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EECS 373 F99 Notes: Analog/Digital Conversion, Study notes of Electrical and Electronics Engineering

University of Michigan (UM) - Ann ArborElectrical and Electronics Engineering

An overview of analog-to-digital (adc) and digital-to-analog (dac) conversion, focusing on the concepts, circuits, and errors involved. It covers resolution, quantization error, accuracy, non-linearity, and conversion time.

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

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EECS 373 F99 Notes 7-1 © 1998, 1999 Steven K. Reinhardt
Analog/Digital Conversion
The real world is analog. Interfacing a microprocessor-based
system to real-world devices often requires conversion between
the microprocessor’s digital representation of values to an
analog representation. We will focus on conversions to and
from analog voltages; converting from electrical signals to
other signals is the domain of sensors (e.g., thermistors) and
transducers (e.g., speakers).
•Analog input signals are converted to digital values using
analog-to-digital converters (ADCs).
•Analog output signals based on digital values are generated
using digital-to-analog converters (DACs).
•ADCs and DACs are commonly available as single-chip
devices that can be easily interfaced to microprocessor
busses.
Outline
•Common conversion concepts
•Digital-to-analog conversion circuits
•Analog-to-digital conversion circuits
pf3
pf4
pf5

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Analog/Digital Conversion

The real world is analog. Interfacing a microprocessor-based system to real-world devices often requires conversion between the microprocessor’s digital representation of values to an analog representation. We will focus on conversions to and from analog voltages; converting from electrical signals to other signals is the domain of sensors (e.g., thermistors) and transducers (e.g., speakers).

  • Analog input signals are converted to digital values using analog-to-digital converters (ADCs).
  • Analog output signals based on digital values are generated using digital-to-analog converters (DACs).
  • ADCs and DACs are commonly available as single-chip devices that can be easily interfaced to microprocessor busses.

Outline

  • Common conversion concepts
  • Digital-to-analog conversion circuits
  • Analog-to-digital conversion circuits

Basics

  • The primary characteristic of a converter is its resolution , expressed as the number of significant data bits on the digital side of the converter. An n -bit converter divides an analog voltage range into 2 n^ sections, providing a resolution of 2 -n^ times the voltage range.
  • Error is the difference between the analog voltage you believe a digital value represents and what that analog voltage acutally is. As we will see shortly, even an ideal converter introduces some error.
  • Accuracy refers to how close an actual converter is to an ideal converter. Inaccuracies are another source of error.
  • The graph below shows the transfer function for an ideal 2-bit ADC. The input voltage range (0, Vref) is divided into 22 = 4 sections, so the ADC’s resolution is 2-2^ = 1/4 of Vref.

Quantization Error and LSBs

  • Each code (digital value) represents a range of analog inputs; e.g., the ADC will read ‘01’ for any voltage in the range (Vref/4, Vref/2). The best we can do is assume that ‘01’ means 3Vref/8. Since the actual voltage could be as low as Vref/4 or as high as Vref/2, there is a potential error of ±Vref/8. This error is called quantization error.
  • Quantization error is inherent in the process of converting a continuous analog voltage to a finite number of discrete digital values. Even an ideal converter introduces quantization error.
  • The absolute value of the quantization error in volts (along with most other types of conversion errors) depends on the voltage range (i.e. the value of Vref) and the resolution of the converter. To normalize these parameters away, errors are typically expressed in terms of the ideal analog voltage difference represented by a unit change in the digital value.
  • Since this unit change represents a change in the least significant bit of the digital value, this voltage difference is referred to as an LSB.
  • Quantization error is always ±1/2 LSB.

11

10

01

00 Vref Vref 4

0 Vref 2

3Vref 4 Input Voltage

Output Code

DAC Types

Voltage divider

  • Fast
  • Expensive: requires 2 n^ resistors, switches
  • accuracy depends on matching all resistor values (but not exact resistor values)
  • Guaranteed monotonic

R/2R Ladder

  • Cheaper: ~2 n resistors, n switches
  • Again, accuracy depends on matching all resistor values (but not exact resistor values)
  • Harder to enforce monotonicity (consider 0111 -> 1000)
  • Provides current output; op-amp required to convert to voltage, increases conversion time

Vref

R

R

R

R

2-to- decoder

Vout

Din[2]

2R

R R 2R

2R

R

2R

Vref

2R

(MSB) (LSB)

D3 D2 D1 D

Iout

ADC Types

Flash

  • ADC equivalent of voltage-divider DAC
  • Same issues: fast but expensive (2 n^ resistors, 2 n - comparators)

Successive Approximation (SA)

  • binary search to match voltage
  • Algorithm:
    1. Set successive approximation register to 0
    2. Starting at MSB, flip one bit to 1
    3. If DAC output < Vin, leave, else reset to 0
    4. go to next bit
  • example: 4-bit ADC, Vref = 4.8V, Vin = 3.2V
  • need fairly stable input through conversion process
  • much cheaper than flash (only one comparator, 2 n^ or 2 n resistors depending on DAC type)
  • conversion time > n times DAC settling time

Vref

R

R

R

R

Vin

priority encoder

Vcc 0

Dout[2]

successive approximation register

DAC

Vin

control

Dout

n

Vref

CLK