Analog to Digital Converters Electronics Unit

1
Analog to Digital Converters Electronics Unit
Lecture 7

• Representing a continuously varying physical
  quantity by a sequence of discrete numerical
  values.

03 07 10 14 09 02 00 04
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Conversion Methods(selected types, there are
others)

• Ladder Comparison
• Successive Approximation
• Slope Integration
• Flash Comparison

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Ladder Comparison
4
Single slope integration

• Charge a capacitor at constant current
• Count clock ticks
• Stop when the capacitor voltage matches the input
• Cannot achieve high resolution
• Capacitor and/or comparator

Vin
Counting time
StartConversion
StartConversion
Enable
S
Q
R
N-bit Output
Counter
C
IN
Clk
Oscillator
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Successive Approximation
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Flash Comparison
If N is the number of bits in the output
word. Then 2N comparators will be required. With
modern microelectronics this is quite possible,
but will be expensive.
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Pro and Cons

• Slope Integration Ladder Approximation
• Cheap but Slow

8
Pro and Cons

• Flash Comparison
• Fast but Expensive
• Slope Integration Ladder Approximation
• Cheap but Slow

9
Pro and Cons

• Successive Approximation
• The Happy Medium ??
• Slope Integration Ladder Approximation
• Cheap but Slow
• Flash Comparison
• Fast but Expensive

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Resolution

• Suppose a binary number with N bits is to
  represent an analog value ranging from 0 to A
• There are 2N possible numbers
• Resolution A / 2N

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Resolution Example

• Temperature range of 0 K to 300 K to be linearly
  converted to a voltage signal of 0 to 2.5 V, then
  digitized with an 8-bit A/D converter
• 2.5 / 28 0.0098 V, or about 10 mV per step
• 300 K / 28 1.2 K per step

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Resolution Example

• Temperature range of 0 K to 300 K to be linearly
  converted to a voltage signal of 0 to 2.5 V, then
  digitized with a 10-bit A/D converter
• 2.5 / 210 0.00244V, or about 2.4 mV per step
• 300 K / 210 0.29 K per step
• Is the noise present in the system well below 2.4
  mV ?

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Quantization Noise

• Each conversion has an average uncertainty of
  one-half of the step size ½(A / 2N)
• This quantization error places an upper limit on
  the signal to noise ratio that can be realized.
• Maximum (ideal) SNR 6 N 1.8 decibels (N
  bits)
• e.g. 8 bit ? 49.8 db, 10 bit ? 61.8 db

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Signal to Noise RatioRecovering a signal masked
by noise

• Some audio examples
• In each successive example the noise power is
  reduced by a factor of two (3 db reduction), thus
  increasing the signal to noise ratio by 3 db each
  time.

Example 1
Example 2
Example 3
Example 4
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Conversion Time

• Time required to acquire a sample of the analog
  signal and determine the numerical
  representation.
• Sets the upper limit on the sampling frequency.
• For the A/D on the BalloonSat board, TC 32 µs,
  
• So the sampling rate cannot exceed about 30,000
  samples per second (neglecting program overhead)

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Data Collection Sampling Rate

• The Nyquist Rate
• A signal must be sampled at a rate at least twice
  that of the highest frequency component that must
  be reproduced.
• Example Hi-Fi sound (20-20,000 Hz) is generally
  sampled at about 44 kHz.
• External temperature during flight need only be
  sampled every few seconds at most.

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Activity E7a

• Do the HuSAC
• a party game for techies...
• Human Successive Approximation Converter

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Activity E7b

• Data Acquisition Using BalloonSat