Low-Pass Filter Effect in the Measurement of

!"#%$&(' %)&*,+-,"./10324)&*056(7' 8
94:%;%<>=@?BA4CEDGF&HJILK6?B:;3FM=@NL<OIL=QPRDGS7NBA>TVUWHYX[Z
^\ ]R_5`badcJef`
ghjiYkMlmYnVoqpsrhutvpvwjiYx^hjiyzhj{[tvpsrVo}|>x~y|[x[rV{>pn|tL||Vo|r5tv{>pvrOhjo*l{wOlY|[{[tvps|[xw&mBx[r5mLohj{^tvpxOxOmJ|5Oi
tL|[xV|.hj{[tvpvr5o|[x1tL|t|[{>xowf6}lLhjxxGot|[{1hjiy
lmB{|[okE{|>x>px[tvpf|Q|yjpmLw[t|[iw5rr5mL{pilLhj{hjo
o}|[o*{wj!tW|bp|[lWwjpitw|Vo|r5tv{>pvrOhjoJ|[iupi|O|[{>piBM ihf|Voqk¡>{wf/h¢i|Vtv,wj{O£.tW|wj{|Vtvpsrdps|VlLwjpiJt¤
wji%|~,wjmLoy¥iwft¦|§>lW|r5t¦tBhft¢hlmL{|[ok¨{|>x>px[tvpf|~|yjpmB©n|[Bhjf|>x^h@x~höwj6lLh@xx.ot|[{VªOiWx>t|huy
tL|M|§fpx>t|VirO|&wEx[wjQ|&rh>lLhurVpvtvpj|Mhjiy>«wj{piyjmYr5tvpj|&|[o}|[Q|[itxE,wjmLoynO|M|§>lY|r5t|yu
Oi¬tpxlLhOlW|V{^|l{|>xV|ViJth¥i%|Vtv,wj{O£tL|wj{|Vtvpsry|>x[r5{Opltvpswji®w~tL|owj6lLh@xOx¢ot|V{|s¯.|rbtEw
&mBx[r5mBohj{Qtvpxx>mJ|5±°¨|6poo6mBxV|~hy|>xVrV{|Vtvp}²b|y¥hjiyx>plop |ytvpxOxOmJ|Qw5y|[oq³¦|bqhi%|Vtv,wj{O£¨w
{|>x>px[twj{xVGwj{4tpxEw5y|VoRtL|4owj6lLh@xxMr[Bhf{hurbt|[{>px[tvpvrQwE&mBx[rVmLohj{4tvpxx>mJ|E6poo n|4f|[{>p ´|yu
µ L|R>mLiyuhjQ|ViJthjo{|h@x[wji4[wf{1tL|.owj6lLh@xx¢r[Bhf{hurbt|[{>px[tvpvrw&mBx[r5mLohj{.tvpxOxOmJ|px1tL| Vhur5t¡tBhft
|Vo|r5tv{>pvrOhjohr5tvpbpvtvktv{hjj|Vox^6ptzxVwjQ|rwfiWx>thjit¦j|[ow5r5ptvkzhjowjihupf|[i¨lLhft® ¶|5tL|^&mBx[r5o|
ńV{|[x¤M¡po|4tL|EQ|h@x>mL{|V|ViJtw¢tpxhurbtvpdptvkMpxEyuwji|hft¡xVwjQ|,R§|y¦lLwfpiJt µ W|Epiy|¶lW|[iyuhjiJt
jhj{OpshnVo|[x·tvpQ|Bªhjiy¸sxlLhur>|B¨rhfi¹nO|ªMh>lulW|y¬wjiJtwº|hr[¬wftL|V{[ µ L|öwj6lLh@xOxot|[{|s¯.|rbt
w5rOrVmL{Oxpi¨xlWhurO|Mywjhjpi
»,¼E½B¾´¿WÀWÁÂ¢Ã.Ä¿WÅ¶Á¾
Æ ÇÈÉYÊ´Ë}Ì}ÈÊVÍÎjÈÏWÍÊÐuÇÈÉWÊÑWÊ5ÒÓ[ÍOÌÔYÈÌÐuÇ¢ÐfÕJÊ5ËÊ5Ó[ÈÍÌ}ÓVÎfËLÎfÓ[ÈÌÖLÌÈ×Ø1ÌÈÉYÌ}ÇË}ÌÖLÌ}ÇWÙÐfÍÙuÎfÇYÌÒÚÒVÛ@ÐuÇWÊ´ÐfÕÈÊ5Ç
Ê5ÇYÓ[ÐuÏJÇÈÊVÍÒEÈÉWÊMÈÊVÍÚÒÜË}ÐbØÝÔJÎfÒÒ¢ÞJËÈÊVÍßÎfÇYÑÜÔÏWÍÊ5Ë×¨ÍÊ5ÒÌ}ÒÈÌ}ÖfÊ&ÚÊ5ÑYÌ}ÏYÚß¥àáãâ@äÛáæå@äÛáãç@äèOéMêWÍÐuÚ
ÈÉWÊ4ÖBÌ}ÊVØÔ%ÐuÌ}ÇÈÐfÕÇWÊVÈëØÐfÍìÈÉWÊVÐfÍ×ÌÈ1Ì}ÒìBÇWÐdØ1Ç*ÛYÈÉJÎjÈ1íJÏYÌË}ÑYÌ}ÇWÙÎfÇ×Èë×Ô%ÊEÐfÕ¡ÕÍÊ5îBÏWÊ5ÇYÓ[×ÒÊ5ËÊ5Ó[ÈÌÖfÊ
ÞJË}ÈÊVÍÒàvÏYÒÌÇWÙMÓ[ÐuÇÈÌ}ÇBÏWÐuÏYÒ1Ê5ËÊ5ÚMÊ5ÇÈÒOèOÛJÓVÎjÔJÎfÓVÌ}ÈÌÖfÊ4ÎfÇYÑïdÐfÍ1Ì}ÇYÑYÏJÓ[ÈÌÖfÊ¦Ê5ËÊ5ÚMÊ5ÇÈÒ1ÎjÍÊEÍÊ5îÏYÌ}ÍÊ5Ñ*éêWÐfÍ
ÈÉWÊ4ÑWÊ5ÒÓ[ÍÌÔJÈÌÐuÇ^ÐfÕ ÈÉYÊEËÐbØÝÔÎfÒÒÞJËÈÊVÍ1Ê[ðÊ5Ó[ÈÐfÕRÈÌ}ÒÒÏWÊfÛWÈÉWÊEÕvÏYÇYÑJÎfÚMÊ5ÇÈÎfË*ÑJÌðÊVÍÊ5ÇÈÌ}ÎfË%Ê5îBÏYÎjÈÌÐuÇÛ
ÇYÎfÚÊ5Ë×7ñ¨Î@òBØ´Ê5Ë}ËsóæÒ&ÓVÏWÍÍÊ5ÇÈ&Ë}Î5ØÛÚ4ÏYÒÈ4í%Ê~ÒÐuËÖfÊ5Ñ*ézô¦ÏWÊ~ÈÐ¥ÈÉWÊÓ[ÐuÚMÔË}Ì}ÓVÎjÈÊ5Ñ7ÕÐfÍÚQÎfË}Ì}ÒÚÒ5Û ÈÉYÊ
ÕvÏYÇYÑYÎfÚÊ5ÇÈÎfËÍÊ5ÎfÒÐuÇÕÐfÍÈÉWÊ¢ËÐdØÝÔJÎfÒÒ´ÞJËÈÊVÍÊ[ð%Ê5Ó[ÈÐfÕGÈÌÒÒÏWÊ.ÍÊ5ÚÎfÌ}ÇJÒ´ÒÐuÚMÊVØ1ÉYÎjÈÉYÌ}ÑJÑWÊ5Ç*é¡õÒÌÇWÙ
Î¦ÑYÌ}ÒÓ[ÍÊVÈÌöVÊ5ÑÚMÐBÑYÊ5ËÐfÕÈÉWÊÔÉ×LÒÌÐuËÐfÙuÌÓVÎfËÔYÍÐBÓ[Ê5ÒÒÊ5ÒRÈÉJÎjÈ¡ÓVÎfÏJÒÊÊ5ËÊ5Ó[ÈÍÌ}ÓVÎfËLÎfÓ[ÈÌÖLÌÈ×4Ø1ÌÈÉYÌÇ¢ÈÌ}ÒÒÏYÊfÛ
ÈÉWÊ4ÇYÎjÈÏWÍÊ¢ÕÐfÍÈÉWÊË}ÐbØÝÔJÎfÒÒÞJËÈÊVÍÊ[ð%Ê5Ó[È1ÐfÕ¡ÈÌ}ÒÒÏWÊ¢ÓVÎfÇí%Ê¢í%ÊVÈÈÊVÍÖfÊVÍÌÞYÊ5ÑªÎfÇYÑÓVË}ÎjÍÌÞJÊ5Ñ*é
ÆÇ&ÈÉYÌ}Ò6ÔÎjÔÊVÍ6Ø´ÊÒÈÎjÍÈ,Ø1ÌÈÉMÎEÒÉYÐfÍÈ¡ÔJÉ×LÒÌÐuË}ÐfÙuÌ}ÓVÎfËWÑWÊ5ÒÓ[ÍÌ}ÔYÈÌÐuÇÐfÕ%Ê5ËÊ5Ó[ÈÍÌ}ÓVÎfËYÎfÓ[ÈÌ}ÖBÌÈë×ÌÇMË}ÌÖLÌ}ÇWÙ
ÐfÍÙuÎfÇJÌ}ÒÚÒVé¡÷.Ò,Î¢ÒÌ}ÚÔJË}ÌÞYÊ5ÑÚMÐLÑWÊ5ËLØ´ÊØ1Ì}Ë}ËÈÉWÊ5ÇMÔJÍÊ5ÒÊ5ÇÈÎEÇWÊVÈØ´ÐfÍì&ÐfÕÍÊ5ÒÌ}ÒÈÐfÍOÒ6Ø1ÉYÌ}ÓOÉMÌ}Ò6ÑWÍÌ}ÖfÊ5Ç
íB×¨ÒÐuÚÊ&ÚÐbÖLÌ}ÇWÙÓVÏWÍÍÊ5ÇÈ¢ÒÐuÏWÍÓ[Ê5ÒVéEø1ÉYÌ}Ò.ÎjÍÍÎfÇWÙfÊ5ÚMÊ5ÇÈ¢Ì}Ò¦ÒÏWùQÓVÌ}Ê5ÇÈ.ÕÐfÍ¦ÈÉWÊMÑWÊ5ÒÓ[ÍÌÔYÈÌÐuÇ¨ÐfÕ,ÈÉYÊ
ÇYÎjÈÏYÍÊªÐfÕ¢ÈÉWÊËÐbØÝÔJÎfÒÒ~ÞJËÈÊVÍÊ[ð%Ê5Ó[ÈÐfÕ¢ÈÌ}ÒÒÏWÊféøÉYÊªËÐbØÝÔJÎfÒÒ~ÞJËÈÊVÍQÊ[ð%Ê5Ó[È^ÐfÕ¢ÈÌ}ÒÒÏWÊ¨Ì}ÒÈÉWÊ5Ç
ÑWÊ5ÒÓ[ÍÌí%Ê5ÑÏYÒÌ}ÇYÙÇWÊVÈëØÐfÍìÈÉWÊVÐfÍÊVÈÌ}Ó¢ÈÊVÍOÚÒVé
ú¼ûü´ýþWÅ¶Á´ÿ¶Áý
ËÊ5Ó[ÈÍÌ}ÓVÎfË¡ÎfÓ[ÈÌÖLÌÈ×¨Ø1ÌÈÉYÌÇÈÌ}ÒÒÏWÊÌÒÓVÎfÏYÒÊ5ÑzÑYÏWÊÈÐ^ÈÉYÊÈÍOÎfÇYÒÔ%ÐfÍÈ.ÐfÕ,Ô%ÐuÒÌÈÌÖfÊ&ÎfÇYÑ¥ÇWÊVÙuÎjÈÌÖfÊ
ÌÐuÇJÒVé6øÉYÌ}Ò,ÈÍÎfÇYÒÔ%ÐfÍÈÐfÕGÌÐuÇYÒ´Ì}Ò´Ì}ÇQÊ[ð%Ê5Ó[ÈØ1ÉWÊ5Ç^Î4ÇYÊVÍÖfÊÐfÍÎÚ4ÏJÒÓVËÊ.ÞYí%ÊVÍ,í%Ê5Ó[ÐuÚMÊ5ÒÎfÓ[ÈÌÖfÊfé,øÉYÊ
ÚÎfÇ×¥íJÌÐLÓÉWÊ5ÚQÌ}ÓVÎfË¡ÔYÍÐLÓ[Ê5ÒÒÊ5Ò¢ÈÉJÎjÈËÊ5ÎfÑzÈÐ¨ÈÉYÌ}Ò¢ÎfÓ[ÈÌÖLÌÈ×zÎjÍÊ~ÇWÐfÈÑYÌ}ÒÓVÏYÒÒÊ5Ñ¥ÉWÊVÍÊféQÆ¶ÇYÒÈÊ5ÎfÑzØÊ
ÎfÒÒÏYÚMÊEÒÐuÚMÊÙuÌÖfÊ5ÇªÑYÌÒÈÍÌíJÏYÈÌÐuÇÐfÕ6ÓVÏWÍÍÊ5ÇÈÒÐuÏYÍÓ[Ê5ÒVé
ÚÏYÒÓVËÊ¢ÞJíÊVÍ
ÓVÏYÍÍÊ5ÇÈÑYÌ}ÒÈÍÌ}íJÏWÈÌÐuÇ
Figure 1. Electrical activity of a muscle fiber (schematically).
ø ÉYÊÊ5ËÊ5Ó[ÈÍÌ}ÓVÎfËÎfÓ[ÈÌÖLÌÈ×¥ÐfÕÎÚÏYÒÓVËÊQÞYí%ÊVÍEØ1ÌÈÉYÌÇ¥ÈÌ}ÒÒÏWÊÌÒEÒÓÉYÊ5ÚÎjÈÌ}ÓVÎfË}Ë×zÑWÊ5ÒÓ[ÍÌí%Ê5ÑÌ}ÇzÞJÙjÝ
ÏWÍÊjéø1ÉWÊÚÏYÒÓVËÊ4ÞYí%ÊVÍÌ}ÒÎQÓ[×LË}Ì}ÇYÑWÊVÍ1Ø1ÌÈÉªÎ^ÑYÌ}ÎfÚÊVÈÊVÍÐfÕÒÐuÚÊÚ ÎfÇYÑÎQËÊ5ÇWÙfÈÉ¨ÐfÕÒÐuÚMÊ
Ó[Ê5ÇÈÌ}ÚMÊVÈÊVÍÒ5é^øÉYÊÓVÏWÍÍÊ5ÇÈEÑYÌ}ÒÈÍOÌíJÏWÈÌÐuÇÓ[ÐuÇYÒÌÒÈÒ¢ÐfÕÎYÐdØÐfÕÔ%ÐuÒÌÈÌÖfÊÎfÇYÑÇWÊVÙuÎjÈÌÖfÊQÌÐuÇJÒ¢í%Ê[Ý
ÈëØÊVÊ5Ç¬ÈÉWÊÌ}ÇYÇWÊVÍMÎfÇYÑ3ÐuÏYÈÊVÍÔJÎjÍÈ&ÐfÕ.ÈÉWÊÚ4ÏJÒÓVËÊÞYí%ÊVÍ5éÆÇ3ÞYÙuÏWÍÊ
ÈÉYÊÎjÍÍÐbØÒÌ}ÇYÑYÌÓVÎjÈÊ^ÈÉYÊ
ÍÊ5ÒÏYËÈÌ}ÇWÙÔ%ÐuÒÌ}ÈÌÖfÊQÓVÏWÍÍÊ5ÇÈJÐbØEéøÉYÊ~ÓVÏWÍÍÊ5ÇÈJÐbØ ÎfËÐuÇWÙªÈÉYÊQÔ%ÊVÍÌ}ÚMÊVÈÊVÍÐfÕÈÉWÊ~ÚÏYÒÓVËÊQÞYí%ÊVÍ
ÒÉJÎfË}Ëí%Ê4Ó[ÐuÇJÒÈÎfÇÈVé¦øÉWÊ4ÇWÊVÈ.ÓVÏYÍÍÊ5ÇÈYÐdØÌ}ÇªÐfÍ¦ÐuÏWÈ1ÐfÕÈÉYÊ4ËÐLÓVÎfËGÍÊVÙuÌÐuÇªÐfÕ6ÈÉJÌ}ÒÓVÏYÍÍÊ5ÇÈÑYÌ}ÒÈÍÌÝ
íJÏYÈÌÐuÇÉYÎfÒÈÐ¨í%ÊLéªÆ¶ÇÐfÈÉWÊVÍ&ØÐfÍÑJÒVÛ ÇYÐ¨ÓVÏWÍÍÊ5ÇÈYÐbØ1Ò4Ì}ÇÐfÍÐuÏWÈ4ÐfÕÈÉYÌ}ÒË}ÐBÓVÎfË,ÍÊVÙuÌÐuÇ*éøÉYÊ
ÓVÏWÍÍÊ5ÇÈÑJÌ}ÒÈÍÌíÏWÈÌÐuÇ~ÈÍÎ5ÖfÊ5Ë}Ò1Ø1ÌÈÉÎÓ[ÐuÇJÒÈÎfÇÈÖfÊ5ËÐLÓVÌÈ× ÎfË}ÐuÇWÙÈÉWÊEÚÏYÒÓVËÊ¢ÞJíÊVÍbé
¼þWÃÀÅ¾
¿Yü¡ÿRÄ¿WÀJÅÄ,ÿÄ¿WÅ.Åë¿fý
øÉYÊ&ÓVÏYÍÍÊ5ÇÈ¦ÑJÌ}ÒÈÍÌíÏWÈÌÐuÇªÌÒ.ÎÓ[ÐuÇÈÌ}ÇWÐuÏJÒEÑYÌ}ÒÈÍOÌíJÏWÈÌÐuÇÐfÕ´ÓVÏWÍÍÊ5ÇÈ¢ÒÐuÏYÍÓ[Ê5ÒVé&øÉWÊ&ÐuÏWÈÊVÍEÔJÎjÍÈ
ÐfÕRÈÉWÊ¢Ú4ÏYÒÓVËÊ¦ÞYí%ÊVÍ¦àÈÌ}ÒÒÏWÊdèÌ}ÒÎÔJÏWÍÊ5Ë×MÍÊ5ÒÌ}ÒÈÌÖfÊ¢ÚMÊ5ÑJÌ}ÏYÚé¡ô.ÊVÔÊ5ÇJÑYÌ}ÇWÙ4ÐuÇÈÉWÊ¢Ó[ÐuÇYÑYÏYÓ[ÈÌÖLÌÈë×QÐfÕ
ÈÉYÌÒ6ÈÌ}ÒÒÏYÊÎÓ[ÊVÍÈÎfÌ}ÇÓVÏWÍÍÊ5ÇÈ6ÞJÊ5Ë}Ñ&Ø1Ì}Ë}ËBí%ÊÊ5ÒÈÎjíJËÌ}ÒÉWÊ5Ñ*é øÉWÊÚMÊ5ÎfÒÏWÍÊ5ÚMÊ5ÇÈÐfÕÊ5ËÊ5Ó[ÈÍÌ}ÓVÎfËYÎfÓ[ÈÌ}ÖBÌÈë×
Ø1Ì}ÈÉYÌ}ÇË}Ì}ÖBÌ}ÇYÙMÐfÍÙuÎfÇYÌ}ÒÚQÒ1Ì}ÒÔ%ÊVÍÕÐfÍOÚMÊ5ÑíB×ÎfÑYÑYÌ}ÇYÙQÒÐuÚMÊ4ìBÌ}ÇJÑÐfÕ6Ê5ËÊ5Ó[ÈÍÐLÑWÊ5ÒVéÆ¶ÇªÙfÊ5ÇWÊVÍÎfËsÛÈÉWÊ5ÒÊ
Ê5ËÊ5Ó[ÈÍÐBÑWÊ5ÒÑYÌ}ÒÈÏWÍízÈÉWÊ^ÓVÏWÍÍÊ5ÇÈEÞYÊ5Ë}Ñé´Ê5ËÐdØEÛ¡ØÊ~Ø1Ì}Ë}Ë6ÎfÒÒÏYÚMÊQÎfÇ7ÎjÍÍÎfÇWÙfÊ5ÚMÊ5ÇÈØ1ÉYÌ}ÓOÉÌ}ÒÇYÐfÈ
ÑYÌÒÈÏWÍí%Ê5Ñ*é
¼ ¾¿!Á´À#" Á%$À&RþWÅþ¿BÁ´ÀYþ
ê¡ÌÙuÏWÍÊ¢ç&ÌÒ´ÎMÑJÌ}ÒÓ[ÍÊVÈÌöVÊ5ÑÑWÊ5ÒÓ[ÍÌÔYÈÌÐuÇ~ÐfÕ¡ÎjíÐdÖfÊEÓ[ÐuÇYÒÌ}ÑYÊVÍÎjÈÌÐuÇYÒVé6Æ¶ÈÌ}ÒÎMÒÇYÎjÔJÒÉWÐfÈÕÐfÍÎ&ÙuÌÖfÊ5Ç
ÈÌ}ÚÊ~Ô%ÐuÌ}ÇÈVéªøÉWÊ~Ô%ÐfÈÊ5ÇÈÌ}ÎfËÒ')(*à+*èEÎfÇJÑ,'.-Yà+*èÎjÍÊ^ÕÏJÇYÓ[ÈÌÐuÇYÒ4ÐfÕÈÉWÊËÐBÓVÎjÈÌ}ÐuÇ/*Wé¥ô¦ÏWÊ^ÈÐÈÉYÊ
ÖfÊ5ËÐLÓVÌÈë× ÛLÎfÇÐfíÒÊVÍÖjÎjÈÌÐuÇÐfÕGÈÉWÊ¦Ô%ÐfÈÊ5ÇÈÌ}ÎfË%ÑYÌ}ÒÈÍÌ}íJÏWÈÌÐuÇMÕÐfÍÎÙuÌÖfÊ5ÇËÐLÓVÎjÈÌÐuÇ*MËÊ5ÎfÑYÒ´ÈÐMÈÌ}ÚÊ[Ý
ÑWÊVÔ%Ê5ÇYÑJÎfÇÈÕvÏYÇYÓ[ÈÌ}ÐuÇYÒ')(à+*10 32 èÎfÇYÑ
'.-Yà+*40 32 èOéø1ÉYÌ}ÒÌ}Ò1ÈÉWÊEÖLÌÊVØÔ%ÐuÌ}ÇÈVÛWØ1ÉWÊ5ÇÈÉYÊEÊ5ËÊ5Ó[ÈÍÌ}ÓVÎfË
ÎfÓ[ÈÌÖLÌÈë×Ø1ÌÈÉJÌ}ÇË}Ì}ÖBÌ}ÇYÙ1ÐfÍÙuÎfÇYÌÒÚÒ Ì}Ò¡ÚMÊ5ÎfÒÏWÍÊ5Ñé øÉYÊ´ÒÔÎfÓ[Ê[ÝÑWÊVÔ%Ê5ÇYÑYÎfÇÈ¡ÎfÇJÑ4ÈÉYÊ´ÈÌÚMÊ[ÝÑWÊVÔ%Ê5ÇYÑYÎfÇÈ
ÑWÊ5ÒÓ[ÍÌÔYÈÌÐuÇJÒ1ÓVÎfÇí%Ê4ÚÎjÔYÔ%Ê5ÑªÐuÇÈÐÊ5ÎfÓÉ¥ÐfÈÉYÊVÍ&àvÓ[ÐuÇYÒÈÎfÇÈ¢ÖfÊ5ËÐLÓVÌÈë× èOé¦øÉWÊÑWÊ5ÒÓ[ÍÌÔJÈÌÐuÇÐfÕÈÉYÊ
ËÐdØÝÔJÎfÒÒÞJËÈÊVÍÊ[ð%Ê5Ó[ÈÌ}ÒÔ%ÊVÍÕÐfÍÚMÊ5ÑÏJÒÌ}ÇWÙ&ÈÉWÊEÒÔÎfÓ[Ê[ÝÑWÊVÔ%Ê5ÇYÑYÎfÇÈ1ÑWÊ5ÒÓ[ÍÌ}ÔYÈÌÐuÇ*é
5zÊ´ÑWÊ5ÒÓ[ÍÌí%Ê¡ÈÉWÊ,Ó[ÐuÇÈÊ5ÇÈÒGÐfÕLÞYÙuÏWÍÊ,çÌ}ÇEÒÐuÚÊ,ÚMÐfÍÊ,ÑYÊVÈÎfÌ}ËséRø1ÉWÊÓVÏWÍÍÊ5ÇÈÒÐuÏWÍOÓ[Ê5ÒGÚMÐLÑWÊ5Ë}ÌöVÊ6ÈÉYÊ
ÓVÏWÍÍÊ5ÇÈ6YÐbØ ÈÉWÍÐuÏWÙuÉMÈÉYÊ1ÒÏWÍÕvÎfÓ[ÊÐfÕ%ÈÉWÊ1ÚÏYÒÓVËÊ1ÞYíYÍÊfé¡øÉWÊÕvÎfÓ[È,ÐfÕ*ÎEËÐLÓVÎfËYÓVÏWÍÍÊ5ÇÈÑJÌ}ÒÈÍÌíÏWÈÌÐuÇ
Ì}Ò~ÕvÏYËÞJË}Ë}Ê5Ñ àvÇWÐ3ÓVÏWÍÍÊ5ÇÈJÐbØ1Ò^ÐuÏWÈ^ÐfÕÈÉWÊ¥ËÐLÓVÎfË1ÍÊVÙuÌÐuÇèOé/øÉWÊÈÌ}ÒÒÏYÊ¨Ì}Ò^Ó[ÐuÇYÒÌ}ÑYÊVÍÊ5Ñ¬ÈÐ3í%Ê¨Î
ÉWÐuÚÐfÙfÊ5ÇWÊVÐuÏYÒVÛYÎfÇYÌÒÐfÈÍÐfÔJÌ}Ó1ÚMÊ5ÑYÌ}ÏYÚé øÉYÊ1ÍÊ5ÒÌÒÈÌÖfÊ.ÔYÍÐfÔ%ÊVÍÈÌÊ5ÒÑWÐ4ÇWÐfÈÓÉJÎfÇWÙfÊ¢ÎfËÐuÇWÙÈÉWÊ4*fÝÎ@òLÌ}Ò
ÎfÇYÑ7ÈÉWÊÎfÇYÌ}ÒÐfÈÍÐfÔ×ÕvÎfÓ[ÈÐfÍMÌ}Ò87#9jé:'#(%à+*è4Ì}Ò4ÈÉWÊ~ÇWÊ5ÎjÍ&ÞYí%ÊVÍ4ÔÐfÈÊ5ÇÈÌ}ÎfË´ÑYÌ}ÒÈÍOÌíJÏWÈÌÐuÇzÎfÇJÑ,'.-Yà+*è
Ì}Ò.ÈÉWÊ&ÕvÎjÍ¦ÞYí%ÊVÍÔ%ÐfÈÊ5ÇÈÌ}ÎfË¡ÑYÌ}ÒÈÍÌ}íJÏWÈÌÐuÇ*é5zÊÎfÒÒÏYÚÊ&Î^ÖfÊVÍ×¨ÈÉYÌ}Ç¨ÔJÌÊ5Ó[ÊÐfÕ,ÈÌ}ÒÒÏWÊféE÷!ÐuÇYÊ[ÝË}Î5×fÊVÍ
ÇWÊVÈëØÐfÍìÐfÕRÍÊ5ÒÌ}ÒÈÐfÍÒÒÉYÎfË}Ëí%ÊEÒÏWùQÓVÌÊ5ÇÈÕÐfÍ1ÌÈÒÑWÊ5ÒÓ[ÍÌÔYÈÌÐuÇé
'.-Yà+* 9 è
' -Jà+*
>è
7 9
')(à+* 9 è
'.-Wà+*bè
7 9
'.-Wà+*
[è
7 9
7 9
'.-Yà+* 9 è
7 9
*
')(à+* 9 è
*jÝÎ@òWÌ}Ò
Figure 2. Discrete network of resistors
¼.Åþ¿ ¾.Ä Á%$/¿WÀ&,¾.þ $ RÀ $VÃ.¾.Ä¿YÅ¶Á´¾
.õ ÒÌ}ÇWÙÒÔÎfÓ[Ê[ÝÌ}ÇÖjÎjÍÌ}ÎfÇJÓ[ÊÎfÇYÑzË}Ì}ÇWÊ5ÎjÍOÌÈ×Ø´ÊMÔYÍÐdÖfÊÈÉWÊMÊ[òWÌ}ÒÈÊ5ÇYÓ[ÊMÐfÕÎÈÍÎfÇYÒÕÊVÍ¢ÕvÏYÇYÓ[ÈÌÐuÇéÊVÈ
ÏYÒ.Ó[ÐuÇYÒÌÑWÊVÍÎ^ÒÌ}ÇWÙuË}ÊÓVÏWÍÍÊ5ÇÈÒÐuÏWÍÓ[Ê4Ë}ÐBÓVÎjÈÊ5Ñ¥ÎjÈ ~ÎfÒ.ÑWÊVÔJÌÓ[ÈÊ5Ñ¨Ì}ÇªÞYÙuÏWÍÊBé1øÉWÊÓ[ÐuÇYÑYÌÈÌ}ÐuÇ
ÐfÕ6ÎËÐLÓVÎfË*ÓVÏWÍÍÊ5ÇÈÑYÌÒÈÍÌíJÏYÈÌÐuÇ~ÌÒÕÏJËÞJË}ËÊ5Ñé
ÉYÐÐuÒÌÇWÙ4ÈÉYÊ.ÖjÎfË}ÏWÊ.ÐfÕGÈÉYÊEÓVÏWÍÍÊ5ÇÈÒÐuÏWÍÓ[Êá @ä¦ÒÉYÎfË}Ë%ËÊ5ÎfÑ^ÈÐMÈÉWÊàvÏYÇWìLÇWÐdØ1ÇèÔÐfÈÊ5ÇÈÌ}ÎfË}Ò
')(á ä! "á ä
à bè
'.-Wá ä! #já ä$
àsçuè
ñªÐbÖLÌ}ÇWÙ¨ÈÉWÊ~ÓVÏWÍÍÊ5ÇÈÒÐuÏWÍÓ[Ê~ÈÐ¨Î¨ÑYÌð%ÊVÍÊ5ÇÈ4ËÐBÓVÎjÈÌ}ÐuÇ%&' à(á ä) bè¢Ø1Ì}Ë}ËÈÉWÊ5ÇËÊ5ÎfÑÈÐ¨ÈÉYÊ
Ô%ÐfÈÊ5ÇÈÌ}ÎfË}ÒàvÒÔÎfÓ[Ê[ÝÌ}ÇÖjÎjÍÌ}ÎfÇJÓ[Êdè
' ( á ä! "%á +*, ä
à-uè
' -Wá ä! #já +*,.
¶ä/
à10è
÷.Ç×ÎjÍÍOÎfÇWÙfÊ5ÚMÊ5ÇÈÐfÕ6ÓVÏWÍÍÊ5ÇÈÒÐuÏWÍÓ[Ê5Ò2á ä354fá äRËÊ5ÎfÑYÒÈÐÈÉWÊ¢Ô%ÐfÈÊ5ÇÈÌÎfË}ÒàvË}Ì}ÇYÊ5ÎjÍÌÈ×Yè
')(%á ä6 798,4fá ä;:"á *<ä
à uè
'.-Yá ä6 7 8 4fá ä;:=#já *,ä$
à->uè
øÉYÊ@?jÝÈÍÎfÇYÒÕÐfÍÚ(ÐfÕRÈÉWÊÔÐfÈÊ5ÇÈÌ}ÎfË}Ò' ( á äRÎfÇYÑ .' -Yá äRÎjÍÊ
A (à(?èB C à(?Bè:EDà(?Bè
A -Wà(?èB C à(?Bè:EFà(?èG
àåfè
àsâuè
'.-Wá *1çdä
7 9
' -Wá *>ä
' ( á *1çdä
'.-Yá @ä
7 9
' ( á *>ä
7 9
'.-Yá >ä
' ( á @ä
7 9
' ( á >ä
á @ä
Figure 3. Discrete network of resistors with single current source
÷ÈÍÎfÇYÒÕÊVÍÕvÏYÇYÓ[ÈÌ}ÐuÇÊ[òLÌ}ÒÈÒÎfÇYÑÓVÎfÇí%ÊEÓVÎfË}ÓVÏJË}ÎjÈÊ5ÑÏYÒÌÇWÙ
A -Wà(?è Fà(?è
à(?è A (à(?Bè Dà(?è àuè
¼ ,ÿÄÃ¦ÿ¡¿WÅ¶Á¾ Á6$^¿Wü¿WÀ&,¾.þ $ RÀ $VÃ.¾.Ä¿YÅ¶Á´¾
5 Ê^ÓVÎfË}ÓVÏYË}ÎjÈÊ~ÈÉWÊÈÍÎfÇYÒÕÊVÍ4ÕÏYÇJÓ[ÈÌÐuÇ
3à(?èOé 5zÊ^Ó[ÐuÇYÒÌ}ÑWÊVÍÎÇYÊVÈØ´ÐfÍìzÐfÕÍÊ5ÒÌ}ÒÈÐfÍÒEÎfÒÒÉWÐbØ1Ç
z
Ì}ÇªÞYÙuÏWÍÊ0Wé 5zÊ&ÎfÒÒÏJÚMÊÎfÇÎjÍíJÌÈÍÎjÍ×^ÇBÏYÚ4íÊVÍ1ÐfÕÓVÏWÍÍÊ5ÇÈÒÐuÏYÍÓ[Ê5Ò2á äéêYÐfÍÈÉWÊËÐLÓVÎjÈÌÐuÇ 6ÈÉYÊ
ÚMÊ5ÒÉÊ5îÏJÎjÈÌÐuÇYÒàvÓ[ÐuÚMÔÎjÍÊEØ1ÌÈÉÞYÙuÏWÍÊ0è
'.-Yá 6
ä -Wá ä&0 '.-Yá #0 >ä
à è
')(á 6
ä 7 9 fá ä 0 '.-Yá ä
à bè
ÚÏYÒÈí%Ê¦ÕvÏYËÞJË}Ë}Ê5Ñ*éRøÉYÊEÓVÏWÍÍÊ5ÇÈÒÌ}ÇÞYÙuÏYÍÊ 0QÓVÎfÇÈÉYÊVÍÊVÕÐfÍÊ¢íÊ¢Ê[òLÔYÍÊ5ÒÒÊ5ÑÎfÒ
-Yá 6
ä à ' -Já ä * ' -Já &0 >äè
à 5çuè
já 6
ä 7 9 à ')(á ä */'.-Yá äè à E uè
êYÏYÍÈÉWÊVÍ5ÛYÈÉYÊ5ÒÊEÓVÏWÍÍÊ5ÇÈÒÉYÎbÖfÊÈÐÕvÏYËÞË}ËJÈÉYÊEìBÇYÐfÈÊ5îÏYÎjÈÌ}ÐuÇàìBÇYÐfÈÕÐfÍ1ÈÉWÊEÔ%ÐfÈÊ5ÇÈÌÎfË'.-Wá äè
-Wá * >ä 0 á ä -Já ä à 0è
ÆÇYÒÊVÍÈÌÇWÙ&Ê5îÏYÎjÈÌ}ÐuÇYÒ5çÎfÇJÑ:E Ì}ÇÈÐMÈÉWÊEÊ5îBÏYÎjÈÌÐuÇ 0~ËÊ5ÎfÑYÒÈÐ
7 9 à ' -Wá 3* >ä */'.-Yá äè 0 ')(á ä */'.-Yá 3ä 7 9 à '.-Wá ä */'.-Wá )0 >äè
à uè
ÐfÍ
*7 9 '.-Wá *6>ä0à 30Mç!7 9 è '.-Yá ä *7 9 '.-Wá 0 >ä ')(%á /ä à E >uè
'.-Wá 3* >ä
' -Já ä
-Yá 3* >ä
7 9
'.-Yá #0 >ä
-Yá ä
-Wá )0 >ä
7 9
já * >ä
fá #0 >ä
'#(%á 3* >ä
7 9
@á ä
')(%á ä
á ä
')(*á #0 >ä
á #0 >ä
Figure 4. Discrete network of resistors with arbitrary current sources
E>MÓVÎfÇªÇYÐbØ¹í%Ê@?jÝÈÍÎfÇJÒÕÐfÍOÚMÊ5ÑÎfÇYÑÈÉYÊ5ÇÒÐuËÖfÊ5ÑÕÐfÍ1ÈÉYÊ¢ÈÍÎfÇYÒÕÊVÍÕvÏYÇYÓ[ÈÌÐuÇ 3à(?è
A -W(à ?è 3(à ?è à båfè
A (à(?è *7 9 ? 0¹à %0±ç!7 9 è */7 9 ? ÉYÐÐuÒÌÇWÙ ? ®Ê[òL
Ô ËÊ5ÎfÑYÒÈÐÈÉYÊ¢ÕÍÊ5îBÏWÊ5ÇYÓ[×^ÍÊ5ÒÔ%ÐuÇYÒÊ
à 5âuè
3à è %03ç!7 9 à &*zÓ[ÐuÒè ÆÇÞYÙuÏWÍÊ ^ÈÉWÊ&ÕÍÊ5îÏYÊ5ÇYÓ[×ªÍÊ5ÒÔÐuÇJÒÊ 3à è.Ì}Ò¦ÑWÍÎbØ1Ç¥ÕÐfÍEÑYÌð%ÊVÍÊ5ÇÈ.ÖjÎfË}ÏWÊ5Ò¦ÐfÕ´ÈÉWÊMÎfÇYÌ}ÒÐfÈÍÐfÔB×
ÕvÎfÓ[ÈÐfÍ 7 9 é,øÉWÊ¢ÕÍÊ5îBÏWÊ5ÇYÓ[×^ÍÊ5ÒÔ%ÐuÇYÒÊ¢ÉYÎfÒ1ÎfËØ´Îb×BÒÎËÐdØÝÔJÎfÒÒÓOÉYÎjÍÎfÓ[ÈÊVÍÌÒÈÌ}Ójé
îÏYÎjÈÌ}ÐuÇ
¼Á´¾.ÄÿÃ.þWÅ¶Á´¾.þ
÷ ÑWÊ5ÒÓ[ÍOÌÔYÈÌÐuÇMÐfÕ%ÈÉWÊ.ËÐbØÝÔJÎfÒÒÞËÈÊVÍ,Ê[ð%Ê5Ó[ÈÐfÕ%ÈÌ}ÒÒÏWÊ1ÉYÎfÒ,í%ÊVÊ5ÇÔYÍÊ5ÒÊ5ÇÈÊ5ÑQÕÍÐuÚÈÉWÊ1ÖLÌÊVØÔ%ÐuÌ}ÇÈ
ÐfÕ&ÇWÊVÈØ´ÐfÍì ÈÉWÊVÐfÍ×fé øÉJÌ}ÒÑWÊ5ÒÓ[ÍÌÔJÈÌÐuÇ®ÙuÌÖfÊ5ÒÎ±Ó[ÐuÚMÔYÍÊ5ÉWÊ5ÇYÒÌÖfÊzÌ}ÇJÒÌÙuÉÈ^ÈÐ±ÈÉYÊzÕÏYÇJÑYÎfÚMÊ5ÇÈÎfË
ÍÊ5ÎfÒÐuÇÐfÕÈÉWÊQË}ÐbØÝÔJÎfÒÒ¢ÞJËÈÊVÍEÊ[ð%Ê5Ó[ÈVéøÉWÊÈëØÐ¨ÈÊVÍÚÒ¨ÜËÐbØÝÔÎfÒÒEÞJË}ÈÊVÍßÎfÇYÑ¹ÜÔÏWÍÊ5Ë×¨ÍÊ5ÒÌ}ÒÈÌ}ÖfÊ
ÚMÊ5ÑJÌ}ÏYÚß^Ó[ÐÊ[òWÌ}ÒÈ¦Ø´Ê5Ë}ËséøÉWÊ&ÑWÊ5ÒÓ[ÍÌÔJÈÌÐuÇªÐfÕ´ÈÉWÊzÜËÐdØÝÔJÎfÒÒ¢ÞËÈÊVÍß~Ê[ðÊ5Ó[ÈÌÒ.ÑYÐuÇWÊMÏYÒÌ}ÇWÙÒÔJÎfÓ[Ê[Ý
ÑWÊVÔ%Ê5ÇYÑYÊ5ÇÈ&ÕvÏYÇYÓ[ÈÌÐuÇYÒ5é
øÉYÊÍÊ5ÒÏYËÈÌÇWÙ¨ÈÍOÎfÇYÒÕÊVÍMÕÏYÇJÓ[ÈÌÐuÇ±Ì}ÒMÇWÐuÇLÝÓVÎfÏJÒÎfËsé,5®ÉYÊ5Ç±ÑWÊ5ÎfË}Ì}ÇWÙ¥Ø1Ì}ÈÉ
ÒÔÎfÓ[Ê[ÝÑWÊVÔ%Ê5ÇYÑWÊ5ÇÈÕÏJÇYÓ[ÈÌÐuÇYÒVÛWÇWÐuÇWÝÓVÎfÏYÒÎfË}ÌÈë×^ÑYÐÊ5ÒÇYÐfÈ1ÉYÎjÍÚ ÍÊ5ÎfËÌö5ÎjíJÌ}Ë}Ì}È×fé
$ RÀ&¡¾.ÄRþ
"!$#&%(')+*,-*./0(12435.-*4764*'+289%:);2<7=&>/(!?.@28,A,B#CEDF:GHI%&*J&KL,-M&*0NA7KJ*0GH,-.O<77,/286,-
P 8,-*4C,-J2QSRUT?TTWV7XUYZ7[\Y^]_Q`ba8Z7[
aZcd`baeHfAg`b]-Yh7T5ZCi`jZkf-f\X@`jZIi'lmonbpq\r lps$tolvuClI'xw24#y$z{|o
0
10
-1
10
-2
10
-6
ÊVÙfÊ5ÇJÑ5
-4
-2
7 9 BÛ
0
2
79 jÛ
4
6
79 Figure 5. Frequency response for different anisotropy factors
lv =M7 J28.29% *\.A,O) 7NA*\#CF>
a oX@ZYh 'sor zm$t9vlC';$zsso
9.
G 2v,-M7*4G 2v,-J642x*28J<728,-y,-M&*/64.-* 647%&<&6,-.FGHI%&*4QFcd`ba8[@`Q]@Yh
p8 > 764"! *.-7K^2I'OO6$#&%I,-*K*4G 28'('*) .@28.@% =&*!
,+F -U*4(' 289% =& +
) %&*/. *4*\.@%(0%I<&,- GH*,-M&I%&N
d*4*46,A.-6$28,19*4 P .-&*4GHN/J P MC#&NAJK#C RUTTT V7XAYZ&[\Y^]_Q`baZ&[ a8Z cdQ` ae fAg`b]-Yh+T5ZCi`jZkf-f\X@`jZIi'?l8z&nU$q\r p8u8tûClI'
=2I<92v.A#:4z|lI
u/%o2-U*4*2 03F27%&*$%2v.$'54;.-687
%I,@286*.-K&'727% O92J% ! 5%&27%&*.-N49%oG0<& 2v,- ,-*6\M&7;:C<7*4NS *4*46,A.-G #C=<
K8.@2 P MI#CRUT?TTWV7XUYZ7[\Y^]_Q`ba8Z7[
aZcd`baeHfAg`b]-Yh7T5ZCi`jZkf-f\X@`jZIi'vlonU2>^q\r {{m$tI{|uo'xDF6,-*./4z|^mC
mv > 287
7D P&P *47M&*4G 27%?/@
%I6\M72 j*\.$B
AO`j[\]X-f\_Bf C@V+`je E
f D7`JiZ9Y@
h FSXAa$]@f\[-[-`jZIi);.-*4C,-J6* <G!O2QI
' HB76'($z|zo
s8 *\.A,d)7NA*# 27%? K*\. 9!S2v.A.$cd`bavfhJfA]_QX@`b]`j_JKMLON,&YZ7_Q`j_ Y8_Q`QPf(LRS9XUa$Y^]I?)*4I<&G
4z||o
) .-*NAN4'53 *3$T8.'
{v )+U NA*4j26kHC,A.@2<F27% *VI,A.@26*4J<&J28. P ,-*4C,-J2W19*4N = 26\,-;*L&*.:27% G0<&NA64*X1I*.-N4YL ]_ YFR8[-`bah;Z
D9]-YZg[Z' P 2K*N @t9$s|o'+4zszo
|8yD
C! [. NA'&=&[. & 2v.'3 'O272 P 28,-MC#C'I27%8\Fo1!O2v.-G 2(()+,-*4C,-J2@19* X
% .-G 28L26,-6^* 7*.^* L2
&M7GHK*4&*4<&N4'C287NA,A.- P 6*^<7GH*?647%&<&6,-.^] ,-M7*R .A3S28.@% P .-=7*4G9RUTT?T &
V XAYZ&[Y]_Q`baZ7[ aZEcd`Qae fAg `b]-Yh
TSZIi` Zkf-f\X\` ZIi'plonbplq\r_ >p^l$t7_>8u&'O*46*4G`*. 4z|mI

Download Report

Low-Pass Filter Effect in the Measurement of

Paperzz.com

Your Paperzz