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ISAT 300
Computer-Based Instrumentation (part 2)
Sampling and A/D Converters
11/14/01
Sampling (In the context of polling)
•Filter input first
Sampling (In the context of polling)
•Then sample
Sampling of Time-Varying Signals (Measurands)
• When using a computerized data acquisition system, measurements are only made at a discrete set of times, not continuously.
• For example, a temperature or voltage reading (called a sample) may be taken every 0.1 s or every 2 min, and no information is taken for the time periods in between the samples.
Sampling of Time-Varying Signals (Measurands)
a) time-varying signal
(e.g., voltage)
b) signal being sampled
c) the sampled points
(dots)
d) signal can be reconstructed by connecting the dots
Sampling of Time-Varying Signals (Measurands)
• The rate at which measurements are made is known as the sampling rate, expressed in samples/sec or Hz.
• Incorrect selection of the sampling rate can lead to misleading results.
The problem of aliasing
10 Hz inputsampled at11 Hz
Outputlooks like1 Hz !
The problem of aliasing (continued)
10 Hz inputsampled at9 Hz
Outputlooks like1 Hz
The problem of aliasing (continued)
10 Hz inputsampled at8 Hz
Outputlooks like2 Hz
The problem of aliasing (continued)
10 Hz inputsampled at12 Hz
Outputlooks like2 Hz
The alias frequency
10 Hz inputsampled at11 Hz
Outputlooks like1 Hz
actualsamplealias fff
When does aliasing happen?
10 Hz inputsampled at11 Hz
Outputlooks like1 Hz
actualsample f2f
Another pathology
10 Hz inputsampled at5 Hz
Outputlooks like0 Hz (dc)
N
ff actual
sample
Beware if
Avoiding aliasing
To avoid aliasing, sample your signal at greater than twice the maximum frequency of interest. This is a minimum -- 10 X the maximum frequency of interest would be better.
Another way to state this rule is the Nyquist criterion:
see""can you frequency maximum 2
ff s
N
The A/D converter--produces binary numbers
A one-bit A/D converter
Vin
Vin > 5 V output = on “1”
Vin < 5 V output = off “0”
InputOutput
A two-bit (unipolar) A/D converter
10.0 V
7.5 V
5.0 V
2.5 V
0 V0d
1d
2d
3d
N = 2
•Output has 2N possible values (error on page 78?)
Input Output
• Range?
• Span?
A two-bit (unipolar) A/D converter
10.0 V
7.5 V
5.0 V
2.5 V
0 V0d
1d
2d
3d
N = 2
(Vru - Vrl) / 2N
•How big is each input bin?
Input Output
Input resolution error = Quantization error
10.0 V
7.5 V
5.0 V
2.5 V
0 V0d
1d
2d
3d
N = 2
0.5 (Vru - Vrl) / 2N
Sampling and A/D Conversion
a) An analog signal has been sampled and then converted to digital (2’s complement).
b) This quantization results in error.
Saturation
10.0 V
7.5 V
5.0 V
2.5 V
0 V0d
1d
2d
3d
N = 2
Vin = 12 V
Input
Output
A two-bit (bipolar) A/D converter
5.0 V
2.5 V
0.0 V
- 2.5 V
- 5.0 V
0d
1d
-1d
-2d
N = 2
0.5 (Vru - Vrl) / 2N
Input Output (2’s complement)
Choosing an A/D converter--resolution
National Instrumentsmodel 16E-4
National Instrumentsmodel 16XE-50
12 bits
16 bits
Choosing an A/D converter--speed
National Instrumentsmodel 16E-4
National Instrumentsmodel 16XE-50
500 kS/s
20 kS/s
(kiloSamples/second)
Choosing an A/D converter--input range
National Instrumentsmodel 16E-4
National Instrumentsmodel 16XE-50
10 V
10 V
Calculating the digital output
• To estimate the digital output of an A/D converter, see page 81.• E.g., for a simple binary A/D converter:
N
rlru
rlinO VV
VVD 2int
Vin = analog input voltageVru = upper value of input rangeVrl = lower value of input rangeN = number of bitsDo = digital output (as a decimal number!)
Calculating the digital output
N
rlru
rlinO VV
VVD 2int
Example: 8-bit, simple binary A/D converter
Range is 0 to 5V. Input is 3.15V. Find output.
V145.3256
V 5161
0001101016128.161int256V 5
V 15.3int
V 5
2562 that so 8
bd
N
O
rlru
D
VV
N