AnalogtoDigital Conversion

1
Analog-to-Digital Conversion

• Terminology
• analog continuously valued signal, such as
  temperature or speed, with infinite possible
  values in between
• digital discretely valued signal, such as
  integers, encoded in binary
• analog-to-digital converter ADC, A/D, A2D
  converts an analog signal to a digital signal
• digital-to-analog converter DAC, D/A, D2A
• An embedded systems surroundings typically
  involve many analog signals.

2
Analog-to-digital converters
Embedded Systems Design A Unified
Hardware/Software Introduction, (c) 2000
Vahid/Givargis
3
Proportional Signals

• Simple Equation
• Assume minimum voltage of 0 V.
• Vmax maximum voltage of the analog signal
• a analog value
• n number of bits for digital encoding
• 2n number of digital codes
• M number of steps, either 2n or 2n 1
• d digital encoding
• a / Vmax d / M

4
Resolution

• Let n 2
• M 2n 1
• 3 steps on the digital scale
• d0 0 0b00
• dVmax 3 0b11
• M 2n
• 4 steps on the digital scale
• d0 0 0b00
• dVmax - r 3 0b11 (no dVmax )
• r, resolution smallest analog change resulting
  from changing one bit

5
DAC vs. ADC

• DAC
• n digital inputs for digital encoding d
• analog input for Vmax
• analog output a
• ADC
• Given a Vmax analog input and an analog input a,
  how does the converter know what binary value to
  assign to d in order to satisfy the ratio?
• may use DAC to generate analog values for
  comparison with a
• ADC guesses an encoding d, then checks its
  guess by inputting d into the DAC and comparing
  the generated analog output a with original
  analog input a
• How does the ADC guess the correct encoding?

6
ADC Digital Encoding

• Guessing the encoding is similar to finding an
  item in a list.
• Sequential search counting up start with an
  encoding of 0, then 1, then 2, etc. until find a
  match.
• 2n comparisons Slow!
• Binary search successive approximation start
  with an encoding for half of maximum then
  compare analog result with original analog input
  if result is greater (less) than the original,
  set the new encoding to halfway between this one
  and the minimum (maximum) continue dividing
  encoding range in half until the compared
  voltages are equal
• n comparisons Faster, but more complex converter
• ? Takes time to guess the encoding start
  conversion input, conversion complete output

7
Digital-to-analog conversion using successive
approximation
Given an analog input signal whose voltage should
range from 0 to 15 volts, and an 8-bit digital
encoding, calculate the correct encoding for 5
volts. Then trace the successive-approximation
approach to find the correct encoding. 5/15
d/(28-1) d 85
Encoding 01010101
Successive-approximation method
½(Vmax Vmin) 7.5 volts Vmax 7.5 volts.
½(5.63 4.69) 5.16 volts Vmax 5.16 volts.
½(7.5 0) 3.75 volts Vmin 3.75 volts.
½(5.16 4.69) 4.93 volts Vmin 4.93 volts.
½(7.5 3.75) 5.63 volts Vmax 5.63 volts
½(5.16 4.93) 5.05 volts Vmax 5.05 volts.
½(5.63 3.75) 4.69 volts Vmin 4.69 volts.
½(5.05 4.93) 4.99 volts
Embedded Systems Design A Unified
Hardware/Software Introduction, (c) 2000
Vahid/Givargis
8
Bit Weight

• Notice the concept of bit weight in the last
  example
• bit 7 7.5 V 15/2
• bit 6 3.75 V 15/4
• Each bit is weighted with an analog value, such
  that a 1 in that bit position adds its analog
  value to the total analog value represented by
  the digital encoding.
• Example -5 V to 5 V analog range, n8

9
Bit Weight

• Example (continued) -5 V to 5 V analog range,
  n8
• Digital numbers for a few analog values
• Values shown increment by 6 bits (weight for bit
  position 5 is 1.25 V)
• Maximum digital number only approximates the
  maximum analog value in the range
• Try (-5) sum of all bit weights

10
Terms Equations

• Offset minimum analog value
• Span (or Range) difference between maximum and
  minimum analog values
• Max - Min
• n number of bits in digital code (sometimes
  referred to as n-bit resolution)
• Bit Weight analog value corresponding to a bit
  in the digital number
• Step Size (or Resolution) smallest analog change
  resulting from changing one bit in the digital
  number, or the analog difference between two
  consecutive digital numbers also the bit weight
  of the LSb
• Span / 2n
• Let AV be Analog Value DN be Digital Number
• AV DN Step Size Offset DN / 2n Span
  Offset
• DN (AV - Offset) / Step Size (AV - Offset)
  2n / Span

11
MPC555 QADC64
CCW Table CCW0 CCW1 CCW63
A CCW tells the ADC which channel to scan and how
long to sample the signal.
AN0 AN1 AN2 AN3
ADC
QACR1 start a scan by setting SSE bit
QASR0 conv. is done when CF flag is set
Result Table Result0 Result1 Result63
A Result is stored for each scan of a channel
when the conversion is complete.
12
Advanced Topics in ADC

• One-shot ADC one analog sample
• What heating temperature is required?
• What is the current angle of the crane?
• What is the humidity level in the greenhouse?
• Sequential ADC sequences of analog samples
• How quickly is the car accelerating?
• How fast is the plane turning?
• What is the frequency of this sound?
• Issues
• Sampling rate
• Signal filtering

13
Sequential ADC

• Example
• Suppose we are required to design a system to be
  used by an environmental organization to record
  and automatically classify the songs of whales
  recorded (underwater) in the Antarctic. Our
  embedded system will be encased in plastic and
  attached to a floating buoy. It will run on
  batteries for a two-year period and will be
  required to send a radio broadcast to base every
  time it detects a whale in the vicinity.
• We will use an underwater pressure transducer
  (hydrophone) to convert the fluctuations in water
  pressure produced by the whale song into a
  voltage value than can be processed by an ADC.
• The output of the ADC will be a sequence of
  numbers. Individually, these numbers have no
  meaning it is the sequence of numbers that
  allows us to determine, for example, the
  frequency components that make up the whale song.

14
Whale Song
Original analog signal, recorded as a
continuously varying voltage from an underwater
microphone
Quantized version of same signal
0.46, 0.42, 0.17, 0.04,
Digital representation of song
15
Design Stages

• Determine required sample rate
• Speech recognition example To recognize spoken
  words from a speech waveform (using the
  time-varying voltage waveform from a microphone),
  how frequently must the signal be sampled?
• Sample at a frequency of at least twice the
  bandwidth of the signal (Nyquist frequency)
• Bandwidth frequency of the highest frequency
  component in the signal being measured
• For a pure tone (sine wave) with frequency f, f
  is the bandwidth.
• For a broadband signal having multiple frequency
  components, fi, the bandwidth is the maximum
  signal frequency, fmax.
• For speech signals, maximum frequency component
  is around 20 kHz, so need to sample at around
  40kHz.
• Need to remove any higher frequencies with an
  anti-aliasing filter

16
Design Stages

• Determine required sample rate
• Speech recognition example this is a signal
  processing system.
• Control system example e.g., controlling a motor
• Different method
• Simplifying assumptions
• Sample at a frequency inversely proportional to
  the rise time
• Rise Time the output response time after
  applying an input (e.g., open the throttle and
  measure the how long the engine takes to go from
  a minimum speed to a maximum speed)

17
Design Stages

• Remove any high-frequency components from input
  signal
• Need to avoid aliasing
• For sampling frequency of f, need to remove all
  frequencies above f/2 Hz
• Example speech in a factory environment
• 5 kHz bandwidth, 10 kHz sample rate
• There will be frequencies over 5 kHz these
  frequencies result in an effect called aliasing.
• Sampling of a high-frequency signal (i.e., one
  with frequency greater than half the sample rate)
  leads to an incorrect result the result is a
  representation for a a different lower frequency
  signal. The two signals are not distinguishable
  after sampling.
• Anti-aliasing (low-pass) filter is needed before
  sampling the data.

18
Design Stages

• Determine required bit resolution
• 3-bit ADC 8 possible signal levels in digital
  representation
• Error introduced by digitization process is half
  the quantization level
• 3-bit ADC quantization is 1/8, so error is /-
  1/16 of analog range
• Quantization noise errors over a sequence of
  samples
• 12-bit ADC is adequate in most applications

19
Design Stages

• Select/configure the ADC
• Sample time for typical ADC 100 ns
• Sample rate requirement?
• Hardware overhead
• Type of ADC
• Configuration
• Software overhead
• Polling vs. interrupts
• Scan mode