Transcript Analog to Digital Converters Electronics Unit – Lecture 7

Analog to Digital Converters
Electronics Unit – Lecture 7
Representing a continuously varying
physical quantity by a sequence of
discrete numerical values.
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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
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Single slope integration
Voltage accross the capacitor
• 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
Start
Conversion
Vin
0
Start
Conversion
IN
+
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Counting time
S
Q
R
Oscillator
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Time
Enable
Counter
-
C
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2
0
N-bit Output
Clk
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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
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Pro and Cons
Flash Comparison
Fast but Expensive
Slope Integration & Ladder Approximation
Cheap but Slow
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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 onehalf 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 Ratio
Recovering 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
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Example 2
Example 3
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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
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