Elektronik 321 Digital-Analog-WandlerProf. Dr. Jörg Vollrath20 Kennwerte Datenwandler |
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Video der 21. Vorlesung 22.12.2021
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Länge: 1:02:43 |
0:0:0 Datenwandler Charakterisierung 0:2:12 FFT und Sinussignal 0:7:0 10 log(NFFT/2) 0:8:55 Klassifizierung: Nyquist, Oversampling, Subsampling 0:14:0 FFT Simulator 0:16:5 R String DAC 0:23:15 R2R DAC 0:26:40 Berechnung 0:28:30 VD1 und VD0 addieren 0:32:30 Gesamtgleichung 0:35:30 LTSPICE Simulation 0:37:30 Settling time 0:39:52 Widerstandsänderung 0:43:30 Kalibrierung 0:45:50 C2C DAC 0:56:20 Beispielrechnung |
Übersicht
- Rstring
- R2R
- C2C
3 Bit R string or ladder DAC
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A R ladder divides VREF voltage into all possible voltage levels. Inherent monotonic Example: Input Code [d2 d1 d0] = 011 LSB = Vref/8 Vout = LSB * (0*4 + 1*2 + 1) = 3/8 Vref |
Version 4 SHEET 1 1884 680 WIRE -304 -464 -304 -480 WIRE -208 -416 -208 -448 WIRE -304 -368 -304 -384 WIRE -240 -368 -304 -368 WIRE -96 -368 -176 -368 WIRE -304 -352 -304 -368 WIRE -64 -352 -64 -448 WIRE -144 -304 -144 -448 WIRE -96 -304 -96 -368 WIRE 32 -304 -32 -304 WIRE -304 -256 -304 -272 WIRE -176 -256 -304 -256 WIRE -96 -256 -96 -304 WIRE -96 -256 -112 -256 WIRE -304 -240 -304 -256 WIRE 64 -240 64 -448 WIRE -208 -192 -208 -416 WIRE 32 -192 32 -304 WIRE 176 -192 96 -192 WIRE -304 -144 -304 -160 WIRE -240 -144 -304 -144 WIRE -96 -144 -176 -144 WIRE -16 -144 -16 -448 WIRE -304 -128 -304 -144 WIRE -96 -96 -96 -144 WIRE -48 -96 -96 -96 WIRE 32 -96 32 -192 WIRE 32 -96 16 -96 WIRE -144 -80 -144 -304 WIRE -304 -32 -304 -48 WIRE -176 -32 -304 -32 WIRE -96 -32 -96 -96 WIRE -96 -32 -112 -32 WIRE -304 -16 -304 -32 WIRE 176 16 176 -192 WIRE 240 16 176 16 WIRE 288 16 240 16 WIRE -208 32 -208 -192 WIRE 240 64 240 16 WIRE -304 80 -304 64 WIRE -240 80 -304 80 WIRE -96 80 -176 80 WIRE -64 80 -64 -352 WIRE -304 96 -304 80 WIRE -96 128 -96 80 WIRE 32 128 -32 128 WIRE -144 144 -144 -80 WIRE 240 160 240 128 WIRE -304 192 -304 176 WIRE -176 192 -304 192 WIRE -96 192 -96 128 WIRE -96 192 -112 192 WIRE 128 192 128 -448 WIRE -304 208 -304 192 WIRE 32 240 32 128 WIRE 96 240 32 240 WIRE 176 240 176 16 WIRE 176 240 160 240 WIRE -208 256 -208 32 WIRE -304 304 -304 288 WIRE -240 304 -304 304 WIRE -96 304 -176 304 WIRE -16 304 -16 -144 WIRE -304 320 -304 304 WIRE -96 352 -96 304 WIRE -48 352 -96 352 WIRE 32 352 32 240 WIRE 32 352 16 352 WIRE -144 368 -144 144 WIRE -304 416 -304 400 WIRE -176 416 -304 416 WIRE -96 416 -96 352 WIRE -96 416 -112 416 WIRE -304 432 -304 416 FLAG -304 432 0 FLAG -304 -480 VREF FLAG -208 -448 D0 FLAG -144 -448 D0b FLAG -64 -448 D1 FLAG -16 -448 D1b FLAG 64 -448 D2 FLAG 128 -448 D2b FLAG 288 16 Vout FLAG 240 160 0 SYMBOL Switch -144 416 M0 SYMATTR InstName X5 SYMBOL res -320 192 R0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res -320 80 R0 SYMATTR InstName R2 SYMATTR Value 100 SYMBOL res -320 -32 R0 SYMATTR InstName R3 SYMATTR Value 100 SYMBOL res -320 -144 R0 SYMATTR InstName R4 SYMATTR Value 100 SYMBOL res -320 -256 R0 SYMATTR InstName R5 SYMATTR Value 100 SYMBOL res -320 -368 R0 SYMATTR InstName R6 SYMATTR Value 100 SYMBOL res -320 -480 R0 SYMATTR InstName R7 SYMATTR Value 100 SYMBOL res -320 304 R0 SYMATTR InstName R8 SYMATTR Value 100 SYMBOL Switch -208 304 M0 SYMATTR InstName X7 SYMBOL Switch -144 192 M0 SYMATTR InstName X8 SYMBOL Switch -208 80 M0 SYMATTR InstName X9 SYMBOL Switch -144 -32 M0 SYMATTR InstName X10 SYMBOL Switch -208 -144 M0 SYMATTR InstName X11 SYMBOL Switch -144 -256 M0 SYMATTR InstName X12 SYMBOL Switch -208 -368 M0 SYMATTR InstName X13 SYMBOL Switch -64 128 M0 SYMATTR InstName X14 SYMBOL Switch -64 -304 M0 SYMATTR InstName X15 SYMBOL Switch -16 -96 M0 SYMATTR InstName X16 SYMBOL Switch -16 352 M0 SYMATTR InstName X17 SYMBOL Switch 64 -192 M0 SYMATTR InstName X18 SYMBOL Switch 128 240 M0 SYMATTR InstName X19 SYMBOL cap 224 64 R0 SYMATTR InstName C1 SYMATTR Value 1p TEXT -352 -584 Left 2 !.model CD4007N NMOS(LEVEL=1 KP=1123u VT0=0.5 LAMBDA=0.018)\n.model CD4007P PMOS(LEVEL=1 KP=1123u VT0=-0.5 LAMBDA=0.018) TEXT 168 -504 Left 2 !.global VDD\n.include opamp.sub\nV4 d2b 0 PULSE(0 5 0 1n 1n 3999n 8000n)\nV1 d2 0 PULSE(5 0 0 1n 1n 3999n 8000n) TEXT 232 -144 Left 2 !.tran 18000n TEXT 160 -392 Left 2 !V2 d0b 0 PULSE(0 5 0 1n 1n 999n 2000n)\nV5 d0 0 PULSE(5 0 0n 1n 1n 999n 2000n)\nV6 d1 0 PULSE(5 0 0 1n 1n 1999n 4000n)\nV7 d1b 0 PULSE(0 5 0 1n 1n 1999n 4000n)\nVDD Vref 0 DC 4 Version 4 SHEET 1 1884 680 WIRE -304 -464 -304 -480 WIRE -208 -416 -208 -448 WIRE -304 -368 -304 -384 WIRE -240 -368 -304 -368 WIRE -96 -368 -176 -368 WIRE -304 -352 -304 -368 WIRE -64 -352 -64 -448 WIRE -144 -304 -144 -448 WIRE -96 -304 -96 -368 WIRE 32 -304 -32 -304 WIRE -304 -256 -304 -272 WIRE -176 -256 -304 -256 WIRE -96 -256 -96 -304 WIRE -96 -256 -112 -256 WIRE -304 -240 -304 -256 WIRE 64 -240 64 -448 WIRE -208 -192 -208 -416 WIRE 32 -192 32 -304 WIRE 176 -192 96 -192 WIRE -304 -144 -304 -160 WIRE -240 -144 -304 -144 WIRE -96 -144 -176 -144 WIRE -16 -144 -16 -448 WIRE -304 -128 -304 -144 WIRE -96 -96 -96 -144 WIRE -48 -96 -96 -96 WIRE 32 -96 32 -192 WIRE 32 -96 16 -96 WIRE -144 -80 -144 -304 WIRE -304 -32 -304 -48 WIRE -176 -32 -304 -32 WIRE -96 -32 -96 -96 WIRE -96 -32 -112 -32 WIRE -304 -16 -304 -32 WIRE 176 16 176 -192 WIRE 240 16 176 16 WIRE 288 16 240 16 WIRE -208 32 -208 -192 WIRE 240 64 240 16 WIRE -304 80 -304 64 WIRE -240 80 -304 80 WIRE -96 80 -176 80 WIRE -64 80 -64 -352 WIRE -304 96 -304 80 WIRE -96 128 -96 80 WIRE 32 128 -32 128 WIRE -144 144 -144 -80 WIRE 240 160 240 128 WIRE -304 192 -304 176 WIRE -176 192 -304 192 WIRE -96 192 -96 128 WIRE -96 192 -112 192 WIRE 128 192 128 -448 WIRE -304 208 -304 192 WIRE 32 240 32 128 WIRE 96 240 32 240 WIRE 176 240 176 16 WIRE 176 240 160 240 WIRE -208 256 -208 32 WIRE -304 304 -304 288 WIRE -240 304 -304 304 WIRE -96 304 -176 304 WIRE -16 304 -16 -144 WIRE -304 320 -304 304 WIRE -96 352 -96 304 WIRE -48 352 -96 352 WIRE 32 352 32 240 WIRE 32 352 16 352 WIRE -144 368 -144 144 WIRE -304 416 -304 400 WIRE -176 416 -304 416 WIRE -96 416 -96 352 WIRE -96 416 -112 416 WIRE -304 432 -304 416 FLAG -304 432 0 FLAG -304 -480 VREF FLAG -208 -448 D0 FLAG -144 -448 D0b FLAG -64 -448 D1 FLAG -16 -448 D1b FLAG 64 -448 D2 FLAG 128 -448 D2b FLAG 288 16 Vout FLAG 240 160 0 SYMBOL Switch -144 416 M0 SYMATTR InstName X5 SYMBOL res -320 192 R0 SYMATTR InstName R1 SYMATTR Value 100 SYMBOL res -320 80 R0 SYMATTR InstName R2 SYMATTR Value 100 SYMBOL res -320 -32 R0 SYMATTR InstName R3 SYMATTR Value 100 SYMBOL res -320 -144 R0 SYMATTR InstName R4 SYMATTR Value 100 SYMBOL res -320 -256 R0 SYMATTR InstName R5 SYMATTR Value 100 SYMBOL res -320 -368 R0 SYMATTR InstName R6 SYMATTR Value 100 SYMBOL res -320 -480 R0 SYMATTR InstName R7 SYMATTR Value 100 SYMBOL res -320 304 R0 SYMATTR InstName R8 SYMATTR Value 100 SYMBOL Switch -144 192 M0 SYMATTR InstName X8 SYMBOL Switch -144 -32 M0 SYMATTR InstName X10 SYMBOL Switch -144 -256 M0 SYMATTR InstName X12 SYMBOL Switch -16 -96 M0 SYMATTR InstName X16 SYMBOL Switch -16 352 M0 SYMATTR InstName X17 SYMBOL Switch 64 -192 M0 SYMATTR InstName X18 SYMBOL cap 224 64 R0 SYMATTR InstName C1 SYMATTR Value 1p SYMBOL SwitchClosed 128 240 R0 SYMATTR InstName X1 SYMBOL SwitchClosed -64 -304 R0 SYMATTR InstName X2 SYMBOL SwitchClosed -64 128 R0 SYMATTR InstName X3 SYMBOL SwitchClosed -208 -368 R0 SYMATTR InstName X4 SYMBOL SwitchClosed -208 -144 R0 SYMATTR InstName X6 SYMBOL SwitchClosed -208 80 R0 SYMATTR InstName X7 SYMBOL SwitchClosed -208 304 R0 SYMATTR InstName X9 TEXT -352 -584 Left 2 !.model CD4007N NMOS(LEVEL=1 KP=1123u VT0=0.5 LAMBDA=0.018)\n.model CD4007P PMOS(LEVEL=1 KP=1123u VT0=-0.5 LAMBDA=0.018) TEXT 168 -504 Left 2 !.global VDD\n.include opamp.sub\nV4 d2b 0 PULSE(0 5 0 1n 1n 3999n 8000n)\nV1 d2 0 PULSE(5 0 0 1n 1n 3999n 8000n) TEXT 232 -144 Left 2 !.tran 18000n TEXT 160 -392 Left 2 !V2 d0b 0 PULSE(0 5 0 1n 1n 999n 2000n)\nV5 d0 0 PULSE(5 0 0n 1n 1n 999n 2000n)\nV6 d1 0 PULSE(5 0 0 1n 1n 1999n 4000n)\nV7 d1b 0 PULSE(0 5 0 1n 1n 1999n 4000n)\nVDD Vref 0 DC 4 |
3 Bit R string or ladder DAC
SpeedTime constant:Ideal voltage source at a series RC low pass. R = (3 R || 5 R) = 15/8 R Maximum resistance for half VDD, code 100... PowerStaticP_{RS} = \frac{V_{ref}^2}{R \cdot 2^{B}} Number of bitsResistance range:1 Ω .. 1 MΩ 20 bits. Resistance for MOSFET switches and contacts. Complexity2B resistors and 2 * 2B switches are a high element count |
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τ = 0.25 · 2B R C
There are 2B of unit resistors.
The highest resistance is at midpoint. Half resistance will be connected to VDD and half to ground.
For equivalent resistance these resistances are in parallel.
There are 2B of unit resistors.
The highest resistance is at midpoint. Half resistance will be connected to VDD and half to ground.
For equivalent resistance these resistances are in parallel.
R2R DAC
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Only R and 2R values are needed. |
Version 4 SHEET 1 1212 680 WIRE -48 -480 -128 -480 WIRE -528 -384 -592 -384 WIRE -496 -384 -528 -384 WIRE -480 -384 -496 -384 WIRE -384 -384 -400 -384 WIRE -368 -384 -384 -384 WIRE -272 -384 -288 -384 WIRE -256 -384 -272 -384 WIRE -160 -384 -176 -384 WIRE -128 -384 -128 -480 WIRE -128 -384 -160 -384 WIRE -96 -384 -128 -384 WIRE 16 -384 -16 -384 WIRE 16 -368 16 -384 WIRE -496 -352 -496 -384 WIRE -384 -352 -384 -384 WIRE -272 -352 -272 -384 WIRE -160 -352 -160 -384 WIRE -592 -336 -592 -384 WIRE 16 -272 16 -304 WIRE -496 -240 -496 -272 WIRE -384 -240 -384 -272 WIRE -272 -240 -272 -272 WIRE -160 -240 -160 -272 WIRE -592 -208 -592 -256 FLAG -592 -208 0 FLAG -496 -240 D0 IOPIN -496 -240 In FLAG 16 -272 0 FLAG 16 -384 Voutfx FLAG -384 -240 D1 IOPIN -384 -240 In FLAG -272 -240 D2 IOPIN -272 -240 In FLAG -160 -240 D3 IOPIN -160 -240 In FLAG -48 -480 Vout IOPIN -48 -480 Out FLAG -528 -384 V0L FLAG -384 -384 V1L FLAG -272 -384 V2L SYMBOL res -608 -352 R0 SYMATTR InstName R0 SYMATTR Value 2k SYMBOL res -512 -368 R0 SYMATTR InstName R1 SYMATTR Value 2k SYMBOL res -496 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R5 SYMATTR Value 1k SYMBOL res 0 -400 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 10k SYMBOL cap 0 -368 R0 SYMATTR InstName C2 SYMATTR Value 1p SYMBOL res -400 -368 R0 SYMATTR InstName R2 SYMATTR Value 2k SYMBOL res -384 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R6 SYMATTR Value 1k SYMBOL res -288 -368 R0 SYMATTR InstName R3 SYMATTR Value 2k SYMBOL res -160 -368 M270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R7 SYMATTR Value 1k SYMBOL res -176 -368 R0 SYMATTR InstName R4 SYMATTR Value 2k TEXT -392 -168 Left 2 !VD0 D0 0 PULSE(1 0 0 1n 1n 99n 200n)\nVD1 D1 0 PULSE(1 0 0 1n 1n 199n 400n)\nVD2 D2 0 PULSE(1 0 0 1n 1n 399n 800n)\nVD3 D3 0 PULSE(1 0 0 1n 1n 799n 1600n) TEXT -608 -160 Left 2 !.tran 2u |
Calculation of output voltage with equivalent sources:
R is 1 kΩ.
All data inputs can be looked at as voltage sources VD0...VD3.
The voltages internally for equivalent sources are V0L..V2L, VoutL.
V_{0L} = V_{D0} \frac{2 R}{4 R} = V_{D0} \frac{1}{2}
R_{i0} = 2 R || 2R = \frac{2 R 2 R}{2 R + 2 R} = R
V_{1L} = (V_{0L} - V_{D1}) \frac{2 R}{4 R} + V_{D1} = V_{0L} \frac{1}{2} + V_{D1} \frac{1}{2} = V_{D0} \frac{1}{4} + V_{D1} \frac{1}{2}
R_{i1} = 2 R || 2R = \frac{2 R 2 R}{2 R + 2 R} = R
V_{nL} = (V_{(n-1)L} - V_{Dn}) \frac{2 R}{4 R} + V_{Dn} = V_{(n-1)L} \frac{1}{2} + V_{Dn} \frac{1}{2} = \sum_{i=0}^{n} \frac{V_{Di}}{2^{n-i+1}}
Capacitors can be used instead of the resistance R giving a C2C DAC.
R is 1 kΩ.
All data inputs can be looked at as voltage sources VD0...VD3.
The voltages internally for equivalent sources are V0L..V2L, VoutL.
V_{0L} = V_{D0} \frac{2 R}{4 R} = V_{D0} \frac{1}{2}
R_{i0} = 2 R || 2R = \frac{2 R 2 R}{2 R + 2 R} = R
V_{1L} = (V_{0L} - V_{D1}) \frac{2 R}{4 R} + V_{D1} = V_{0L} \frac{1}{2} + V_{D1} \frac{1}{2} = V_{D0} \frac{1}{4} + V_{D1} \frac{1}{2}
R_{i1} = 2 R || 2R = \frac{2 R 2 R}{2 R + 2 R} = R
V_{nL} = (V_{(n-1)L} - V_{Dn}) \frac{2 R}{4 R} + V_{Dn} = V_{(n-1)L} \frac{1}{2} + V_{Dn} \frac{1}{2} = \sum_{i=0}^{n} \frac{V_{Di}}{2^{n-i+1}}
Capacitors can be used instead of the resistance R giving a C2C DAC.
C2C DAC
Was sind Vorteile und Nachteile eines C2C DAC?
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Only C and 2C values are needed. Wie berechnen Sie die Ausgangsspannung? Was passiert bei einem Gleichspannungssignal? |
Version 4 SHEET 1 1884 680 WIRE 160 -96 112 -96 WIRE 256 -96 224 -96 WIRE 288 -96 256 -96 WIRE 368 -96 352 -96 WIRE 400 -96 368 -96 WIRE 480 -96 464 -96 WIRE 512 -96 480 -96 WIRE 592 -96 576 -96 WIRE 688 -96 592 -96 WIRE 736 -96 688 -96 WIRE 112 -80 112 -96 WIRE 256 -80 256 -96 WIRE 368 -80 368 -96 WIRE 480 -80 480 -96 WIRE 592 -80 592 -96 WIRE 816 -80 800 -80 WIRE 864 -80 816 -80 WIRE 736 -64 720 -64 WIRE 720 -32 720 -64 WIRE 816 -32 816 -80 WIRE 816 -32 720 -32 WIRE 256 0 256 -16 WIRE 368 0 368 -16 WIRE 480 0 480 -16 WIRE 592 0 592 -16 WIRE 240 160 240 144 WIRE 352 160 352 144 WIRE 352 160 240 160 WIRE 464 160 464 144 WIRE 464 160 352 160 WIRE 576 160 576 144 WIRE 576 160 464 160 WIRE 720 160 576 160 WIRE 112 176 112 -16 WIRE 272 176 272 144 WIRE 272 176 112 176 WIRE 384 176 384 144 WIRE 384 176 272 176 WIRE 496 176 496 144 WIRE 496 176 384 176 WIRE 608 176 608 144 WIRE 608 176 496 176 WIRE 720 176 608 176 WIRE 224 192 224 112 WIRE 336 192 336 112 WIRE 448 192 448 112 WIRE 560 192 560 112 WIRE 720 192 720 176 FLAG 864 -80 Vout IOPIN 864 -80 Out FLAG 720 160 Vref IOPIN 720 160 In FLAG 720 192 0 FLAG 448 192 D2 IOPIN 448 192 In FLAG 336 192 D1 IOPIN 336 192 In FLAG 224 192 D0 IOPIN 224 192 In FLAG 688 -96 Vint FLAG 560 192 D3 IOPIN 560 192 In SYMBOL Opamps\\opamp 768 -16 M180 SYMATTR InstName U1 SYMBOL cap 464 -80 R0 SYMATTR InstName C1 SYMATTR Value 10p SYMBOL cap 352 -80 R0 SYMATTR InstName C2 SYMATTR Value 10p SYMBOL cap 240 -80 R0 SYMATTR InstName C3 SYMATTR Value 10p SYMBOL Switch2 256 112 R270 SYMATTR InstName X1 SYMBOL Switch2 368 112 R270 SYMATTR InstName X2 SYMBOL Switch2 480 112 R270 SYMATTR InstName X3 SYMBOL cap 464 -112 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C4 SYMATTR Value 10p SYMBOL cap 576 -80 R0 SYMATTR InstName C5 SYMATTR Value 10p SYMBOL Switch2 592 112 R270 SYMATTR InstName X6 SYMBOL cap 96 -80 R0 SYMATTR InstName C6 SYMATTR Value 10p SYMBOL cap 224 -112 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C7 SYMATTR Value 10p SYMBOL cap 352 -112 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C8 SYMATTR Value 10p SYMBOL cap 576 -112 R90 WINDOW 0 0 32 VBottom 2 WINDOW 3 32 32 VTop 2 SYMATTR InstName C9 SYMATTR Value 10p SYMBOL cap 240 0 R0 SYMATTR InstName C10 SYMATTR Value 10p SYMBOL cap 352 0 R0 SYMATTR InstName C11 SYMATTR Value 10p SYMBOL cap 464 0 R0 SYMATTR InstName C12 SYMATTR Value 10p SYMBOL cap 576 0 R0 SYMATTR InstName C13 SYMATTR Value 10p TEXT 0 -208 Left 2 !.model CD4007N NMOS(LEVEL=1 KP=1123u VT0=0.5 LAMBDA=0.018)\n.model CD4007P PMOS(LEVEL=1 KP=1123u VT0=-0.5 LAMBDA=0.018) TEXT -64 296 Left 2 !.global VDD\n.include opamp.sub\nV0 reset 0 PULSE(-1 5 0 1n 1n 499n 16000n)\nV4 d3 0 PULSE(5 -1 0 1n 1n 7999n 16000n)\nV1 d2 0 PULSE(5 -1 0 1n 1n 3999n 8000n) TEXT 776 -136 Left 2 !.tran 16000n TEXT 448 320 Left 2 !V2 d1 0 PULSE(5 -1 0 1n 1n 1999n 4000n)\nV3 d0 0 PULSE(5 -1 0n 1n 1n 999n 2000n)\nVref Vref 0 DC 4\nVDD VDD DC 4 TEXT 712 24 Left 2 !.save V(vout) |
Beispiel eines R2R DAC
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Der Widerstand R2 wurde auf 2.5 kΩ geändert. Berechnen Sie die Ausgangsspanungen. |
Version 4 SHEET 1 1212 680 WIRE -48 -480 -128 -480 WIRE -432 -384 -496 -384 WIRE -400 -384 -432 -384 WIRE -384 -384 -400 -384 WIRE -288 -384 -304 -384 WIRE -272 -384 -288 -384 WIRE -176 -384 -192 -384 WIRE -128 -384 -128 -400 WIRE -128 -384 -176 -384 WIRE -96 -384 -128 -384 WIRE 16 -384 -16 -384 WIRE 16 -368 16 -384 WIRE -400 -352 -400 -384 WIRE -288 -352 -288 -384 WIRE -176 -352 -176 -384 WIRE -496 -336 -496 -384 WIRE 16 -272 16 -304 WIRE -400 -240 -400 -272 WIRE -288 -240 -288 -272 WIRE -176 -240 -176 -272 WIRE -496 -208 -496 -256 FLAG -496 -208 0 FLAG -400 -240 D0 IOPIN -400 -240 In FLAG 16 -272 0 FLAG 16 -384 Voutfx FLAG -288 -240 D1 IOPIN -288 -240 In FLAG -176 -240 D2 IOPIN -176 -240 In FLAG -48 -480 Vout IOPIN -48 -480 Out FLAG -432 -384 V0L FLAG -288 -384 V1L FLAG -176 -384 V2L SYMBOL res -512 -352 R0 SYMATTR InstName R0 SYMATTR Value 2k SYMBOL res -416 -368 R0 SYMATTR InstName R1 SYMATTR Value 3k SYMBOL res -400 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R5 SYMATTR Value 1k SYMBOL res 0 -400 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 10k SYMBOL cap 0 -368 R0 SYMATTR InstName C2 SYMATTR Value 1p SYMBOL res -304 -368 R0 SYMATTR InstName R2 SYMATTR Value 2k SYMBOL res -288 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R6 SYMATTR Value 1k SYMBOL res -192 -368 R0 SYMATTR InstName R3 SYMATTR Value 2k SYMBOL res -144 -496 R0 SYMATTR InstName R4 SYMATTR Value 1 TEXT -392 -168 Left 2 !VD0 D0 0 PULSE(1 0 0 1n 1n 99n 200n)\nVD1 D1 0 PULSE(1 0 0 1n 1n 199n 400n)\nVD2 D2 0 PULSE(1 0 0 1n 1n 399n 800n) TEXT -608 -160 Left 2 !.tran 2u TEXT 72 -416 Left 2 !.meas tran v000 FIND V(Vout) AT=50n\n.meas tran v001 FIND V(Vout) AT=150n\n.meas tran v010 FIND V(Vout) AT=250n\n.meas tran v011 FIND V(Vout) AT=350n\n.meas tran v100 FIND V(Vout) AT=450n\n.meas tran v101 FIND V(Vout) AT=550n\n.meas tran v110 FIND V(Vout) AT=650n\n.meas tran v111 FIND V(Vout) AT=750n |
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Äquivalente Quellen und Zusammenfassen: R2 = 2.5k Die Dateneingänge sind ideale Quellen VD0...VD3. V_{0L} = V_{D0} \frac{R0}{R0 + R1} = V_{D0} \frac{1}{2} R_{i0} = R0 || R1 = \frac{R0 R1}{R0 + R1} = R0 V_{1L} = (V_{0L} - V_{D1}) \frac{R2}{R2 + R5 + Ri0} + V_{D1} = (V_{0L} - V_{D1}) 0.45 + V_{D1} V_{1L} = 0.56 \cdot V_{0L} + 0.44 \cdot V_{D1} R_{i1} = R2 || (Ri0 + R5) = \frac{R2 * (Ri0 + R5) }{R2 + Ri0 + R5} = 1.1 R0 V_{2L} = (V_{1L} - V_{D2}) \frac{R3}{R3 + R6 + R_{i1}} + V_{D2} V_{2L} = (V_{1L} - V_{D2}) 0.486 + V_{D2} V_{2L} = 0.486 V_{1L} + 0.514 V_{D2} R0 = 2 kΩ, R1 = 2 kΩ, R2 = 2.5 kΩ, R3 = 2 kΩ, R5 = 1 kΩ, R6 = 1
V0L = 0.5 VD1 Ri0 = 1 R0 V1L = 0.56 V0L + 0.44 VD1 Ri1 = 1.11 R0 V2L = 0.49 V1L + 0.51 VD2 V2L ( 000)= 0 V V2L ( 001)= 0.135 V V2L ( 010)= 0.216 V V2L ( 011)= 0.351 V V2L ( 100)= 0.514 V V2L ( 101)= 0.649 V V2L ( 110)= 0.73 V V2L ( 111)= 0.865 V LSBreal = (0.865 V - 0 V) / 7 = 0.124 V |
Version 4 SHEET 1 1212 680 WIRE -48 -480 -128 -480 WIRE -480 -384 -512 -384 WIRE -384 -384 -400 -384 WIRE -288 -384 -304 -384 WIRE -272 -384 -288 -384 WIRE -176 -384 -192 -384 WIRE -128 -384 -128 -480 WIRE -128 -384 -176 -384 WIRE -96 -384 -128 -384 WIRE 16 -384 -16 -384 WIRE 16 -368 16 -384 WIRE -288 -352 -288 -384 WIRE -176 -352 -176 -384 WIRE 16 -272 16 -304 WIRE -288 -240 -288 -272 WIRE -176 -240 -176 -272 FLAG 16 -272 0 FLAG 16 -384 Voutfx FLAG -288 -240 D1 IOPIN -288 -240 In FLAG -176 -240 D2 IOPIN -176 -240 In FLAG -48 -480 Vout IOPIN -48 -480 Out FLAG -512 -384 V0L FLAG -288 -384 V1L FLAG -176 -384 V2L SYMBOL res -400 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R5 SYMATTR Value 1k SYMBOL res 0 -400 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 10k SYMBOL cap 0 -368 R0 SYMATTR InstName C2 SYMATTR Value 1p SYMBOL res -304 -368 R0 SYMATTR InstName R2 SYMATTR Value 2.5k SYMBOL res -288 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName R6 SYMATTR Value 1k SYMBOL res -192 -368 R0 SYMATTR InstName R3 SYMATTR Value 2k SYMBOL res -496 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName Ri0 SYMATTR Value 1k TEXT -392 -168 Left 2 !V0L V0L 0 PULSE(0.5 0 0 1n 1n 99n 200n)\nVD1 D1 0 PULSE(1 0 0 1n 1n 199n 400n)\nVD2 D2 0 PULSE(1 0 0 1n 1n 399n 800n) TEXT -440 -216 Left 2 !.tran 2u Version 4 SHEET 1 1212 680 WIRE -48 -464 -128 -464 WIRE -368 -384 -384 -384 WIRE -352 -384 -368 -384 WIRE -176 -384 -192 -384 WIRE -128 -384 -128 -464 WIRE -128 -384 -176 -384 WIRE -96 -384 -128 -384 WIRE 16 -384 -16 -384 WIRE 16 -368 16 -384 WIRE -176 -352 -176 -384 WIRE 16 -272 16 -304 WIRE -176 -256 -176 -272 FLAG 16 -272 0 FLAG 16 -384 Voutfx FLAG -176 -256 D2 IOPIN -176 -256 In FLAG -48 -464 Vout IOPIN -48 -464 Out FLAG -368 -384 V1L FLAG -176 -384 V2L SYMBOL res 0 -400 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value 10k SYMBOL cap 0 -368 R0 SYMATTR InstName C2 SYMATTR Value 1p SYMBOL res -368 -368 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 0 56 VBottom 2 SYMATTR InstName Ri1 SYMATTR Value 1.1k SYMBOL res -192 -368 R0 SYMATTR InstName R3 SYMATTR Value 2k SYMBOL res -176 -400 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R6 SYMATTR Value 1k TEXT -312 -184 Left 2 !V0L V0L 0 PULSE(0.5 0 0 1n 1n 99n 200n)\nVD1 D1 0 PULSE(1 0 0 1n 1n 199n 400n)\nB1 V1L 0 V=0.6*V(V0L)+0.4*V(D1)\nVD2 D2 0 PULSE(1 0 0 1n 1n 399n 800n) TEXT -296 -320 Left 2 !.tran 2u |
R2R DAC
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Realer R2R DAC 8-Bit |
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