Transcript Analog to Digital (A/D) Conversion

Analog to Digital (A/D) Conversion
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A/D fundamentals
• A / D conversion is a process where an analog signal
is converted into a numeric representation.
– Analog input is normally classified into one of two types and
a voltage range
• Types and typical ranges
– Uni-polar (0 -1 V, 0 - 5V, 0 - 10V)
– Bi-polar (-1 to 1V, -5 to 5V, -10 to 10V)
– Digital output is normally binary at the hardware level and
typically decimal at the software interface level
• Primary critical specifications for A/D conversions
– Resolution
– Conversion rate
– Elements contributing to inaccuracy (non-linearity,
offset/bias, missing codes, non-monotonicity)
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A/D fundamentals
• Resolution
– Normally specified in terms of the number of binary digits
that the analog value is converted to:
• eg. 8 bit conversion, 12 bit conversion, 16 bit conversion
– Analog resolution can be computed from the specified
resolution:
• analog resolution = analog range / [2^(binary digits in result)]
• example: a bi-polar A/D converter set to input a range of -10 to
+10 V with a 12 bit conversion
• analog resolution = 20V / [2^12] = 20/4096 V / bit = 4.9 mV/bit
• Conversion Rate
– The rate at which an A/D converter can make a conversion is
critical. In general higher resolutions require greater time of
greater cost or both.
– Typically specified in samples per second (sometimes
MSPS)
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Transfer Function
• The ideal output from an A/D
converter is a stair-step
function (see right)
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Nominal Quantized
value + 1/2 LSB
1101
1100
1011
1010
1001
1000
Output Code
Output Code
– Ideal worst case error in
conversion is  1/2 bit.
– Missing codes or the
imperfections where
increasing voltage does not
result in the next step being
output are described as
non-monotonicity.
– Errors in A/D conversion
may be significant
particularly if the full range
of the analog signal is
significantly less than the
range of the analog input of
the A/D.
0111
0110
1 LSB
0101
0100
0011
Missing Code
0010
0001
0000
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Input Voltage
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A/D Converter Types
• Dual Slope Integrating
Integrator
Comparator
Analog Input (Va)
-
-Vreference
+
+
Control Logic
Start of Conversion
Status
Digital Output
Comparator output
12
Counter
Clock
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A/D Converter Types
Start of Conversion
• Input signal is integrated for a
fixed time
• Input is switched to the negative
reference and the negative
reference is then integrated until
the integrator output is zero
• The time required to integrate the
signal back to zero is used to
compute the value of the signal
• Accuracy dependent on Vref and
timing
Analog Voltage level
• Operation
Integrator output
with Vreference Input
Analog Input
......
T2
.......
T1
Analog Input
Constant
Slope
.......
T1
• Characteristics
......
T2
Time
• Noise tolerant (Integrates
variations in the input signal
during the T1 phase)
• Typically slow conversion rates
(Hz to few kHz)
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Integrator output
with Va Input
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T1
T
1
1 2
Vin dt    Vref dt

C0
C 0
T
Vin  Vref 2
T1
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A/D Converter Types
• Successive Approximation
(Digital to Analog Conversion + null balancing)
R
– 4 bit D/A using a summing
amplifier and switch
1V
D0
D1
8R
D2
4R
D3
2R
+
R
– 4 bit D/A using R-2R ladder
R
1V
2R
i=1/2R
R
2R
R
2R
2R
2R
i=1/4R
i=1/8R i=1/16R
D3
D2
D1
D0
R
+
• Digital value (D1, D2, D3
etc.) is converted to an
analog value
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1 1
Vout  å +
4 8
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A/D Converter Types
• Successive Approximation
Converter Schematic
Analog Input
+
Comparator output
-
D/A Converter
Digital Output
Start of Conversion
Status
12
Successive
Approximation
Register
Clock
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• Conversion
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D/A Converter
output
T4
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T5
T7
T6
Analog Input
T3
Start of Conversion
Analog level
– At start of conversion, the
clock is used to cycle a
counter that drives the D/A
converter.
– When the D/A output is
larger than the input then
the count is reduced
otherwise it is increased
using an algorithm to home
in on the matching value.
– When the counter step size
is within the tolerance
desired (usually 1 count)
then conversion is stopped
and the digital value being
output to the D/A is output
T2
T1
Time
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Sample and hold devices
• Some A/D converters require
the input analog signal to be
held constant during
conversion, (eg. successive
approximation devices)
• In other cases, peak capture
or sampling at a specific
point in time necessitates a
sampling device.
• This function is
accomplished by a sample
and hold device as shown to
the right:
• These devices are
incorporated into some A/D
converters
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Sampling
switch
Analog Input
Signal
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Output
Signal
Hold
Capacitor
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A/D Converter Types
• Flash Conversion
1V
3R
– A multi-level voltage divider
is used to set voltage levels
over the complete range of
conversion.
– A comparator is used at
each level to determine
whether the voltage is lower
or higher than the level.
– The series of comparator
outputs are encoded to a
binary number in digital
logic (an encoder)
Comparators
+
2R
+
2R
+
2R
-
2R
+
Encoder
3
+
2R
-
2R
+
-
R
+
-
Vin
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A/D Converter Types
• Sigma / Delta
Integrator
Analog Input (Va)
+
-
-
VF
+
Comparator
+
-
Analog Voltage level
Digital Output
Decimation
Start of Conversion
Status
Analog Input
Digital
Filter
Comparator output
Bit stream
Control
Logic
Comparator
output
Time
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A/D Converter Types
• Operation
– Comparator feedback signal
is subtracted from analog
input and the difference is
integrated.
– The average value of VF is
forced to equal Va.
– VF is a digital pulse stream
whose duty cycle is
proportional to Va This is
known as Delta modulation
– This pulse stream is
sampled digitally and
averaged numerically
(decimation) Giving a
numerical representation of
the voltage in.
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– The error in the average or
mean is:
 

n
– The greater the number of
samples averaged, the
greater the accuracy
– The greater the number of
samples averaged, the
greater the time between
the start of gathering
samples and the output of
the mean (group delay)
– This A/D does not work well
if switched from channel to
channel because of the
delay till valid result
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