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von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "imZ:=evalc(Im(Z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG,$*,%\"RG\"\"\"%&omegaGF(%\"LGF(,&F'!\"\"**F)\"\"#%\"CGF( F'F(F*F(F(F(,&*&F)F.F*F.F(*$F+F.F(F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Vergleich der oben angegebenen Betragsdefinition absZ und der MapleProzedur evalc(abs(Z))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "'[Z]'=simplify(absZ);\n'[Z]'=simplify(evalc(abs(Z)));" }}{PARA 0 "" 0 "" {TEXT 275 11 "Identisch !" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#% \"ZG*$**%\"RG\"\"#%&omegaGF)%\"LGF),**&F*F)F+F)\"\"\"*$F(F)F.**F*F)%\" CGF.F(F)F+F.!\"#**F*\"\"%F1F)F(F)F+F)F.!\"\"#F.F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$**%\"RG\"\"#%&omegaGF)%\"LGF),**&F*F)F+F)\"\" \"*$F(F)F.**F*F)%\"CGF.F(F)F+F.!\"#**F*\"\"%F1F)F(F)F+F)F.!\"\"#F.F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Allgemeine Terme f\374r" }} {PARA 0 "" 0 "" {TEXT -1 20 "1.Phasenverschiebung" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "'phi'=(phi);" }}{PARA 0 "" 0 "" {TEXT -1 18 "2. Res onanfrequenz" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "omega[0]=resofrq(re Z,imZ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$phiG,$-%'arctanG6#*(%&om egaG!\"\"%\"LGF+,&%\"RGF+**F*\"\"#%\"CG\"\"\"F.F2F,F2F2F2F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"!6$*(%\"LG!\"\"%\"CGF+*&F*\" \"\"F,F.#F.\"\"#,$F)F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Werte f \374r R, L und C:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "R:=1500; L:=29 0e-3; C:=5010e-12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG\"%+:" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG$\"$!H!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"%5]!#7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Resonanzfrequenz:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "omega[0]=reso frq(reZ,imZ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"!6$$! +hk]BE!\"&$\"+hk]BEF+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Diagramm von " }{XPPEDIT 270 0 "absZ(omega)" "-%%absZG6#%&omegaG" }{TEXT -1 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "plot(\{[[omega[0][1],0],[omeg a[0][1],10000]],absZ\},\nomega=0..100000);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Diagramm von" }{TEXT 274 1 " " }{TEXT 271 14 "evalc(abs(Z )):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "plot(\{[[omega[0][1],0],[ome ga[0][1],10000]],evalc(abs(Z))\},\nomega=0..100000);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Diagramm der " }{TEXT 272 19 "Phasenverschiebun g " }{XPPEDIT 273 0 "phi(omega)" "-%$phiG6#%&omegaG" }{TEXT -1 1 ":" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "plot(\{phi,[[omega[0][1],-1.57],[o mega[0][1],1.57]]\},\nomega=0..100000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 60 "Parallel- und Serienschaltungen ( Parallelkreise 2. Ordnung)\n" }{TEXT 285 1 "-" }{TEXT 330 10 "Sperrkre is" }{TEXT 331 22 ": Ohmscher Widerstand " }{TEXT 315 1 "R" }{TEXT 316 21 " und Selbstinduktion " }{TEXT 313 2 "L " }{TEXT 314 48 "in Rei he und dazu parallelgeschaltete Kapazit\344t " }{TEXT 312 2 "C\n" } {TEXT 317 21 "-Ohmscher Widerstand " }{TEXT 319 1 "R" }{TEXT 320 15 " \+ und Kapazit\344t " }{TEXT 324 2 "C " }{TEXT 318 54 "in Reihe und dazu \+ parallelgeschaltete Selbstinduktion " }{TEXT 325 2 "L\n" }{TEXT 321 17 "-Selbstinduktion " }{TEXT 326 1 "L" }{TEXT 323 15 " und Kapazit \344t " }{TEXT 327 2 "C " }{TEXT 322 59 "in Reihe und dazu parallelges chalteter Ohmscher Widerstand " }{TEXT 328 1 "R" }}{SECT 1 {PARA 3 "" 0 "" {TEXT 276 108 " Sperrkreis: Ohmscher Widerstand R und Selbstinduk tion L in Reihe mit dazu\n parallelgeschalteter Kapazit\344t C" } {TEXT 332 1 "\n" }{METAFILE 297 197 197 1 "iXmGh`B:Vmw=Z:VeQG:MZ= n]MZ:>xLZ:f:V[D:VbI>>S@m OC?:;B:m?B:K;_V:FQ;B:=B:=J:x:Zy=::BvyEyyryyyy:::vWya y=::BvZy=::ju[y=::BvZy=::Jw[y=::BxycyYjy;::JawYxI::Zr=yA:::[I:ry:::\\I vY:::VXyay=::Bxjy;::Jcwyyuy:::\\IvY:::NRyay=::BxybyIryyyyyA::J[[y=::Bx :yA::Ja[y=::Bx:yAZvyAxIjbwYxI::Zry[xy:vY:\\yYxyyyIJ`wyyuy:::\\yA:yAru; F:yryxIJw[y=::BxVZyyyyyY`YZC:v=xIJ]wYxI::ZrM:Syay=:jIQ=X;B::jAB:<::]BxyryxIj\\wyyuy:;I :<::v;B:wvYyqy[xy=xIJswYxIJZ?Z:::Yj;xyywY:tIxIJrwYxIJZC:Jr=j=xwy=yAxy= xyywY:tIxIJi[y=>ryyYyAZruyI:yAZvy=xIj^[y=FryyyyyY:lyAxy=jy;ByyZy=fUyay =VryyYyAZvy;jy;byYjy;FVry:A@yAZv=vY:tyIry:Oqysy:A@yAZv=vY:tIxIjb[y=FRv Y:lixy:vY:tIxIJbwYxIj[ky;Byly=xyywY:tyAvY:o@xIj;yyywY:lIjy;byvY:Kqysy: A>yAZv=vY:tIyAJ][y=VRvY:liry;yyy:byvY:OAxIj[ky;BylyAxyyyI:tIyAJjwYxIj[ ky;BytyIry:byvY:Ipysy:A@yA:yryxI:byvY:W@xIj[ky;:::tIyAJZ=jysy:A@yA:::b yvY:kI:yay=VRvY:::Zxmy;NWry:A@yA:::byvY:Mqysy:A@yA:::byyZy=^Sry:A@yA:: :byYjy;NVyay=VRvY:::Zxmy;nSry:A@yA:::byvY:[@xIj[ky;Jx=jysy:byvY:Y@xIj[ ky;Jr=jyxyyyI:tIyAJ`[y=FRvY:>Xysyyyy:byvY:u@xIjZky;JZw=xI:tIyAJewYxIjZ ky;JZ=qAxiy=Zxmy;ny:vYxIjZky;jZuyIry:byYjy;FWry:A@yA:=vyyqy;Zxmy;nXry: A@yA:=>yA:tIyAJe[y=VRvY:FJvY:byvY:mI:ry:A@yA:=>yA:tyIry:]qysy:A@yA:=>y A:tyAvY:epysy:A@yA:=>yA:tIyAJk[y=VRvY:Frymy;Zxmy;>Try:A@yA:;xyvY:byyZy =^Yry:A@yA:;yyvY:byry:[qysy:A@yA:[yYyqy;Zx]y=>Try:A@yA:[AyA:tIxIJi[y=V RvY:>xyVrymy;byry:k@xIj[ky;JvWZyyYyAZx]y=nRry:A@yA:kAvY:tIxIjowYxIj[ky ;JxWZymy;byry:KAxIj[ky;Jy=jIxiy=Zxy=xIJb[y=VRvY:B:ysyxI:tIxikyYxY\\wYx Ij[ky;Z:]y=Zx]yEjysyxYo[y=VRvY:::Zx]yqy:v;xy]wYxIj[ky;:::lyIrysI:IryyQ f[y=VRvY:::Zvy=xYvwZyMg[y=VRvY:::Zxy=xYjym;xIcpysywyYvYA@yA:::byyZyAvy Wjymj[yAyYvYyq[ky;:::tIlhyGryMlwYxYZIjysyA@yA:::by;B:;B:xyZyIY@xY:Ajyy iyyryyYyA:::byB:xy[yIKAxY:yAv[vy:vY:Zx]y=VVry:A@yAtyAty=xIyA:byy[y=NXry:A@yAtyIxy=xI yAxwywYbyy[y=vw:jyyIj;kysAwiIyj;kyKr=jYrybyry:=H:yqyyIj=yyywYwy=sIIyry A>yA[AxItyYry:_@xIj=kyoyI>yvv[yYJvY>Xrybyy[y=Vy:vYxIj;kys=[iIYj=kyKrMj yxiy]vyayuy:KAxIj;kys=[AI>yA[yIvYByxiy=>y:vYxIj;kys;[yIIryIryyqyKryAyA lIxIjs[y=vJvYXZyGZvyZymyKry=yAlyIvyy=fRry:I>yaA>V;jAryJrky[vyAxIJ_[y=v JvYX:;nAryJrky[v]y=FRry:I>ya=@jyAVy[y=kyIyqy[v]y=Vr:Zy=vJvY YvYByry:Y@xIj=kyCZxMxAjyyiy=kAyAlIxIJZ=Zyuy:I>ya:u;ry:sAyAlIxIjdsyxIj= kyCjZy=^YvYByry:e@xIj=xIya:=xIJyy;yAlIxIjr=:xIj=jySryy:yay=nYvYByry:wI :yay=v:vY@h=xYxIJyy;yAlIxIjlwYxIj=jyCryyjry:wy=xIByry:ipysy:I:yaZyi=Zy =nyAZy]v]y=fVry:I:yaZAZAZy=nYryByry:oAxIj=jyCv;r;ry:wAxIlIxIJjwYxIj=jy Cvx:yAJy[y]v]y=vr:Zy=v:vY:xqywYTyay=v:^yYjyoYxIHrZGjZMjyyywyjyIxIJj [y=ty=Jxy=yQxy:ya=HjyYj:UjvyxAVvyy=VXryZxy;yQxy=yQxy;ya=XjyYj;MZCx;R:y yyxIjkkyyIbyvYkyYvYsI:jIBZvyAjyyI:vymy?vywYIZ:L:Crysy[yAxyy;Jv=jys y:JjyIyQjyAI:>JJryryyA:<:xI:FRvY; yyFJ:wqAty:xyyyyy;JZ=jysy:jZky?V>jyqy:v]xMxwZvIZymy;Z:vYxI:FJvY=qy ?ry>YYBvXJrC:AZyyY:B:ry:j;kyGR>x:>Z::\\:yjyyI:B:ry:j;kyGJyQrC@nA;bAvIx I:B:ry:j;kyGJ>Y;BInI;J:@jysy:JZ=:xI:>Z:>Z:j;jy=r:>r=BrAJyy;yA:>Rry:J:B :V:yqy=vYxYxy=yA::>r:Zy=:;Z:j;jy;:::>Rry:J:=Z:jAry::::>Rry:JZWZ:jIry:: ::>Ryay=:::::::;@xI:::::::>Rry:::::::JZ[y=:::::::;@xI:::::::>Rry:::::: :JZ[y=:::::::;@xI:::::::>Rry:::::::JZW:>:1:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 76 "R:='R':L:='L':l:='l':C:='C':\nZ:='Z':Z1:='Z1':Z2:=' Z2':\nomega[0]:='omega[0]':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "An satz f\374r Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "eq1:=1/Z=1/Z1+1/Z 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/*$%\"ZG!\"\",&*$%#Z1GF( \"\"\"*$%#Z2GF(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Z1:=R+ I*omega*L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z1G,&%\"RG\"\"\"*(%\" IGF'%&omegaGF'%\"LGF'F'" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 80 "<- Zu r Ber\374cksichtigung des Ohmschen Widerstandes des Spulendrahtes hier \366ffnen!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Z1:=R+l+I*(om ega*L);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Z2:=1/(I*omega* C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z2G,$*(%\"IG\"\"\"%&omegaG! \"\"%\"CGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Z:=solve(e q1,Z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG*&,(%\"RG\"\"\"%\"lGF( *(%\"IGF(%&omegaGF(%\"LGF(F(F(,*F(F(**F+F(F'F(F,F(%\"CGF(F(**F+F(F,F(F 0F(F)F(F(*(F,\"\"#F0F(F-F(!\"\"F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Realteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "reZ:=simplif y(evalc(Re(Z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$reZG*&,&%\"RG\" \"\"%\"lGF(F(,.*(%&omegaG\"\"#%\"CGF-F)F-F(**F,F-F.F-F)F(F'F(F-*(F'F-F ,F-F.F-F(*(F,\"\"%F.F-%\"LGF-F(*(F,F-F.F(F3F(!\"#F(F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Imagin\344rteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "imZ:=simplify(evalc(Im(Z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG,$*(%&omegaG\"\"\",,*(F'\"\"#%\"CGF(%\"LGF+F(F-! \"\"*&%\"RGF+F,F(F(*(F,F(F0F(%\"lGF(F+*&F,F(F2F+F(F(,.*(F'F+F,F+F2F+F( **F'F+F,F+F2F(F0F(F+*(F0F+F'F+F,F+F(*(F'\"\"%F,F+F-F+F(*(F'F+F,F(F-F(! \"#F(F(F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Vergleich der oben angegebenen Betragsdefinition absZ und der MapleProzedur evalc(abs(Z) )" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "'[Z]'=simplify(absZ);\n'[Z]'=s implify(evalc(abs(Z)));" }}{PARA 0 "" 0 "" {TEXT 277 11 "Identisch !" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*&,**&%&omegaG\"\"#%\"LGF+ \"\"\"*$%\"RGF+F-*&F/F-%\"lGF-F+*$F1F+F-F-,.*(F*F+%\"CGF+F1F+F-**F*F+F 5F+F1F-F/F-F+*(F/F+F*F+F5F+F-*(F*\"\"%F5F+F,F+F-*(F*F+F5F-F,F-!\"#F-F- !\"\"#F-F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*&,**&%&omegaG \"\"#%\"LGF+\"\"\"*$%\"RGF+F-*&F/F-%\"lGF-F+*$F1F+F-F-,.*(F*F+%\"CGF+F 1F+F-**F*F+F5F+F1F-F/F-F+*(F/F+F*F+F5F+F-*(F*\"\"%F5F+F,F+F-*(F*F+F5F- F,F-!\"#F-F-!\"\"#F-F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Allgeme ine Terme f\374r" }}{PARA 0 "" 0 "" {TEXT -1 20 "1.Phasenverschiebung " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "'phi'=(phi);" }}{PARA 0 "" 0 " " {TEXT -1 18 "2. 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o<-1$FW$!1S&38>rx;\"FZ7$$\"1LL3-$=-@$FW$!1#)R[FW$!1/2^tw#f_\"FZ7$$\"1m; a)3rf&\\FW$!1Mhy:iTI:FZ7$$\"1++]Zaq0^FW$!1cKoY8jM:FZ7$$\"1K$3-\"QfY_FW $!1(\\:;)R0Q:FZ7$$\"1+]PWF'QR&FW$!1pVR7d;T:FZ7$$\"1LL$e/Xy`&FW$!1GKlDH #Qa\"FZ7$$\"1+](=<\"e)o&FW$!1Zbo,BEY:FZ7$$\"1nmmwzvLeFW$!1_W@W9L[:FZ7$ $\"1mm\"zAAA)fFW$!1AAz%e0-b\"FZ7$$\"1L$3-7d%HhFW$!1,%[zGd=b\"FZ7$$\"1+ ++&p]ZE'FW$!1)[8u0=Kb\"FZ7$$\"1LLe*R7)>kFW$!1!G)>)R " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 " " 0 "" {TEXT -1 38 " Ohmscher Widerstand R und Kapazit\344t C" }{TEXT 336 1 " " }{TEXT -1 54 "in Reihe und dazu parallelgeschaltete\n Selbst induktion" }{TEXT 339 1 " " }{TEXT -1 1 "L" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 75 "R:='R':L:='L':l:='l':C:='C':Z:='Z':Z1:='Z1':Z2:='Z2 ':\nomega[0]:='omega[0]':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Ansa tz f\374r Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "eq1:=1/Z=1/Z1+1/Z2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/*$%\"ZG!\"\",&*$%#Z1GF(\" \"\"*$%#Z2GF(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Z1:=(R-I /(omega*C));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z1G,&%\"RG\"\"\"*(% \"IGF'%&omegaG!\"\"%\"CGF+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Z2:=(I*omega*L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z2G*(%\"I G\"\"\"%&omegaGF'%\"LGF'" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 80 "<- Z ur Ber\374cksichtigung des Ohmschen Widerstandes des Spulendrahtes hie r \366ffnen!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Z2:=l+I*omeg a*L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z2G,&%\"lG\"\"\"*(%\"IGF'%& omegaGF'%\"LGF'F'" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "eq1;Z :=solve(eq1,Z);simplify(evalc(\"));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/*$%\"ZG!\"\",&*$,&%\"RG\"\"\"*(%\"IGF+%&omegaGF&%\"CGF&F&F&F+*$,&%\" lGF+*(F-F+F.F+%\"LGF+F+F&F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG* &,***%\"RG\"\"\"%&omegaGF)%\"CGF)%\"lGF)F)*,%\"IGF)F(F)F*\"\"#F+F)%\"L GF)F)*&F.F)F,F)!\"\"*&F*F)F0F)F)F),**(F*F)F+F)F,F)F)**F.F)F*F/F+F)F0F) F)*(F(F)F*F)F+F)F)F.F2F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,2**%&om egaG\"\"#%\"CGF'%\"RG\"\"\"%\"lGF'F***F&F'F(F'F)F'F+F*F***F&\"\"%%\"LG F'F)F*F(F'F*F+F**,%\"IGF*F&\"\"$F/F*F)F'F(F'F***F1F*F&F*F(F*F+F'!\"\"* *F1F*F&F2F(F*F/F'F4*(F1F*F&F*F/F*F*F*,.*(F&F'F(F'F+F'F***F&F'F(F'F+F*F )F*F'*(F)F'F&F'F(F'F**(F&F.F(F'F/F'F**(F&F'F(F*F/F*!\"#F*F*F4" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Realteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "reZ:=simplify(evalc(Re(Z)));\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$reZG*&,***%&omegaG\"\"#%\"CGF)%\"RG\"\"\"%\"lGF)F, **F(F)F*F)F+F)F-F,F,**F(\"\"%%\"LGF)F+F,F*F)F,F-F,F,,.*(F(F)F*F)F-F)F, **F(F)F*F)F-F,F+F,F)*(F+F)F(F)F*F)F,*(F(F0F*F)F1F)F,*(F(F)F*F,F1F,!\"# F,F,!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Imagin\344rteil von \+ Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "imZ:=simplify(evalc(Im(Z))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG*(%&omegaG\"\"\",***F&\"\"# %\"LGF'%\"RGF*%\"CGF*F'*&F-F'%\"lGF*!\"\"*(F&F*F-F'F+F*F0F+F'F',.*(F&F *F-F*F/F*F'**F&F*F-F*F/F'F,F'F**(F,F*F&F*F-F*F'*(F&\"\"%F-F*F+F*F'*(F& F*F-F'F+F'!\"#F'F'F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Vergleich der oben angegebenen Betragsdefinition absZ und der MapleProzedur eva lc(abs(Z))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "'[Z]'=simplify(absZ); \n'[Z]'=simplify(evalc(abs(Z)));" }}{PARA 0 "" 0 "" {TEXT 333 11 "Iden tisch !" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*(,&*$%\"lG\"\"# \"\"\"*&%&omegaGF+%\"LGF+F,F,,&*(%\"RGF+F.F+%\"CGF+F,F,F,F,,.*(F.F+F3F +F*F+F,**F.F+F3F+F*F,F2F,F+F1F,*(F.\"\"%F3F+F/F+F,*(F.F+F3F,F/F,!\"#F, F,!\"\"#F,F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*(,&*$%\"lG \"\"#\"\"\"*&%&omegaGF+%\"LGF+F,F,,&*(%\"RGF+F.F+%\"CGF+F,F,F,F,,.*(F. 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Resonanfrequenz" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " omega[0]:=resofrq(reZ,imZ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$phiG -%'arctanG6#*(%&omegaG\"\"\",***F)\"\"#%\"LGF*%\"RGF-%\"CGF-F**&F0F*% \"lGF-!\"\"*(F)F-F0F*F.F-F3F.F*F*,***F)F-F0F-F/F*F2F-F***F)F-F0F-F/F-F 2F*F***F)\"\"%F.F-F/F*F0F-F*F2F*F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >&%&omegaG6#\"\"!6%F'*&,&*(%\"LG\"\"\"%\"RG\"\"#%\"CGF/F-*&F0F-F,F/!\" \"F2**F0F-F,F-,&*&F.F/F0F-F-F,F2F-,&*&F0F-%\"lGF/F-F,F2F-#F-F/,$F)F2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Werte f\374r R, L und C:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "R:=5000; L:=0.290; l:=15; C:=5000e- 12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG\"%+]" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"LG$\"$!H!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"lG\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"%+]!#7" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Resonanzfrequenz:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "omega[0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\" !$!+mja\"[$!\"&$\"+mja\"[$F&" 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0 0 0 0 0 0 0 1 1 467 6695 0 250 -17200 0 0 0 0 0 0 }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 34 " Selbstinduktion L un d Kapazit\344t C" }{TEXT 334 1 " " }{TEXT -1 61 "in Reihe und dazu par allelgeschalteter\n Ohmscher Widerstand R" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "R:='R':L:='L':l:='l':C:='C':Z:='Z':\nZ1:='Z1':Z2:='Z2 ':omega[0]:='omega[0]':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Ansatz f\374r Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "eq1:=1/Z=1/Z1+1/Z2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/*$%\"ZG!\"\",&*$%#Z1GF(\"\" \"*$%#Z2GF(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Z1:=(I*ome ga*L)-I/(omega*C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z1G,&*(%\"IG \"\"\"%&omegaGF(%\"LGF(F(*(F'F(F)!\"\"%\"CGF,F," }}}{SECT 1 {PARA 5 " " 0 "" {TEXT -1 80 "<- Zur Ber\374cksichtigung des Ohmschen Widerstand es des Spulendrahtes hier \366ffnen!" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Z1:=(l+I*(omega*L-1/omega/C));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z1G,&%\"lG\"\"\"*&%\"IGF',&*&%&omegaGF'%\"LGF'F'*&F, !\"\"%\"CGF/F/F'F'" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Z2:=R ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z2G%\"RG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Z:=solve(eq1,Z);(evalc(\"));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG*(,(*(%&omegaG\"\"\"%\"CGF)%\"lGF)F)**%\"IGF )F(\"\"#F*F)%\"LGF)F)F-!\"\"F)%\"RGF),*F'F)F,F)*(F1F)F(F)F*F)F)F-F0F0 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*.%\"RG\"\"\"%&omegaGF&%\"CGF&% \"lGF&,&*(F'F&F(F&F)F&F&*(F%F&F'F&F(F&F&F&,&*$F*\"\"#F&*$,&*(F'F/F(F&% \"LGF&F&!\"\"F&F/F&F4F&*(F1F/F%F&F-F4F&*&%\"IGF&,&**F1F&F%F&F*F&F-F4F& *.F%F&F'F&F(F&F)F&F1F&F-F4F4F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Realteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "reZ:=simplif y(evalc(Re(Z)));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$reZG*(%\"RG\" \"\",,*(%&omegaG\"\"#%\"CGF+%\"lGF+F'**F*F+F,F+F-F'F&F'F'*(F*\"\"%F,F+ %\"LGF+F'*(F*F+F,F'F1F'!\"#F'F'F',.F)F'F.F+*(F&F+F*F+F,F+F'F/F'F2F3F'F '!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Imagin\344rteil von Z: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "imZ:=simplify(evalc(Im(Z)));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG*,,&*(%&omegaG\"\"#%\"CG\"\"\" %\"LGF+F+!\"\"F+F+%\"RGF)F(F+F*F+,.*(F(F)F*F)%\"lGF)F+**F(F)F*F)F1F+F. F+F)*(F.F)F(F)F*F)F+*(F(\"\"%F*F)F,F)F+F'!\"#F+F+F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Vergleich der oben angegebenen Betragsdefinitio n absZ und der MapleProzedur evalc(abs(Z))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "'[Z]'=simplify(absZ);\n'[Z]'=simplify(evalc(abs(Z))); " }}{PARA 0 "" 0 "" {TEXT 338 11 "Identisch !" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*(%\"RG\"\"#,**(%&omegaGF)%\"CGF)%\"lGF)\"\" \"F/F/*(F,\"\"%F-F)%\"LGF)F/*(F,F)F-F/F2F/!\"#F/,.F+F/**F,F)F-F)F.F/F( F/F)*(F(F)F,F)F-F)F/F0F/F3F4F/F/!\"\"#F/F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/7#%\"ZG*$*(%\"RG\"\"#,**(%&omegaGF)%\"CGF)%\"lGF)\"\" \"F/F/*(F,\"\"%F-F)%\"LGF)F/*(F,F)F-F/F2F/!\"#F/,.F+F/**F,F)F-F)F.F/F( F/F)*(F(F)F,F)F-F)F/F0F/F3F4F/F/!\"\"#F/F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Allgemeine Terme f\374r" }}{PARA 0 "" 0 "" {TEXT -1 20 "1 .Phasenverschiebung" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "'phi'=(phi); " }}{PARA 0 "" 0 "" {TEXT -1 18 "2. Resonanfrequenz" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "omega[0]=resofrq(reZ,imZ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$phiG-%'arctanG6#*,,&*(%&omegaG\"\"#%\"CG\"\"\"%\"LGF .F.!\"\"F.F.%\"RGF.F+F.F-F.,,*(F+F,F-F,%\"lGF,F.**F+F,F-F,F4F.F1F.F.*( F+\"\"%F-F,F/F,F.F*!\"#F.F.F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&o megaG6#\"\"!6%F'*(%\"CG!\"\"%\"LGF+*&F*\"\"\"F,F.#F.\"\"#,$F)F+" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Werte f\374r R, L und C:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "R:=5000; L:=0.290; l:=15; C:=5010e-12;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG\"%+]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG$\"$!H!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"lG\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"%5]!#7" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Resonanzfrequenz:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "omega[0]:=resofrq(reZ,imZ);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&omegaG6#\"\"!6%F'$!+hk]BE!\"&$\"+hk]BEF+" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Grenzwerte von Z f\374r " } {XPPEDIT 18 0 "omega" "I&omegaG6\"" }{TEXT -1 7 " gegen " }{XPPEDIT 18 0 "infinity" "I)infinityG6\"" }{TEXT -1 7 " und 0." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "Limit('absZ',omega=0)=limit(absZ,omega=0);\nLimi t('absZ',omega=infinity)=limit(absZ,omega=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6$%%absZG/%&omegaG\"\"!$\"%+]F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6$%%absZG/%&omegaG%)infinityG$\"%+ ]\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Diagramm von " } {XPPEDIT 340 0 "absZ(omega)" "-%%absZG6#%&omegaG" }{TEXT -1 1 ":" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot([absZ,[[omega[0][2],0],[omega[ 0][2],50000]]],omega=1..50000);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Diagramm von " }{XPPEDIT 341 0 "ph i(omega)" "-%$phiG6#%&omegaG" }{TEXT -1 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "plot(\{phi,[[omega[0][2],-1.57],[omega[0][2],1.57]]\} ,omega=0..70000);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Frequenzweichen" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 28 "Butterworth-Filter 1.Ordnung" }}{EXCHG {PARA 0 "" 0 "" {TEXT 343 8 "Tiefpa\337:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Z:='Z': L:='L':C:='C':R:='R': f:='f':ft:='ft': omega:='omega':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Ansatz f\374r Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Z:=(R+I*(omega*L));evalc(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG,&%\"RG\"\"\"*(%\"IGF'%&omegaGF'%\"LGF'F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"RG\"\"\"*(%\"IGF%%&omegaGF%%\"LGF %F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Realteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "reZ:=evalc(Re(Z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$reZG%\"RG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Im agin\344rteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "imZ:=evalc( Im(Z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG*&%&omegaG\"\"\"%\"L GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "absZ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&*$%\"RG\"\"#\"\"\"*&%&omegaGF'%\"LGF'F(#F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "#q:=solve(absZ,L^2);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "F\374r den Spulenwert bei einer T rennfrequenz f gilt:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "L:=f->1/2*R /Pi/f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG:6#%\"fG6\"6$%)operato rG%&arrowGF(,$*(%\"RG\"\"\"%#PiG!\"\"9$F1#F/\"\"#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "omega:=2*Pi*f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaG,$*&%#PiG\"\"\"%\"fGF(\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "D ie Funktion f\374r die abgegebene Leistung am Tieft\366ner: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "Ueff:='Ueff':\ni[tief]:=(f,L)->Ueff/(R^2+ omega^2*L^2)^(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"iG6#%%tief 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}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Ansatz f\374r Z:" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Z:=(R-I/(omega*C));evalc(\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG,&%\"RG\"\"\"*(%\"IGF'%&omegaG! \"\"%\"CGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"RG\"\"\"*(%\"IGF %%&omegaG!\"\"%\"CGF)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "Realte il von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "reZ:=evalc(Re(Z));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$reZG%\"RG" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 19 "Imagin\344rteil von Z:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "imZ:=evalc(Im(Z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$imZG,$* &%&omegaG!\"\"%\"CGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a bsZ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&*$%\"RG\"\"#\"\"\"*&%&omeg aG!\"#%\"CGF+F(#F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "q:= solve(absZ^2,1/C^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,$*&%\"R G\"\"#%&omegaGF(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "F\374r d en Kondensatorwert 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2-2*omega^4*L1*C2^2*R^2*L2+2*omega^2*L1*C2*R^2+omega^4*L2^2*C2^2*R^2-2 *omega^2*L2*C2*R^2+R^2)^2)^(1/2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "#i[tief](a,a,b,b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "omega:=2*Pi*f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%& omegaG,$*&%#PiG\"\"\"%\"fGF(\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "R:=4;Ueff:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"RG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%UeffG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "ftu:=100;fto:=300;\nevalf(L(ftu)), evalf(C(ftu));\nevalf(L1(ftu)),evalf(C1(ftu)),evalf(L2(fto)),evalf(C2( fto));\nevalf(L(fto)),evalf(C(fto));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$ftuG\"$+\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ftoG\"$+$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+eJ;.!*!#7$\"+([)[8G!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$\"+eJ;.!*!#7$\"+([)[8G!#8$\"+'Qa5+$F%$\"+b \\Hy$*!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+'Qa5+$!#7$\"+b\\Hy$*! #9" }}}{EXCHG {PARA 0 "> " 0 "" 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