Analog/Digital and Sampling

Size: px

Start display at page:

Download "Analog/Digital and Sampling"

Simon Rodgers
5 years ago
Views:

1 Analog/Digital and Sampling Alexander Nelson October 22, 2018 University of Arkansas - Department of Computer Science and Computer Engineering

2 Analog Signals in the real world are analog signals Process them as digital signals Analog Continuous in time and amplitude Digital Discrete in time and amplitude 1

3 Conversion To work with sensor data, analog signals must be converted to digital Analog to Digital Conversion (A to D) 2

4 Sampling Sampling Converting Analog to Digital Values Sample Single Measurement in time Nyquist Rate Minimum rate at which periodic signal can be sampled without introducing aliasing errors 3

5 Sampling Green Analog signal Blue Digital samples 4

6 Error Sources Measurement Error Instantaneous value measurement error e.g. Voltage measurement within ± 0.05V Quantization Error Difference between measured value and discrete value Aliasing Errors Missing signals by sampling too slowly 5

7 Digital Representation How do you represent a real number in a given number of bits? 6

8 Digital Representation Quantization representing a real number in a given number of bits? Choosing Quantization Levels: Assume you want to represent 0V-5V given a 10-bit value 0V = 0b0; 5V = 0b = 1023 How much is each bit worth? 7

9 Digital Representation Quantization representing a real number in a given number of bits? Choosing Quantization Levels: Assume you want to represent 0V-5V given a 10-bit value 0V = 0b0; 5V = 0b = V V LSB LSB 512 = 2.502V MSB Any measurement difference from a multiple of is quantization error 8

10 Quantization Error Example Assume a 10-bit ADC measuring a 0-5V signal: A sample is measured when instantaneous value is 2.83V Assume measurement error is 0 What is the quantization error? 9

11 Quantization Error Example Assume a 10-bit ADC measuring a 0-5V signal: A sample is measured when instantaneous value is 2.83V Assume measurement error is 0 What is the quantization error? 2.83V 5V = = is the ADC value V (LSB) V 10

12 Sampling Theorem Bridge between continuous-time and discrete-time signals (i.e. analog and digital) Meaning that Analog Digital Analog can reproduce the original signal 11

13 Shannon s Theorem If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart. If a sampling rate is 2 times faster than fastest analog signal, the original signal can be reconstructed from the sampled signal 12

14 Aliasing Error Aquisition-and-IO/The-Fine-Art-of-Analog-Signal-Sampling.aspx 13

15 Analog to Digital Converters Analog to Digital Converter A2D/ADC/(A/D), A to D Device to convert physical quantity (voltage) to a discrete (digital) value Multiple types of ADC architectures: Parallel/Serial stages Single/Multiple conversion steps One or more clock cycles Each architecture has trade-offs e.g. Power/size/speed/accuracy/etc... 14

16 ADC Features 15

17 ADC Circuit 16

18 Successive Approximation ADC 2 2 By White Flye - Own work, CC BY-SA 2.5, 17

19 Successive Approximation ADC Components: Successive Approximation Register Digital to Analog Converter Comparator Sample and Hold Amplifier 18

20 Sample and Hold For serialized ADC circuits, the S/H circuit is important Composed of two amplifiers, a switch, and a hold capacitor 19

21 Sample and Hold Sample and hold maintains voltage for a length of time Top: Samples at given time Bottom: Samples held until start of next sample 20

22 Sample and Hold Hold command sent switch is opened H c maintains the voltage on output terminal Charge on output terminal should change < 1 LSB during conversion H c should have low leakage and dielectric absorption 21

23 Digital to Analog Converter (DAC) Convert a digital value to an analog voltage Different methods: Pulse Width Modulation with low pass filter Oversampling/Interpolating DACs (sigma-delta) Binary-weighted DAC (switched resistor, switched capacitor, switched current source) Successive-Approximation/Cyclic DAC 22

24 PWM DAC More filtering = better approximation, longer settle time 23

25 Analog Comparator Circuit that produces a digital signal determining which of two inputs is higher 1 V + V V 0 = 0 V + < V In other words: Voltage out = Vdd if analog input greater than reference; GND if input less than reference 24

26 Analog Comparator 3 3 By Rakesh310 - Own work, CC BY-SA 4.0, 25

27 Successive Approximation Algorithm Algorithm: 1. Compare against half of range 2. Continue narrowing until limited by LSB 3. Error upper bounded by 1 LSB Assuming value just less than next LSB, and no nearest bit comparison 26

28 Successive Approximation Timing Assuming DAC can obtain stable comparison voltage in < 1 cycle How many clock cycles to convert Successive Approximation for a 10-bit ADC? 27

29 Successive Approximation Timing Assuming DAC can obtain stable comparison voltage in < 1 cycle How many clock cycles to convert Successive Approximation for a 10-bit ADC? Binary Search Tree N-bit conversion takes N-steps e.g. 10-bit ADC = 10 clock cycles 28

30 What about 16 bits? 29

Systems & Devices Part 1

Systems & Devices Part 1 Alexander Nelson February 5th, 2018 University of Arkansas - Department of Computer Science and Computer Engineering What composes wearable, ubiquitous, or invisible systems? 0