Cyber-Physical Systems ADC / DAC

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1 Cyber-Physical Systems ADC / DAC ICEN 553/453 Fall 2018 Prof. Dola Saha 1

2 Analog-to-Digital Converter (ADC) Ø ADC is important almost to all application fields Ø Converts a continuous-time voltage signal within a given range to discrete-time digital values to quantify the voltage s amplitudes x(t) x(n) continuous-time analog signal ADC quantize discrete-time digital values 2

3 Analog-to-Digital Converter (ADC) Ø Three performance parameters: sampling rate number of conversions per unit time Resolution number of bits an ADC output power dissipation power efficiency Ø Many ADC implementations: sigma-delta (low sampling rate, high resolution) successive-approximation (low power data acquisition) Pipeline (high speed applications) 3

4 Successive-approximation (SAR) ADC 4

5 Digital Quantization Ø SAR Control Logic performs Binary Search algorithm DAC output is set to 1/2V REF If V IN > V REF, SAR Control Logic sets the MSB of ADC, else MSB is cleared V DAC is set to ¾ V REF or ¼ V REF depending on output of previous step Repeat until ADC output has been determined Ø How long does it take to converge? 5

6 Successive-approximation (SAR) ADC Binary search algorithm to gradually approaches the input voltage Settle into ½ LSB bound within the time allowed T "#$ = T &'()*+,- + T $/,012&+/, T $/,012&+/, = N T "#$_$*/67 T &'()*+,- is software configurable 6

7 ADC Conversion Time T "#$ = T &'()*+,- + T $/,012&+/, Ø Suppose ADC CLK = 16 MHz and Sampling time = 4 cycles For 12-bit ADC T "#$ = = 16 cycles = 1µs For 6-bit ADC T "#$ = = 10 cycles = 625ns 7

8 Determining Minimum Sampling Time Ø When the switch is closed, the voltage across the capacitor increases exponentially. t= time required for the sample capacitor voltage to V " t = V %& (1 e, -. /) settle to within one-fourth of an LSB of the input voltage Larger sampling time Smaller sampling error Slower ADC speed Sampling time is often software programmable! Tradeoff 8

9 Resolution Ø Resolution is determined by number of bits (in binary) to represent an analog input. Ø Example of two quantization methods (N = 3) Δ ½ Δ Digital Result =,loor 2 0 V Digital Result = round 2 0 V V 345 V 345 Max quantization error = Δ = V REF /2 3 Max quantization error = ½ Δ = V REF /2 4 round x =,loor(x + 0.5) 9

10 Quantization Error Ø For N-bit ADC, it is limited to ±½Δ Ø Δ = is the step size of the converter. Ø Example: for 12-bit ADC and input voltage range [0, 3V]!"# $%"&'()"'(*& +,,*, = 1 2 Ø How to reduce error? Δ 32 = = 0.367:

11 Aliasing Ø Example 1: Consider a sinusoidal sound signal at 1 khz :! " = cos(2000*") Sampling interval T = 1/8000 Samples, - =.! -/ = cos(*-/4) Ø Example 2: Consider a sinusoidal sound signal at 9 khz :! " = cos(18000*") Sampling interval T = 1/8000 Samples, 5 6 =.! -/ = cos = cos *- = cos 86 9 =,(-) Ø There are many distinct functions x that when sampled will yield the same signal s. 11

12 Minimum Sampling Rate Ø Ø In order to be able to reconstruct the analog input signal, the sampling rate should be at least twice the maximum frequency component contained in the input signal Example of two sine waves have the same sampling values. This is called aliasing. Nyquist Shannon Sampling Theorem Ø Antialiasing Pre-filtering: use analog hardware to filtering out high-frequency components and only sampling the low-frequency components. The high-frequency components are ignored. Post-filtering: Oversample continuous signal, then use software to filter out high-frequency components 12

13 ADC Conversion Ø Input Range Unipolar (0, V ADCMAX ) Bipolar (-V ADCMAX, +V ADCMAX ) Clipping: o If V IN > V ADCMAX, then V OUT = V ADCMAX 13

14 Automatic Gain Control (AGC) Ø Closed loop Feedback regulating circuit in an amplifier Ø Maintains a suitable signal amplitude at its output, despite variation of the signal amplitude at the input Ø The average or peak output signa level is used to dynamically adjust the gain of the amplifiers Ø Example Use: Radio Receivers, Audio Recorders, Microphone 14

15 Power and RMS of Signal Ø Average Power of a signal 56) / 0 = ! - * Ø Crest Factor 8 =! 9:;<! "#$ Ø Square root of the arithmetic mean of the squares of the values! "#$ = 1 ' (! ) * +! * * + +! - * ) Ø Crest Factor Sine Wave ~ 3.01dB, OFDM ~12dB 15

16 PAPR Ø Crest Factor in db! "# = 20'() *+ -./ Ø Peak to Average Power Ratio (PAPR) 5657 = -./ "# = 10'() *+ -./ =! "# 16

17 Example Gain Control Ø AD

18 Digital-to-analog converter (DAC) Ø Converts digital data into a voltage signal by a N-bit DAC Ø For 12-bit DAC!"# $%&'%& = ) *+,!./.012 ) Ø Ø Many applications: digital audio waveform generation Performance parameters speed resolution power dissipation glitches!./.012 )1234!"# $%&'%& = ) *+,

19 DAC Implementations Pulse-width modulator (PWM) Binary-weighted resistor (We will use this one as an example) R-2R ladder (A special case of binary-weighted resistor) 19

20 Binary-weighted Resistor DAC -V ref D 3 D 2 D 1 D 0 R/8 R/4 R/2 R R ref V out! "#$ =! &'( * &'( * (, , , 1 2 +, 2 ) 20

Digital Music 0 1 2 3 4 5 6 7 8 C 16.352 32.703 65.406 130.813 261.626 523.251 1046.502 2093.005 4186.009 C# 17.324 34.648 69.296 138.591 277.183 554.365 1108.731 2217.461 4434.922 D 18.354 36.708 73.

21 Digital Music C C# D D# E F F# G G# A A# B Musical Instrument Digital Interface (MIDI) standard assigns the note A as pitch 69.! = (()*+)/./ = = log /!

22 Digital Music Generate Sine Wave Ø Ø Ø No FPU available on the processor to compute sine functions Software FP to compute sine is slow Solution: Table Lookup Compute sine values and store in table as fixpoint format Look up the table for result Linear interpolation if necessary 22 22

23 Digital Music: Attack, Decay, Sustain, Release (ADSR) Ø Amplitude Modulation of Tones (modulate music amplitude) Attack Decay Sustain Release Implemented by a simple digital filter: ADSR n = g ADSR + (1 g) ADSR(n 1) where ADSR is the target modulated amplitude value, g is the gain parameter

24 Digital Music: ADSR Amplitude Modulation Attack + Decay Sustain Release 24 24

PHYS225 Lecture 22. Electronic Circuits

PHYS225 Lecture 22. Electronic Circuits PHYS225 Lecture 22 Electronic Circuits Last lecture Digital to Analog Conversion DAC Converts digital signal to an analog signal Computer control of everything! Various types/techniques for conversion