQ/HLWXQJVVWUXNWXUVFKULWWZHLVHEHUHFKQHWZHUGHQ>@

'XUFKGLH$XIWHLOXQJGHU/HLWXQJVVWUXNWXUHUKlOWPDQHLQ]HOQH6HJPHQWHGLHGXUFKLKUH

/lQJHXQGGLH,PSHGDQ]PDWUL]HQGHILQLHUWVLQG-HGHV6HJPHQWVWHOOWHLQHHOHNWULVFKH

NXU]H /HLWXQJ GDU 'LHVH NXU]HQ /HLWXQJHQ N|QQHQ GXUFK NRQ]HQWULHUWH %DXHOHPHQWH

QDFKJHELOGHW ZHUGHQ 'LH )HOGHLQNRSSOXQJ ZLUG GXUFK 6WURP XQG 6SDQQXQJVTXHOOHQ

EHUFNVLFKWLJW 'DPLW LVW HV PLW 1HW]ZHUNEHUHFKQXQJVYHUIDKUHQ P|JOLFK GLH

(LQNRSSOXQJYRQLQKRPRJHQHQ)HOGHULQ/HLWXQJVVWUXNWXUHQ]XEHUHFKQHQGLHLQLKUHP

9HUODXIVRZRKOLQKRPRJHQDOVDXFKQLFKWOLQHDUDEJHVFKORVVHQVHLQGUIHQ


0RGHOOLHUXQJOLQHDUHU9LHUSROHGXUFK0DNURPRGHOOH

/HLWXQJVVWUXNWXUHQEHU gIIQXQJHQ LQPHWDOOLVFKHQ )OlFKHQ RGHU .DQWHQ6WHFNHU XQG

3ODWLQHQ ODVVHQ VLFK XP QXU HLQLJH %HLVSLHOH ]X QHQQHQ QLFKW PHKU SUl]LVH PLW GHU

/HLWXQJVWKHRULH PRGHOOLHUHQ $XFK ZHQQ $EVWUDKOYHUOXVWH QLFKW PHKU ]X

YHUQDFKOlVVLJHQ VLQG VW|‰W GLH /HLWXQJVWKHRULH DQ LKUH *UHQ]HQ 0DNURPRGHOOH DXV

0R0%HUHFKQXQJHQRGHU0HVVXQJHQXQWHUOLHJHQGLHVHQ(LQVFKUlQNXQJHQQLFKW

= w = w

= w

= w = w

= w

%LOG (LQIDFKHV0DNURPRGHOOPLW

IUHTXHQ]DEKlQJLJHQ,PSHGDQ]HQ

%LOG (UZHLWHUWHV0DNURPRGHOOPLW

KRPRJHQHU/HLWXQJIUEHOLHELJH

/HLWXQJVVWUXNWXUHQ


'


&


¥



¥


&


¥


¢

£


¢


¥

¤

¢

¥

¤

¢

¢

£

¤

£

¢

-HGHUEHOLHELJH]ZHLSROLJH/HLWXQJVDEVFKQLWWELOGHWHLQHQ9LHUSROGHUVLFKVRODQJHGLH

/HLWXQJ DOV HLQ 6\VWHP PLQLPDOHU 3KDVH EHWUDFKWHW ZLUG EHLVSLHOVZHLVH GXUFK HLQ 7

1HW]ZHUNPLWIUHTXHQ]DEKlQJLJHQ,PSHGDQ]HQ%LOGEHVFKUHLEHQOlVVW

'LH LQ $EVFKQLWW YRUJHVWHOOWHQ 9HUIDKUHQ HUODXEHQ GLH (LQELQGXQJ GHU IUHTXHQ]

DEKlQJLJHQ,PSHGDQ]HQLQ63,&(

%HL GHP 0RGHOO LQ %LOG KDQGHOW HV VLFK XP HLQH PLQLPDOSKDVLJH %HVFKUHLEXQJ

/HLWXQJVUHVRQDQ]HQ GLH EHVRQGHUV EHL VFKZDFK JHGlPSIWHQ 6\VWHPHQ GHXWOLFK

KHUYRUWUHWHQ N|QQHQ GDPLW QLFKW ZLHGHUJHEHQ ZHUGHQ 'XUFK GLH (UZHLWHUXQJ GHV

(OHPHQWDUYLHUSROVGXUFK/HLWXQJVPRGHOOH%LOGGLHEHLGHU%HVWLPPXQJGHU9LHUSRO

SDUDPHWHUEHUFNVLFKWLJWZHUGHQPVVHQLVWGLH%HKDQGOXQJYRQ/HLWXQJVUHVRQDQ]HQ

P|JOLFK

%HVWLPPXQJGHU0DNURPRGHOOSDUDPHWHU

'LH %HVWLPPXQJ YRQ = ¥ = XQG =¡ DXV %LOG NDQQ GXUFK 0HVVXQJ GHU =0DWUL[

HOHPHQWHRGHU%HUHFKXQJHQHUIROJHQ'LH%HVWLPPXQJGHU3DUDPHWHUGHVHUZHLWHUWHQ

0DNURPRGHOOV NDQQ EHU GLH 0HVVXQJ E]Z %HUHFKQXQJ GHU =3DUDPHWHU GHV

*HVDPWV\VWHPV JHVFKHKHQ = ¥ = XQG =¡ VLQG GHU 0HVVXQJ QLFKW GLUHNW ]XJlQJOLFK

'DV0RGHOONDQQDOVHLQH.HWWHQVFKDOWXQJYRQHLQHP/HLWXQJVYLHUSROXQGGHP9LHUSRO

GHV7*OLHGHVDXIJHIDVVWZHUGHQ'LH=0DWUL[GLHVHU6FKDOWXQJHUKlOWPDQQDFKNXU]HU

5HFKQXQJ

Î=

M= VLQb

O

+ =

+ = FRVb

O

= = ¦¨§© D Ï

Ð

= =

PLW D = = FRVb O

+ M=

+ = VLQb

O

=

=

+ =

FRVb

O

+

=

=

M=

=

+ = =

+ = =

Þ

VLQb

O

ß

à

$XVGHU0DWUL[= ODVVHQVLFKGLH,PSHGDQ]HQ= = XQG= EHVWLPPHQ

=

=

=

-=

=




+ =

FRVb

O

- M=




FRVb

O

- M=


VLQb

O

VLQb

O

=

=

=

=

!"#

- =

=

=

!"#

FRVb

O

+

FRVb

O

+

M=

M=

!"#

!"#

=

VLQb

!"#

- =

O

!"#

VLQb

O

=

=

=

=

FRV $ b O

-

$ M=

% ()* $

=

()*

VLQb

O

'HU :HOOHQZLGHUVWDQG GHV /HLWXQJVHOHPHQWV LP 0DNURPRGHOO VROOWH XQJHIlKU GHP

:HOOHQZLGHUVWDQGGHUPRGHOOLHUWHQ/HLWXQJVVWUXNWXUHQWVSUHFKHQ

%HUFNVLFKWLJXQJGHU(LQNRSSOXQJYRQ)HOGHUQ

'LH(LQNRSSOXQJYRQ)HOGHUQNDQQGXUFKGLH(UJlQ]XQJPLW6WURPTXHOOHQEHUFNVLFKWLJW

ZHUGHQ+LHU]XZLUG]XQlFKVWHLQ0DNURPRGHOODXVGHU/HLWXQJVVWUXNWXUHQWVSUHFKHQG

GHPYRUKHULJHQ$EVFKQLWWEHVWLPPWRKQHGLH)HOGHU]XEHUFNVLFKWLJHQ$QVFKOLH‰HQG

ZHUGHQ GLH 6WU|PH DQ GHQ $EVFKOVVHQ GHU 6WUXNWXU EHL )HOGHLQNRSSOXQJ JHPHVVHQ

RGHU PLW HLQHP 0R00RGHOO EHUHFKQHW 'LH $EVFKOVVH VLQG GDEHL NXU]JHVFKORVVHQ

'DV 0DNURPRGHOO ZLUG GDQQ XP GLH 6WURPTXHOOHQ HUZHLWHUW ,Q %LOG LVW GHU $EODXI

VFKHPDWLVFKGDUJHVWHOOW


+, -.-/ 0-/ 12,

) # *

¤¥

%HVWLPPXQJYRQ

= w= w= w=

O

¦ § ¨ ©

¤& ' (

¢¡ ¤£

)HOGHLQNRSSOXQJ

¤£

¤& ' ( ¢¡

£ % ¡ % ¤¥

%HVWLPPXQJYRQ

, ¦ w , § w

%HUHFKQXQJGHU

6\VWHPUHDNWLRQ

!" #$

%LOG %HUHFKQXQJGHU)HOGHLQNRSSOXQJPLW0DNURPRGHOOHQ

10 0 A bsc hluss 1 Ohm

10 -1 A bsc hlus s 10 Ohm

10 -1

M oM Z1

M ac ro Z1

M oM Z1

M ac ro Z1

S trom [A ]

10 -2

S trom [A ]

10 -2

10 -3

0 0.5 1

Frequenz [Hz ]

1.5 2

x 10 8

10 -3

0 0.5 1

Frequenz [Hz ]

1.5 2

x 10 8

10 -2 Abschlus s 100 Ohm

10 -2 A bschluss 1000 Ohm

M oM Z1

M acro Z1

S trom [A ]

10 -3

M oM Z1

M acro Z1

S trom [A ]

10 -3

10 -4

0 0.5 1

Frequenz [Hz ]

1.5 2

x 10 8

10 -4

0 0.5 1

Frequenz [Hz ]

1.5 2

x 10 8

%LOG %HUHFKQXQJGHU)HOGHLQNRSSOXQJ9PÃHQGILUHµ>@PLW0DNURPRGHOOHQXQG

UHLQHQ0R0%HUHFKQXQJHQLQ$EKlQJLJNHLWYRQGHQ$EVFKOXVVZLGHUVWlQGHQ


$OV%HLVSLHOIUHLQ(UJHEQLVHU]LHOWPLW0DNURPRGHOOHQZLUGKLHUGLH(LQNRSSOXQJHLQHU

HEHQHQ:HOOHLQHLQHUHFKWHFNI|UPLJH6FKOHLIHPLWHLQHU/lQJHYRQFPGLHDQHLQH

KRPRJHQH =ZHLGUDKWOHLWXQJ YRQ P /lQJH DQJHVFKORVVHQ LVW JH]HLJW 0LW GHU

0RPHQWHQPHWKRGHZXUGHQIUGLH6FKOHLIHXQGIUGLH/HLWXQJMHZHLOV0DNURPRGHOOHIU

63,&(JHELOGHW)UGLH6FKOHLIHZXUGHHLQ0DNURPRGHOOQDFK%LOGXQGIUGLH/HLWXQJ

HLQ 0RGHOO QDFK %LOG JHQHULHUW )U YHUVFKLHGHQH ,PSHGDQ]HQ VLQG LQ %LOG GLH

(UJHEQLVVH PLW GHQ 0DNURPRGHOOHQ (UJHEQLVVHQ DXV UHLQHQ 0R0%HUHFKQXQJHQ

JHJHQEHUJHVWHOOW


=XVDPPHQIDVVXQJ

,Q GLHVHP %HLWUDJ ZXUGH GDUJHVWHOOW ZLH GXUFK GLH 8QWHUWHLOXQJ GHU 9HUNDEHOXQJ

LQQHUKDOE YRQ .UDIWIDKU]HXJHQ VRZLH GLH %LOGXQJ YRQ 7/6WUXNWXUHQ XQG 0DNUR

PRGHOOHQGLH%HUHFKQXQJGHU)HOGHLQNRSSOXQJHUIROJHQNDQQ'XUFKGLH9HUZHQGXQJ

YRQ0DNURPRGHOOHQXQGK\EULGHQ9HUIDKUHQZLUGGLH%HUHFKQXQJGHU)HOGHLQNRSSOXQJ

LQ VHKU NRPSOH[H /HLWXQJVVWUXNWXUHQ JHQDXHU VFKQHOOHU RGHU ]XP 7HLO EHUKDXSW HUVW

P|JOLFK:HLWHUKLQZXUGHDXIGLH%HKDQGOXQJYRQ OLQHDUHQ $EVFKOVVHQHLQJHJDQJHQ

XQG9HUIDKUHQ]XGHUHQ(LQELQGXQJLQ63,&(GDUJHVWHOOW

'LH 0DNURPRGHOOH N|QQHQ GXUFK YHUVFKLHGHQH DXI GHQ MHZHLOV ]X EHVFKUHLEHQGHQ

%HUHLFKRSWLPDODQJHSDVVWH9HUIDKUHQJHELOGHWZHUGHQ%HLVSLHOVZHLVH6WHFNHU/HLWHU

SODWWHQRGHU/HLWXQJHQEHUgIIQXQJHQODVVHQVLFKGDPLWSUl]LVHQDFKELOGHQ

'XUFK GLH $XIWHLOXQJ LQ 7HLOPRGHOOH PXVV QLFKW GDV NRPSOHWWH )DKU]HXJ ]XVDPPHQ

KlQJHQGJHUHFKQHWZHUGHQ'DGXUFKLVWHLQHGHXWOLFKVFKQHOOHUH%HUHFKQXQJP|JOLFK

XQG HLQPDO HUVWHOOWH 7HLOPRGHOOH N|QQHQ XQDEKlQJLJ YRQ GHQ $EVFKOVVHQ

ZLHGHUYHUZHQGHW ZHUGHQ (LQ ZHLWHUHU EHVRQGHUV ZLFKWLJHU 9RUWHLO LVW GLH 0|JOLFKNHLW

GHU(LQELQGXQJLQ1HW]ZHUNDQDO\VHSURJUDPPH63,&(1DKH]XEHOLHELJHQLFKWOLQHDUH

$EVFKOVVHODVVHQVLFKVRPLWEHKDQGHOQ

/LWHUDWXU

>@ &53DXO$QDO\VLVRI0XOWLFRQGXFWRU7UDQVPLVVLRQ/LQHV:LOH\,QWHUVFLHQFH

>@ 6)UHL5-REDYD&RXSOLQJRI,QKRPRJHQHXV)LHOGVLQWRDQ$XWRPRWLYH&DEOH

+DUQHVVZLWK$UELWUDU\7HUPLQDWLRQV ¡ ,QWHUQDWLRQDO=XULFK6\PSRVLXPRQ(0&


>@ ,(UGLQ061DNKOD5$FKDU&LUFXLW$QDO\VLVRI(OHFWURPDJQHWLF5DGLDWLRQDQG

)LHOG&RXSOLQJ(IIHFWVIRU1HWZRUNZLWK(PEHGGHG)XOO:DYH0RGXOHV,(((

7UDQVDFWLRQVRQ(OHFWURPDJQHWLF&RPSDWLELOW\9RO1R

>@ ZZZHLDRUJHLJLELVLELVKWP

>@ )+DVOLQJHU%8QJHU00DXUHU07U|VFKHU5:HLJHO(0&0RGHOLQJRI

1RQOLQHDU&RPSRQHQWVIRU$XWRPRWLYH$SSOLFDWLRQV ¡ ,QWHUQDWLRQDO=XULFK

6\PSRVLXPRQ(0&

>@ 58QEHKDXHQ6\QWKHVHHOHNWULVFKHU1HW]ZHUNHXQG)LOWHU52OGHQERXUJ9HUODJ


>@ 2%UXQH6\QWKHVLVRIDILQLWHWZRWHUPLQDOQHWZRUNZKRVHGULYLQJSRLQWLPSHGDQFH

LVDSUHVFULEHGIXQFWLRQRIIUHTXHQF\-0DWK3K\V

More magazines by this user
Similar magazines