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Version 4 SymbolType CELL LINE Normal -8 36 8 36 LINE Normal -8 76 8 76 LINE Normal 0 28 0 44 LINE Normal 0 96 0 88 LINE Normal 0 16 0 24 CIRCLE Normal -32 24 32 88 WINDOW 0 24 16 Left 0 WINDOW 3 24 104 Left 0 SYMATTR Value V SYMATTR Prefix V SYMATTR Description Voltage Source, either DC, AC, PULSE, SINE, PWL, EXP, or SFFM PIN 0 16 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 0 96 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 0 56 4 44 LINE Normal 0 56 -4 44 LINE Normal -4 44 4 44 LINE Normal 0 24 0 44 LINE Normal 0 80 0 72 LINE Normal 0 0 0 8 CIRCLE Normal -32 8 32 72 WINDOW 0 24 0 Left 0 WINDOW 3 24 88 Left 0 SYMATTR Value I SYMATTR Prefix I SYMATTR Description Current source, either DC, AC, PULSE, SINE, PWL, EXP, or SFFM PIN 0 0 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal -44 80 -40 92 LINE Normal -40 92 -36 80 LINE Normal -36 80 -44 80 LINE Normal -40 18 -40 80 LINE Normal 0 96 0 16 CIRCLE Normal -32 24 32 88 WINDOW 0 24 16 Left 0 WINDOW 3 24 104 Left 0 SYMATTR Value V SYMATTR Prefix V SYMATTR Description Voltage Source, either DC, AC, PULSE, SINE, PWL, EXP, or SFFM PIN 0 16 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 0 96 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 0 80 4 68 LINE Normal 0 80 -4 68 LINE Normal -32 40 32 40 LINE Normal 0 80 0 72 LINE Normal 0 0 0 8 CIRCLE Normal -32 8 32 72 WINDOW 0 24 0 Left 0 WINDOW 3 24 88 Left 0 SYMATTR Value I SYMATTR Prefix I SYMATTR Description Current source, either DC, AC, PULSE, SINE, PWL, EXP, or SFFM PIN 0 0 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 16 88 16 96 LINE Normal 0 80 16 88 LINE Normal 32 64 0 80 LINE Normal 0 48 32 64 LINE Normal 32 32 0 48 LINE Normal 16 16 16 24 LINE Normal 16 24 32 32 WINDOW 0 36 40 Left 0 WINDOW 3 36 76 Left 0 SYMATTR Value R SYMATTR Prefix R SYMATTR Description A resistor PIN 16 16 NONE 0 PINATTR PinName A PINATTR SpiceOrder 1 PIN 16 96 NONE 0 PINATTR PinName B PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 16 88 16 96 LINE Normal 0 88 32 88 LINE Normal 0 88 0 24 LINE Normal 32 88 32 24 LINE Normal 0 24 32 24 LINE Normal 16 16 16 24 WINDOW 0 36 40 Left 0 WINDOW 3 36 76 Left 0 SYMATTR Value R SYMATTR Prefix R SYMATTR Description A resistor PIN 16 16 NONE 0 PINATTR PinName A PINATTR SpiceOrder 1 PIN 16 96 NONE 0 PINATTR PinName B PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 16 36 16 64 LINE Normal 16 28 16 0 LINE Normal 0 28 32 28 LINE Normal 0 36 32 36 WINDOW 0 24 8 Left 0 WINDOW 3 24 64 Left 0 SYMATTR Value C SYMATTR Prefix C SYMATTR Description Capacitor PIN 16 0 NONE 0 PINATTR PinName A PINATTR SpiceOrder 1 PIN 16 64 NONE 0 PINATTR PinName B PINATTR SpiceOrder 2

Version 4 SymbolType CELL ARC Normal 0 40 32 72 4 68 4 44 ARC Normal 0 64 32 96 16 96 4 68 ARC Normal 0 16 32 48 4 44 16 16 WINDOW 0 36 40 Left 0 WINDOW 3 36 80 Left 0 SYMATTR Value L SYMATTR Prefix L SYMATTR Description Inductor PIN 16 16 NONE 0 PINATTR PinName A PINATTR SpiceOrder 1 PIN 16 96 NONE 0 PINATTR PinName B PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 0 44 32 44 LINE Normal 0 20 32 20 LINE Normal 32 20 16 44 LINE Normal 0 20 16 44 LINE Normal 16 0 16 20 LINE Normal 16 44 16 64 WINDOW 0 24 0 Left 0 WINDOW 3 24 72 Left 0 SYMATTR Value D SYMATTR Prefix D SYMATTR Description Diode PIN 16 0 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 16 64 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 0 44 32 44 LINE Normal 0 20 32 20 LINE Normal 32 20 16 44 LINE Normal 0 20 16 44 LINE Normal 16 0 16 20 LINE Normal 16 44 16 64 LINE Normal 72 32 68 40LINE Normal 72 32 64 32LINE Normal 72 48 68 56LINE Normal 72 48 64 48ARC Normal 40 20 56 36 56 28 40 24ARC Normal 56 20 72 36 56 28 72 32ARC Normal 40 36 56 52 56 44 40 40ARC Normal 56 36 72 52 56 44 72 48WINDOW 0 24 0 Left 0 WINDOW 3 24 72 Left 0 SYMATTR Value D SYMATTR Prefix D SYMATTR Description Diode PIN 16 0 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 16 64 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Version 4 SymbolType CELL LINE Normal 48 80 48 96 LINE Normal 16 80 48 80 LINE Normal 40 48 48 48 LINE Normal 16 48 40 44 LINE Normal 16 48 40 52 LINE Normal 40 44 40 52 LINE Normal 16 8 16 24 LINE Normal 16 40 16 56 LINE Normal 16 72 16 88 LINE Normal 0 80 8 80 LINE Normal 8 16 8 80 LINE Normal 48 16 16 16 LINE Normal 48 0 48 16 WINDOW 0 56 32 Left 0 WINDOW 3 56 72 Left 0 SYMATTR Value NMOS SYMATTR Prefix MN SYMATTR Description N-Channel MOSFET transistor with explicit substrate connection(used for monolithic MOSFETS) PIN 48 0 NONE 0 PINATTR PinName D PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName G PINATTR SpiceOrder 2 PIN 48 96 NONE 0 PINATTR PinName S PINATTR SpiceOrder 3 PIN 48 48 NONE 0 PINATTR PinName B PINATTR SpiceOrder 4

Version 4 SymbolType CELL LINE Normal 48 80 48 96 LINE Normal 16 80 48 80 LINE Normal 16 48 24 48 LINE Normal 48 48 24 44 LINE Normal 48 48 24 52 LINE Normal 24 44 24 52 LINE Normal 16 8 16 24 LINE Normal 16 40 16 56 LINE Normal 16 72 16 88 LINE Normal 0 80 8 80 LINE Normal 8 16 8 80 LINE Normal 48 16 16 16 LINE Normal 48 0 48 16 WINDOW 0 56 32 Left 0 WINDOW 3 56 72 Left 0 SYMATTR Value PMOS SYMATTR Prefix MP SYMATTR Description P-Channel MOSFET transistor with explicit substrate connection(used for monolithic MOSFETS) PIN 48 0 NONE 0 PINATTR PinName D PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName G PINATTR SpiceOrder 2 PIN 48 96 NONE 0 PINATTR PinName S PINATTR SpiceOrder 3 PIN 48 48 NONE 0 PINATTR PinName B PINATTR SpiceOrder 4

Version 4 SymbolType CELL LINE Normal 48 80 48 96 LINE Normal 16 80 48 80 LINE Normal 40 48 48 48 LINE Normal 16 48 40 44 LINE Normal 16 48 40 52 LINE Normal 40 44 40 52 LINE Normal 16 8 16 24 LINE Normal 16 40 16 56 LINE Normal 16 72 16 88 LINE Normal 0 80 8 80 LINE Normal 8 16 8 80 LINE Normal 48 16 16 16 LINE Normal 48 0 48 16 LINE Normal 48 48 48 80 WINDOW 0 56 32 Left 0 WINDOW 3 56 72 Left 0 SYMATTR Value NMOS SYMATTR Prefix MN SYMATTR Description N-Channel MOSFET transistor with explicit substrate connection(used for monolithic MOSFETS) PIN 48 0 NONE 0 PINATTR PinName D PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName G PINATTR SpiceOrder 2 PIN 48 96 NONE 0 PINATTR PinName S PINATTR SpiceOrder 3 PIN 48 48 NONE 0 PINATTR PinName B PINATTR SpiceOrder 4

Version 4 SymbolType CELL LINE Normal 48 80 48 96 LINE Normal 16 80 48 80 LINE Normal 16 48 24 48 LINE Normal 48 48 24 44 LINE Normal 48 48 24 52 LINE Normal 24 44 24 52 LINE Normal 16 8 16 24 LINE Normal 16 40 16 56 LINE Normal 16 72 16 88 LINE Normal 0 80 8 80 LINE Normal 8 16 8 80 LINE Normal 48 16 16 16 LINE Normal 48 0 48 16 LINE Normal 48 48 48 80 WINDOW 0 56 32 Left 0 WINDOW 3 56 72 Left 0 SYMATTR Value PMOS SYMATTR Prefix MP SYMATTR Description P-Channel MOSFET transistor with explicit substrate connection(used for monolithic MOSFETS) PIN 48 0 NONE 0 PINATTR PinName D PINATTR SpiceOrder 1 PIN 0 80 NONE 0 PINATTR PinName G PINATTR SpiceOrder 2 PIN 48 96 NONE 0 PINATTR PinName S PINATTR SpiceOrder 3 PIN 48 48 NONE 0 PINATTR PinName B PINATTR SpiceOrder 4

Version 4 SymbolType CELL LINE Normal 44 76 36 84 LINE Normal 64 96 44 76 LINE Normal 64 96 36 84 LINE Normal 40 80 16 64 LINE Normal 16 80 16 16 LINE Normal 16 32 64 0 LINE Normal 16 48 0 48 WINDOW 0 56 32 Left 0 WINDOW 3 56 68 Left 0 SYMATTR Value NPN SYMATTR Prefix QN SYMATTR Description Bipolar NPN transistor PIN 64 0 NONE 0 PINATTR PinName C PINATTR SpiceOrder 1 PIN 0 48 NONE 0 PINATTR PinName B PINATTR SpiceOrder 2 PIN 64 96 NONE 0 PINATTR PinName E PINATTR SpiceOrder 3

Version 4 SymbolType CELL LINE Normal -32 32 32 64 LINE Normal -32 96 32 64 LINE Normal -32 32 -32 96 LINE Normal -8 73 -28 73 LINE Normal -18 64 -18 83 LINE Normal -8 55 -28 55 WINDOW 0 0 32 Left 0 SYMATTR Prefix X SYMATTR Description Ideal single-pole operational amplifier. You must .lib opamp.sub SYMATTR Value opamp SYMATTR SpiceLine Aol=100K SYMATTR SpiceLine2 GBW=10Meg PIN -32 48 NONE 0 PINATTR PinName invin PINATTR SpiceOrder 1 PIN -32 80 NONE 0 PINATTR PinName noninvin PINATTR SpiceOrder 2 PIN 32 64 NONE 0 PINATTR PinName out PINATTR SpiceOrder 3

Version 4 SymbolType CELL LINE Normal -32 36 32 36 LINE Normal -32 60 32 60 LINE Normal 0 96 0 76 LINE Normal 0 16 0 36 LINE Normal -20 24 -12 24 LINE Normal -16 20 -16 28 RECTANGLE Normal -16 44 16 52 RECTANGLE Normal -16 68 16 76 WINDOW 0 24 16 Left 0 WINDOW 3 24 104 Left 0 SYMATTR Value V SYMATTR Prefix V SYMATTR Description Voltage Source, either DC, AC, PULSE, SINE, PWL, EXP, or SFFM PIN 0 16 NONE 0 PINATTR PinName + PINATTR SpiceOrder 1 PIN 0 96 NONE 0 PINATTR PinName - PINATTR SpiceOrder 2

Ersatzquellen

Berechnung einer Spannung unter Verwendung von Ersatzquellen

Folgendes Netzwerk ist gegeben: $\underline{U}_{1} = 38V \underline{/0°}$ $\underline{U}_{2} = 38V \underline{/120°}$ f = 50Hz Gesucht ist die Spannung $\underline{U}_{3}$ .	ErsatzAuf01.asc Version 4 SHEET 1 880 680 WIRE 128 32 96 32 WIRE 240 32 208 32 WIRE 304 32 240 32 WIRE 400 32 368 32 WIRE 240 48 240 32 WIRE 240 144 240 128 WIRE 240 224 240 208 FLAG 240 224 0 FLAG 96 32 U1 FLAG 400 32 U2 FLAG 240 32 U3 SYMBOL res 224 16 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res 224 32 R0 SYMATTR InstName R3 SYMATTR Value 200 SYMBOL cap 224 144 R0 SYMATTR InstName C3 SYMATTR Value 31.8µ SYMBOL cap 368 16 R90 WINDOW 0 0 32 VBottom 0 WINDOW 3 32 32 VTop 0 SYMATTR InstName C2 SYMATTR Value 31.8µ TEXT 168 128 Left 0 ;U3 LINE Normal 208 224 208 48 LINE Normal 208 224 208 224 LINE Normal 208 224 208 224 LINE Normal 224 208 208 224 LINE Normal 192 208 208 224
Man kann diese Aufgabe durch Superposition, Knotenpotentialanalyse oder Ersatzquellen lösen. Bei der Superposition werden die Quellen nacheinander betrachtet. Es wird die gesuchte Größe berechnet, wenn nur eine Quelle aktiv ist und die anderen Spannungsquellen durch Kurzschlüsse und Stromquellen durch Unterbrechungen ersetzt werden. Die Überlagerung (Addition) aller berechneten Größen ergibt die Gesamtgröße. Hier wird mit Hilfe der Ersatzquellen gerechnet. Zum besseren Verständnis werden die Schaltbilder der Zwischenschritte gezeichnet.	ErsatzAuf02.asc Version 4 SHEET 1 880 680 WIRE 128 32 96 32 WIRE 240 32 208 32 WIRE 304 32 240 32 WIRE 400 32 368 32 WIRE 240 48 240 32 WIRE 96 96 96 32 WIRE 400 96 400 32 WIRE 240 144 240 128 WIRE 96 224 96 176 WIRE 240 224 240 208 WIRE 240 224 96 224 WIRE 400 224 400 176 WIRE 400 224 240 224 WIRE 240 240 240 224 FLAG 240 240 0 FLAG 96 32 U1 FLAG 400 32 U2 FLAG 240 32 U3 SYMBOL res 224 16 R90 WINDOW 0 0 56 VBottom 0 WINDOW 3 32 56 VTop 0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res 224 32 R0 SYMATTR InstName R3 SYMATTR Value 200 SYMBOL cap 224 144 R0 SYMATTR InstName C3 SYMATTR Value 31.8µ SYMBOL cap 368 16 R90 WINDOW 0 0 32 VBottom 0 WINDOW 3 32 32 VTop 0 SYMATTR InstName C2 SYMATTR Value 31.8µ SYMBOL voltage 96 80 R0 WINDOW 123 24 132 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value "" SYMATTR Value2 AC 38 0 SYMBOL voltage 400 80 R0 WINDOW 123 24 132 Left 0 SYMATTR InstName V2 SYMATTR Value "" SYMATTR Value2 AC 38 120 TEXT 176 128 Left 0 ;U3 LINE Normal 208 208 208 48 LINE Normal 208 208 208 208 LINE Normal 224 192 208 208 LINE Normal 208 208 192 192
Bringt man die Spannungsquellen nach links und die gesuchte Spannung nach rechts, sieht man die Parallelschaltung der Quellen. Um die Quellen zusammen zu fassen müssen Sie in die äquivalenten Ersatzstromquellen umgerechnet werden.	ErsatzAuf03.asc Version 4 SHEET 1 880 680 WIRE 128 0 0 0 WIRE 288 0 128 0 WIRE 0 16 0 0 WIRE 128 16 128 0 WIRE 288 16 288 0 WIRE 0 112 0 96 WIRE 128 112 128 80 WIRE 288 112 288 96 WIRE 0 128 0 112 WIRE 128 128 128 112 WIRE 0 224 0 208 WIRE 128 224 128 208 WIRE 128 224 0 224 WIRE 288 224 288 176 WIRE 288 224 128 224 WIRE 288 240 288 224 FLAG 288 240 0 FLAG 0 112 U1 FLAG 128 112 U2 FLAG 288 0 U3 SYMBOL res -16 0 R0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res 272 0 R0 SYMATTR InstName R3 SYMATTR Value 200 SYMBOL cap 272 112 R0 SYMATTR InstName C3 SYMATTR Value 31.8µ SYMBOL cap 144 80 R180 WINDOW 0 24 64 Left 0 WINDOW 3 24 8 Left 0 SYMATTR InstName C2 SYMATTR Value 31.8µ SYMBOL voltage 0 112 R0 WINDOW 123 24 132 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value "" SYMATTR Value2 AC 38 0 SYMBOL voltage 128 112 R0 WINDOW 123 24 132 Left 0 SYMATTR InstName V2 SYMATTR Value "" SYMATTR Value2 AC 38 120 TEXT 224 128 Left 0 ;U3 LINE Normal 256 192 256 32 LINE Normal 256 208 256 208 LINE Normal 272 176 256 192 LINE Normal 256 192 240 176
Man berechnet die Kurzschlussströme: $\underline{I}_{1} = \frac{ \underline{U}_{1} }{R_1}$ $\underline{I}_{2} = \underline{U}_{2} j \omega C_2$ Die Ströme werden addiert, der Gesamtwiderstand und die Spannung berechnet: $\underline{U}_{3} = \frac{\underline{I}_{1} + \underline{I}_{2}} {\frac{1}{R_1}+ j \omega C_2 + \frac{1}{R_3 + \frac{1}{ j \omega C_3}}}$ $\underline{I} = \underline{I}_{1} + \underline{I}_{2} = 0.38 A - j 0.19 A - 0.329 A$ $\underline{I} = 0.059 A - j 0.19 A = 0.197 A \underline{/-75°}$ Man benötigt noch den Gesamtwiderstand. $\underline{Y} = \frac{1}{R_1}+ j \omega C_2 + \frac{1}{R_3 + \frac{1}{ j \omega C_3}}$ $\underline{Y} = \frac{1}{R_1}+ \frac{R_3}{{R_3}^2 + \left( \frac{1}{ \omega C_3} \right)^2} + j \omega C_2 - \frac{\frac{1}{ j \omega C_3}}{{R_3}^2 + \left( \frac{1}{ \omega C_3} \right)^2}$ $\underline{Y} = 14 mS + j 12 mS = 18.4 mS \big/\!\!\!\underline{\;\,40.6°}$ $\underline{U}_{3} = \frac{\underline{I}}{\underline{Y}} = \frac{0.197 A \underline{/-75°}}{ 18.4 mS \big/\!\!\!\underline{\;\,40.6°}} = 10.7V \big/\!\!\!\underline{\;\,-115.6°}$	ErsatzAuf04.asc Version 4 SHEET 1 880 680 WIRE -16 0 -96 0 WIRE 80 0 -16 0 WIRE 192 0 80 0 WIRE 288 0 192 0 WIRE 288 16 288 0 WIRE 192 64 192 0 WIRE -96 80 -96 0 WIRE -16 80 -16 0 WIRE 80 80 80 0 WIRE 288 112 288 96 WIRE -96 224 -96 160 WIRE -16 224 -16 160 WIRE -16 224 -96 224 WIRE 80 224 80 160 WIRE 80 224 -16 224 WIRE 192 224 192 128 WIRE 192 224 80 224 WIRE 288 224 288 176 WIRE 288 224 192 224 WIRE 288 240 288 224 FLAG 288 240 0 FLAG 288 0 U3 SYMBOL res -32 64 R0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res 272 0 R0 SYMATTR InstName R3 SYMATTR Value 200 SYMBOL cap 272 112 R0 SYMATTR InstName C3 SYMATTR Value 31.8µ SYMBOL cap 208 128 R180 WINDOW 0 24 64 Left 0 WINDOW 3 24 8 Left 0 SYMATTR InstName C2 SYMATTR Value 31.8µ SYMBOL current 80 80 R0 SYMATTR InstName I2 SYMBOL current -96 80 R0 SYMATTR InstName I1 TEXT 224 128 Left 0 ;U3 LINE Normal 256 192 256 32 LINE Normal 256 208 256 208 LINE Normal 272 176 256 192 LINE Normal 256 192 240 176

Literatur

[1] Elektroniktutor Ersatzquelle
[2 ] Thevenin-Theorem Wikipedia