Interface Electronics12 Sigma Delta Oversampling ADCProf. Dr. Jörg Vollrath11 Pipeline ADC |
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0:0:0 Oversampling ADC 0:4:36 Sigma Delta ADC Architecture 0:12:38 First order passive Sigma Delta Modulator 0:16:51 Internal voltage calculation 0:17:10 0 0:17:10 Example Sigma Delta 0:19:46 Transfer function 0:22:10 f3dB = 15.9 kHz 0:25:46 Output data sequence 0:29:16 dt/R/C = 0.05 0:33:6 Time sequence of voltages 0:36:6 High level simulator (webpage) 0:42:12 LTSPICE simulation sine 0:48:4 General signal and noise transfer function 0:51:14 Noise Shaping 0:52:48 Digital filter and decimator 0:56:16 Example simulation ramp 1:0:46 Example simulation sine 1:5:46 Discussion understanding and simulation 1:9:21 Increasing Signal to noise with oversampling |
Nyquist ADCOversamplingfCLK = OSR · 2 · fbw Clock frequency is much higher than bandwidth. Pulse count Modulation (PCM)Predictive CodingQuantize difference of the signal Sigma delta converter |
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Version 4 SHEET 1 1168 680 WIRE 0 128 -32 128 WIRE 160 128 80 128 WIRE 272 128 160 128 WIRE 320 128 272 128 WIRE 464 144 432 144 WIRE 496 144 464 144 WIRE 80 160 80 128 WIRE 864 160 832 160 WIRE 976 160 944 160 WIRE 1040 160 976 160 WIRE 320 176 288 176 WIRE 160 208 160 192 WIRE 976 240 976 224 WIRE 80 304 80 240 WIRE 128 304 80 304 WIRE 352 304 128 304 WIRE 464 304 464 144 WIRE 464 304 416 304 FLAG -32 128 In IOPIN -32 128 In FLAG 496 144 Out FLAG 272 128 INT FLAG 128 304 ND FLAG 288 176 CMP FLAG 160 208 0 FLAG 976 240 0 FLAG 832 160 Out FLAG 1040 160 out1 SYMBOL Diffamp 384 144 R0 SYMATTR InstName X3 SYMBOL cap 144 128 R0 SYMATTR InstName C1 SYMATTR Value 10p SYMBOL res 64 144 R0 SYMATTR InstName R1 SYMATTR Value 200k SYMBOL res 96 112 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 200k SYMBOL INVx 384 304 M0 SYMATTR InstName X1 SYMBOL res 960 144 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value 200k SYMBOL cap 960 160 R0 SYMATTR InstName C2 SYMATTR Value 10p TEXT 560 48 Left 2 !.global VDD CE RSTb CLK\nVCLK CLK 0 PULSE(0 1 0 0.1n 0.1n 100n 200n)\nVIN IN 0 SINE( 0.55 0.4 5798.33984375)\n*VIN IN 0 DC 0.5\nVDD VDD 0 DC 1\nVCMP CMP 0 DC 0.5\nVRST RSTb 0 DC 1\nVCE CE 0 DC 1\n.tran 0 3.2808m 4u\n* 100ns * 4 * 4096 (punkte fft) = 3.2768ms trans\n* 19 Perioden => 1/3.2768m*19 = 5798.33984375 TEXT -72 64 Left 2 !.include cmosedu_models.txt TEXT -88 328 Left 2 !.options plotwinsize=0
Internal voltage levels:The voltage V(INT n+1) at clock cycle n+1 is:V_{int n+1} = V_{int n} + \frac{\delta t}{C} \left( \frac{ V_{not(Dout)} - V_{int n}}{R} + \frac{V_{in} - V_{int n}}{R} \right) V_{int n+1} = V_{int n} + \frac{\delta t}{C \cdot R} \left( V_{not(Dout)} + V_{in} - 2 \cdot V_{int n} \right) \delta t is the period of the clock. V_{Dout} in a real logic circuit is 0V or VDD. \frac{\delta t}{C \cdot R} = \frac{2 \pi f_{sample}}{f_{CLK}} = \frac{2 \pi }{OSR} These equations are used for a high level simulation. High level simulation: 1st order sigma delta simulation Since Vint has to stay between 0V and VDD: \frac{\delta t}{C \cdot R} 2 V_{DD} \lt V_{DD} C \cdot R \gt \frac{2}{f_{sample} } \frac{1}{C \cdot R} \lt \frac{f_{sample} }{2} The bandwidth limit of RC has to be smaller than fsample/2. The bandwidth limit of RC has to be greater than the interested bandwith. fsample/2/OSR 2 \pi f_{bw} \lt \frac{1}{C \cdot R} \lt \frac{f_{sample} }{2} |
t [µs] | 0 | 1 | 2 | 3 | 4 |
vin | 0.3V | ||||
vint | 0.5V | ||||
vout | 0V |
t [µs] | 0 | 1 | 2 | 3 | 4 |
vin | 0.3V | 0.3V | 0.3V | 0.3V | 0.3V |
vint | 0.5V | 0.515V | 0.479V | 0.496V | 0.511V |
vout | 0V | 1V | 0V | 0V | 1V |
Signal pole: ω=3/(RC) Noise zero: ω=2/(RC) Noise pole: ω=3/(RC) Position fclk Position fbw = 3/(2 π R C) Noise is digitally filtered. \epsilon_q = \frac{LSB}{\sqrt{12}} - 20 log \sqrt{12} = -10.8 dB |
SINC Filter Filter order: SINC, SINC2, SINC3 The order of the filter has to be one more than the sigma delta modulator to realize the full signal to noise benefit. |
![]() A decimating Sinc2 filter has the following schematic with 2 integrators and 2 differentiators: ![]() |
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Example: fbw = 1 kHz 1. Order 1-bit sigma delta 8-bit resolution desired. |
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Example: 8-bit signal with 4-bit noise amplitude. Signal: V_{rms} = \frac{V_{amplitude}}{\sqrt{2}} Noise: Vrms = VPP/6 = Vamplitude/3
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Version 4 SymbolType BLOCK LINE Normal -25 -16 -57 -16 LINE Normal -41 -1 -41 -33 LINE Normal -26 32 -58 32 LINE Normal -64 -64 48 0 LINE Normal -64 64 -64 -64 LINE Normal 48 0 -64 64 WINDOW 0 32 -40 Bottom 2 PIN -64 32 NONE 8 PINATTR PinName M PINATTR SpiceOrder 1 PIN -64 -16 NONE 8 PINATTR PinName P PINATTR SpiceOrder 2 PIN 48 0 NONE 8 PINATTR PinName Y PINATTR SpiceOrder 3
Version 4 SymbolType BLOCK LINE Normal -31 -15 9 1 LINE Normal -31 17 9 1 LINE Normal -31 17 -31 -15 LINE Normal 25 1 33 1 CIRCLE Normal 25 9 9 -7 WINDOW 0 0 -24 Bottom 0 PIN -32 0 NONE 8 PINATTR PinName A PINATTR SpiceOrder 1 PIN 32 0 NONE 8 PINATTR PinName Y PINATTR SpiceOrder 2