Transcript a-d conversion

Computer Based Data
Acquisition Basics
Outline
• Basics of data acquisition
• Analog to Digital Conversion
– Quantization
– Aliasing
Acquisition Basics
Signal
Physical
Phenomenon
Transducer
Conditioning
Interface
Card
Computer
Analog to Digital Conversion
• In this process, we convert an analog
voltage into a number
• Computers store numbers in “bits”
• Typically use a 12 bit converter - converts
each input voltage into some number
between 0 and 4095 (212-1)
• Maximum sample rate - if 100 kHz
– takes 10 sec to perform the conversion
Sources of Error
• The fact that we are using a converter which
has a finite number of bits introduces an
error called “quantization error”
• The fact that it takes a finite (non-zero)
amount of time to perform the conversion
introduces the possibility of an error called
“aliasing”
Quantization Error
V
Analog to Digital Conversion
n+3
n+2
n+1
V
n
n-1
n-2
n-3
Quantization Error
• For example, if we have a
– 10 volt input range
– n ranges from 0-4095
10 V
 V 
 2.44mV
4096
• Uncertainty of 1.22 mV
Aliasing
• Aliasing can lead to incorrect frequency
information
• Sampling Theorem - Maximum frequency
component that can be correctly identified
is that frequency which is 1/2 the sample
frequency. This maximum frequency is
called the Nyquist frequency.
Voltage
Voltage vs Time
Time (sec)
Voltage
Voltage vs Time
Time (sec)
Voltage
Voltage vs Time
Time (sec)
Voltage
Voltage vs Time
Time (sec)
Voltage
Voltage vs Time
Time (sec)
Aliasing
• Once the observed frequency exceeds 1/2
half the sampling frequency, trouble starts
0.6
0.4
nal
fmeasured /fsig
Relation between Measured Frequency,
Sampling Frequency and Signal
Frequency
0.2
0
0
0.5
1
1.5
2
fsignal /fsample
2.5
3