Version 4
SHEET 1 1932 2496
WIRE 80 -96 48 -96
WIRE 192 -96 160 -96
WIRE -96 0 -224 0
WIRE -32 0 -96 0
WIRE 48 0 48 -96
WIRE 48 0 -32 0
WIRE 80 0 48 0
WIRE 192 0 192 -96
WIRE 192 0 144 0
WIRE 240 0 192 0
WIRE 304 0 240 0
WIRE -224 16 -224 0
WIRE -32 16 -32 0
WIRE 240 16 240 0
WIRE -224 112 -224 96
WIRE -32 112 -32 96
WIRE 240 112 240 96
FLAG -32 112 0
FLAG 240 112 0
FLAG -224 112 0
FLAG -96 0 UE
FLAG 304 0 UA
SYMBOL Misc\\EuropeanResistor 64 -80 R270
WINDOW 0 27 56 VTop 2
WINDOW 3 5 56 VBottom 2
SYMATTR InstName R1
SYMATTR Value 5k
SYMBOL cap 144 -16 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C1
SYMATTR Value 10n
SYMBOL Misc\\EuropeanResistor 224 0 R0
SYMATTR InstName R3
SYMATTR Value 10k
SYMBOL Misc\\EuropeanResistor -48 0 R0
SYMATTR InstName R2
SYMATTR Value 10k
SYMBOL voltage -224 0 R0
WINDOW 123 24 124 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V1
SYMATTR Value 0
SYMATTR Value2 AC 1
TEXT 600 -176 Left 2 ;R1=5kOhm, R2=R3=10kOhm, C=10nF\n \nSchaltung siehe angehängtes Bild.\n \na)\nR1=5kOhm, R2=R3=10kOhm, C=10nF\n \nSchaltung siehe angehängtes Bild.\n \na)\nXc_ = 1/(jwC)\n \nXc -> 0Ohm für sehr hohe Frequenzen.\nDas bedeutet R1 wird kurzgeschlossen bzw. überbrückt.\n \nUa_/Ue_ = 1\n \nb)\n \nXc_ = 1/(jwC)\n \nXc -> unendlich bei sehr tiefen Frequenzen.\nDas bedeutet er kann vernachlässigt werden.\n \nZe_ = R2*(R1+R3)/(R2+R1+R3)\n \nZe_ = 6kOhm\n \n\nZe_ allgemein\n \nZ1_ = R1*(1/(jw*C))/(R1+1/(jw*C))\nZ1_ = R1/(1+jw*R1*C)\n \nZ13_ = R3 + R1/(1+jw*R1*C)\nZ13_ = (R3 + R1 + jw*R3*R1*C)/(1+jw*R1*C)\n \nZe_ = R2*Z13_/(R2+Z13_)\n \nZe_ = ( R2*(R3 + R1 + jw*R3*R1*C)/(1+jw*R1*C) ) / ( R2 + (R3 + R1 + \njw*R3*R1*C)/(1+jw*R1*C) )\n \nZe_ = R2*(R3 + R1 + jw*R3*R1*C) / ( R2*(1+jw*R1*C) + R3 + R1 +jw*R3*R1*C \n)\n \nZe_ = R2*(R1+R3+jw*R3*R1*C) / ( R1+R2+R3 + jw*R1*C*(R2+R3) )\n \nZe = \nR2*Wurzel((R1+R3)^2+(w*R3*R1*C)^2)/Wurzel((R1+R2+R3)^2+(w*R1*C*(R2+R3))^ \n2)\n \nphi = arctan(w*R3*R1*C/(R1+R3)) - arctan(w*R1*C*(R2+R3)/(R1+R2+R3))\n \n\nDas folgende war gar nicht gefragt.\nUa_/Ue_ = R3/(R1+R3)\nUa_/Ue_ = 2/3\n \n\nc)\n \nUa_/Ue_ = R3/(R3 + R1/(1+jw*R1*C))\n \nUa_/Ue_ = R3*(1+jw*R1*C)/(R3*(1+jw*R1*C)+R1)\n \nUa_/Ue_ = R3*(1+jw*R1*C)/(R1+R3+R3*jw*R1*C)\n \nUa_/Ue_ = (R3/(R1+R3))*(1+jw*R1*C)/(1+R3*jw*R1*C/(R1+R3))\n \nUa_/Ue_ = (R3/(R1+R3))*(1+jw*R1*C)/(1+jw*R1*C/(1+R1/R3))\n \nUa/Ue = (R3/(R1+R3))*Wurzel(1+(w*R1*C)^2)/Wurzel(1+(w*R1*C/(1+R1/R3))^2)\n \nphi = arctan(w*R1*C) - arctan(w*R1*C/(1+R1/R3))
TEXT -8 -192 Left 2 !.ac dec 100 10 1Meg
TEXT -296 240 Left 2 ;>> R1=5e3;R2=10e3;R3=10e3;C=10e-9;\n>> w=2*pi*1000;\n>> Ze_ = R2*(R1+R3+i*w*R3*R1*C) / ( R1+R2+R3 + i*w*R1*C*(R2+R3) )\n \nZe_ =\n \n  5.9406e+003 -2.3640e+002i\n \n>> Ze=abs(Ze_)\n \nZe =\n \n  5.9453e+003\n \n>> phi=180/pi*(atan(w*R3*R1*C/(R1+R3))-atan(w*R1*C*(R2+R3)/(R1+R2+R3)))\n \nphi =\n \n   -2.2788