Download Analog to Digital (A/D) Conversion

Analog to Digital (A/D) Conversion
An overview of A/D techniques
5/4/2006
BAE 5413
1
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. Hardware
generally controls observed voltage resolution.
• Primary critical specifications for A/D conversions
– Resolution (voltage resolution)
– Conversion rate (time resolution)
– Elements contributing to inaccuracy (non-linearity,
offset/bias, missing codes, non-monotonicity)
5/4/2006
BAE 5413
2
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 sequential a
conversions. In general higher resolutions require greater
time or greater cost or both.
– Typically specified in samples per second (sometimes
MSPS)
5/4/2006
BAE 5413
3
Transfer Function
• The ideal output from an A/D
converter is a stair-step
function (see right)
5/4/2006
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
BAE 5413
0
Input Voltage
4
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
5/4/2006
BAE 5413
5
• Reference signal is
integrated for a fixed time
• Input is switched to the
analog input and is
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
Integrator Voltage Output
• Operation
• Characteristics
Integrator output
with small Va
Input
Integrator output with
Vreference Input
.......
T1
Integrator output
with large Va
Input
......
T2
Constant
Slope
.......
T1
......
T2
Time
• Noise tolerant (Integrates
variations in the input signal
during the T1 phase)
• Typically slow conversion
rates (Hz to few kHz)
5/4/2006
Start of Conversion
A/D Converter Types
BAE 5413
T
T
1 1
1 2
Vreference dt   Vadt

C0
C0
VreferenceT1  VaT2
T
Va  Vreference 1
T2
6
A/D Converter Types – D to A conversion
• 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
5/4/2006
BAE 5413
1 1
Vout  å +
4 8
7
A/D Converter Types
• Successive Approximation
Analog Input
+
Comparator output
-
Converter Schematic
D/A Converter
Digital Output
Start of Conversion
Status
12
Successive
Approximation
Register
Clock
– The input signal must be “held at a single level during conversion.
(A sample and hold circuit is required on the input.
– Note that conversion time depends on the input level and the
convergence method.
5/4/2006
BAE 5413
8
• Conversion
5/4/2006
D/A Converter
output
T4
BAE 5413
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
9
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
5/4/2006
Sampling
switch
Analog Input
Signal
BAE 5413
Output
Signal
Hold
Capacitor
10
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
5/4/2006
BAE 5413
11
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
5/4/2006
BAE 5413
12
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.
5/4/2006
BAE 5413
– 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
13