E1C07 09/14/2010
14:43:49 Page 274
2
8
¼ 256 different binary values. Principal considerations in selecting a type of A/D converter
include resolution, voltage range, and conversion speed.
Resolution
The A/D converter resolution is defined in terms of the smallest voltage increment that causes a bit
change. Resolution is specified in volts and is determined by
Q ¼ E FSR =2
M
ð7:14Þ
Primary sources of error intrinsic to any A/D converter are the resolution and associated
quantization error, saturation error, and conversion error.
Quantization Error
An A/D converter has a finite resolution, and any input voltage that falls between two adjacent
output codes results in an error. This error is referred to as the quantization error e Q . It behaves as
noise imposed on the digital signal.
The analog input to digital output relationship for a 0- to 4-V, 2-bit A/D converter is represented
in Figure 7.7. From Equation 7.14, the resolution of this device is Q ¼ 1 V. For such a converter, an
input voltage of 0.0 V would result in the same binary output of 00 as would an input of 0.9 V. Yet an
input of 1.1 V results in an output of 01. Clearly, the output error is directly related to the resolution.
In this encoding scheme, e Q is bounded between 0 and 1 LSB above E i , so we estimate e Q ¼ Q. This
scheme is common in digital readout devices.
A second common scheme makes the quantization error symmetric about the input voltage.
For this, the analog voltage is shifted internally within the A/D converter by a bias voltage, E bias , of
an amount equivalent to ½ LSB. This shift is transparent to the user. The effect of such a shift is
shown on the second lower axis in Figure 7.7. This now makes e Q bounded by Æ1/2 LSB about E i ,
5
01
00
Volts
Binary output
10
11
4
3
2
Analog input, E i
Q
Saturated output
Ideal
conversion
Actual
quantization
Highest binary number
Saturated
output
1
0
–1
Volts
4
3
2
1
0
–1
Analog input, E i – E bias
Figure 7.7 Binary quantization
and saturation.
274 Chapter 7 Sampling, Digital Devices, and Data Acquisition
14:43:49 Page 274
2
8
¼ 256 different binary values. Principal considerations in selecting a type of A/D converter
include resolution, voltage range, and conversion speed.
Resolution
The A/D converter resolution is defined in terms of the smallest voltage increment that causes a bit
change. Resolution is specified in volts and is determined by
Q ¼ E FSR =2
M
ð7:14Þ
Primary sources of error intrinsic to any A/D converter are the resolution and associated
quantization error, saturation error, and conversion error.
Quantization Error
An A/D converter has a finite resolution, and any input voltage that falls between two adjacent
output codes results in an error. This error is referred to as the quantization error e Q . It behaves as
noise imposed on the digital signal.
The analog input to digital output relationship for a 0- to 4-V, 2-bit A/D converter is represented
in Figure 7.7. From Equation 7.14, the resolution of this device is Q ¼ 1 V. For such a converter, an
input voltage of 0.0 V would result in the same binary output of 00 as would an input of 0.9 V. Yet an
input of 1.1 V results in an output of 01. Clearly, the output error is directly related to the resolution.
In this encoding scheme, e Q is bounded between 0 and 1 LSB above E i , so we estimate e Q ¼ Q. This
scheme is common in digital readout devices.
A second common scheme makes the quantization error symmetric about the input voltage.
For this, the analog voltage is shifted internally within the A/D converter by a bias voltage, E bias , of
an amount equivalent to ½ LSB. This shift is transparent to the user. The effect of such a shift is
shown on the second lower axis in Figure 7.7. This now makes e Q bounded by Æ1/2 LSB about E i ,
5
01
00
Volts
Binary output
10
11
4
3
2
Analog input, E i
Q
Saturated output
Ideal
conversion
Actual
quantization
Highest binary number
Saturated
output
1
0
–1
Volts
4
3
2
1
0
–1
Analog input, E i – E bias
Figure 7.7 Binary quantization
and saturation.
274 Chapter 7 Sampling, Digital Devices, and Data Acquisition