Transcript Chapter 12

Chapter 12
Interfacing Analog and
Digital Circuits
Analog Signals
• Signals that vary continuously
throughout a defined range.
• Representative of many physical
quantities, such as temperature and
velocity.
• Usually a voltage or current level.
2
Digital Signals
• Signals that take on specific values
only.
• Required for operation with digital logic.
• A representative of physical quantities
by a series of binary numbers.
3
Advantages of Analog
Representation
• Varies continuously, like the property
being measured.
• Represents continuous values.
4
Advantages of Digital
Representation
• Values are limited to specific discrete
segments.
• Not subject to the same distortions as
an analog signal.
• Can be easily copied and stored.
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Advantages of Digital
Representation
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Analog Voltage Sampling
• A sample is an instantaneous
measurement of an analog voltage.
• Sampling frequency is the number of
samples taken per unit time.
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Accuracy of Digital
Representation
• Depends on sampling frequency and
quantization.
• Quantization is the number of bits used
to represent an analog voltage as a
digital number.
• Resolution is the analog step size.
8
Accuracy of Digital
Representation
9
Accuracy of Digital
Representation
10
Accuracy of Digital
Representation
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Accuracy of Digital
Representation
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Resolution of a Digital
Representation
• The difference in analog voltage
corresponding to two adjacent digital
codes.
• Directly proportional to the reciprocal of
2n, where n is the number of bits used in
the digital code.
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Analog-to-Digital Conversion
• Uses a circuit that converts an analog
signal at its input to a digital code.
• Called an A-to-D converter, A/D
converter, or ADC.
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Unipolar ADC
• Converts positive input voltages.
• Generates a 2n-bit binary code for any
given input voltage.
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Unipolar ADC Code Equation
Va
n
code 
2
FS
• Va = analog input voltage to be sampled.
• FS = Full scale range of input voltage.
• n = number of bits in the output code.
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Unipolar ADC Code Equation
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Unipolar ADC Output Codes
Nominal Voltage of Input Step (volts) Range (volts) Output Code
000
0.0 - 0.5
0.0
001
0.5 - 1.5
1.0
010
1.5 - 2.5
2.0
011
2.5 - 3.5
3.0
100
3.5 - 4.5
4.0
101
4.5 - 5.5
5.0
110
5.5 - 6.5
6.0
111
6.5 - 8.0
7.0
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Bipolar ADC
(Offset Binary Coding)
• Used to represent positive and negative
input voltages.
• Output code an unsigned binary
number.
• Numbers below 0 V are negative.
• Numbers above 0 V are positive.
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Bipolar ADC
(Offset Binary Coding)
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Bipolar ADC Code Equation
 Va
n
code  
 2   offset
 FS

n
V
2
 a
n

2 
 FS
 2
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Bipolar ADC Output Codes
- 4.0
- 3.0
- 4.0 to - 3.5
- 3.5 to - 2.5
000
001
- 2.0
- 1.0
- 2.5 to - 1.5
- 1.5 to - 0.5
010
011
0
+ 1.0
- 0.5 to + 0.5
+ 0.5 to + 1.5
100
101
+ 2.0
+ 3.0
+ 1.5 to + 2.5
+ 2.5 to + 4.0
110
111
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Bipolar ADC
(2’s Complement Coding)
•
•
•
•
Uses a 2’s complement number system.
Most significant bit (MSB) is the sign bit.
MSB = ‘1’ sign negative.
MSB = ‘0’ sign negative.
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2’s Complement Output Codes
Nominal Voltage of Input Step (volts)
- 4.0
- 3.0
- 2.0
- 1.0
0
+ 1.0
+ 2.0
+ 3.0
Range (volts) Output Code
- 4.0 to - 3.5
100
- 3.5 to - 2.5
101
- 2.5 to - 1.5
110
- 1.5 to - 0.5
111
- 0.5 to + 0.5
000
+ 0.5 to + 1.5
001
+ 1.5 to + 2.5
010
+ 2.5 to + 4.0
011
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2’s Complement Output Codes
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Digital-to-Analog Conversion
• Uses a circuit that converts a digital
code at its input to an analog voltage or
current.
• Called a D-to-A converter, D/A
converter, or DAC.
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Unipolar DAC
• One input code corresponds to a single
digital code.
• DAC has 2n discrete output voltage
values.
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Unipolar DAC
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Unipolar DAC Equation
 code 
Va   n   FS for an n-bit code
 2 
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Bipolar DAC
(Offset Binary Coding)
• Input code for 0 V is halfway through
the range of digital input codes.
• Output voltage equation:
  code 
  FS 
Va    n   FS  - 

 2 
  2 
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Bipolar DAC
(Offset Binary Coding)
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Bipolar DAC
(2’s Complement)
• Accepts digital codes in 2’s complement
format.
 code 
Va   n   FS
 2 
• Code = a 2’s complement signed
number.
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Bipolar DAC
(2’s Complement)
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DAC General Operation
• Uses digital inputs to control
proportionally weighted currents.
• Currents are binary weighted – the MSB
has the largest, the second LSB has ½
the current, and so on.
• Currents feed an op-amp that converts
current to voltage.
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DAC General Operation
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DAC Output Voltage
• If Va is the output, Iref a fixed reference
current, and RF the op-amp feedback
resistor, then for n bits:
Ia 
bn -1 2 n -1  ... b2 2 2  b1 21  b0 2 0
2
n
I ref
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DAC Characteristics
• The maximum output is always one
least significant bit less than full scale.
• An n-bit converter has 2n input codes,
ranging from 0 to 2n – 1.
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Weighted Resistor D/A Converter
• Uses a parallel network of binaryweighted resistors to feed the op-amp.
• Seldom used since a wide range of
resistor values is required for a large
number of bits.
• Difficult to achieve accuracy for a high
number of bits.
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Weighted Resistor D/A Converter
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R-2R Ladder DAC
• Produces an analog current that is the
sum of binary-weighted currents.
• Uses only two values of resistors.
• Easily modified to add additional bits –
each new bit requires 2 resistors, values
R and 2R.
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R-2R Ladder DAC
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R-2R DAC Equation
 b3 b2 b3 b0 
Va        Vref
 2 4 8 16 
• b3, b2, b1, and b0 are binary values
either ‘1’ or ‘0’.
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MC1408 Integrated Circuit DAC
• Popular, inexpensive 8-bit multiplying
DAC.
• Also designated DAC0808.
• Output is proportional to the reference
voltage.
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Operation of the MC1408
• Requires an external op-amp to
increase the output voltage and current.
• Can be wired to produce a bipolar
output voltage, that is, voltages that
have both positive and negative values.
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Operation of the MC1408
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MC1408 Equations
Iref  Vref (  )/R14
IO
 digital code 
 
Iref
256


 digital code  RF
Va  IORF 

256

 R14

  Vref

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DAC Performance Specifications – 1
• Monotonicity means that the
magnitude of the output voltage
increases every time the input digital
code increases.
• Absolute accuracy is the measure of
the DAC output voltage with respect to
its expected value.
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DAC Performance Specifications – 2
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DAC Performance Specifications – 3
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DAC Performance Specifications – 4
• Relative accuracy is the deviation of
the actual from the ideal output voltage
as a fraction of the full-scale voltage.
• Settling time is the time required for
the outputs to switch and settle within
½ LSB when the input switches form
all 0s to all 1s.
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DAC Performance Specifications – 5
• Gain error occurs when the output
saturates before reaching the maximum
output code.
• Linearity error is the deviation from a
straight line output with increasing
digital input codes.
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DAC Performance Specifications – 6
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DAC Performance Specifications – 7
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DAC Performance Specifications – 8
• Differential nonlinearity is the difference
between actual and expected step size
when the input code is changed by 1
LSB.
• Offset error occurs when the DAC
output is not 0 V when the input code is
all 0s.
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DAC Performance Specifications – 9
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Flash ADC
• Uses a resistive voltage divider,
comparators, and a priority encoder to
produce a digital code.
• Conversion occurs in one clock cycle
(fastest conversion time).
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Flash ADC
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Flash ADC
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Disadvantage of Flash ADC
• Requires 2n resistors and 2n – 1
comparators for an n-bit output.
• For any large number of bits, the circuit
becomes overly complex.
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Successive Approximation ADC
• The most widely used ADC.
• Finds the digital representation using a
“binary search.”
• Also called a SAR.
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Binary Search – 1
1. Set the MSB of the digital representation to
1, all other bits to 0.
2. Compare the analog value produced in the
first step to the voltage being converted.
2A. If the test voltage is higher than the voltage
being converted, reset the MSB and set the
second MSB.
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Binary Search – 2
2B. If the test voltage is less than the voltage being
converted, leave the MSB set and set the
second MSB.
3. Repeat Steps 2, 2A, and 2B until all the bits
have been tested.
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Binary Search – 3
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Binary Search – 4
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Binary Search – 5
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SAR - ADC Characteristics
• Final answer is always less than the
input voltage.
• Conversion always requires a fixed
number of clock cycles.
• Conversion requires n clock cycles
where n is the number of bits in the
digital representation.
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Dual Slope ADC
• Based on an integrator, a circuit whose
output is the accumulated sum of all
previous input values.
• Circuit relies on storing charge
representing current flow in a capacitor.
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Dual Slope ADC Characteristics
• High accuracy.
• Relatively slow conversion time.
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Dual Slope ADC Characteristics
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Dual Slope ADC Characteristics
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Sigma - Delta ADC – 1
• Uses an integrator and DAC to produce
a serial bit stream based on the sum of
the voltage changes at the input to the
ADC.
• Alternately recognized by -  ADC.
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Sigma - Delta ADC – 2
• Output is a serial stream of bits rather
than the standard parallel outputs.
• Produces a highly accurate digital
outputs of up to 24 bits.
• 24-bit precision not available in
standard parallel ADCs.
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Sigma - Delta ADC – 3
• Begins by integrating an input value
then sending a ‘0’ or ‘1’ to the output of
the comparator.
• The output of the comparator is
converted to one of two values (–Vref or
+Vref) by a 1-bit DAC.
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Sigma - Delta ADC – 4
• DAC output is then subtracted from the
input voltage (Va) at a summing
junction.
• Sum is inverted and added to the
previous output value of the integrator.
• In effect, the integrator sums the
changes introduced by the DAC.
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Sigma - Delta ADC – 5
• Process continues for a defined number
of iterations.
• Each iteration represents a new sample
of Va.
• Each iteration produces a bit in the
serial output stream (Figure 12.38 in
textbook).
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Sigma - Delta ADC – 6
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Sample and Hold Circuit
• Required to sample an analog signal at
periodic intervals and hold the value
long enough for the ADC to convert it to
a digital code.
• Generally consists of an input voltage
follower, a hold capacitor, and an output
voltage follower.
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Sample and Hold Circuit
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Sample and Hold Circuit
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Track and Hold Circuit
• Used in cases where large changes in
signal levels between samples are
expected.
• Samples the analog signal continuously,
minimizing charging delays of the hold
capacitor.
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Sampling Frequency
• A signal must be sampled at a high
enough frequency so that no
information is lost.
• Aliasing occurs when an unwanted lowfrequency component is produced by
too slow a sampling frequency.
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Sampling Frequency
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Nyquist Sampling Theorem
• To preserve all information in a signal,
the signal must be sampled at a rate of
twice the highest-frequency component
of the signal fs  2 fmax .
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Sampling Frequency Examples
• Since the range of human hearing is 20
Hz to 20 kHz, the sampling frequency
for compact disks is set at 44.1 kHz.
• Since the classic telephone bandwidth
is 300 Hz to 3300 Hz, telephone-quality
signals are sampled at 8 kHz.
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Filtering
• An anti-aliasing filter is used to remove
unwanted high frequency components.
• The filter is a low-pass filter with the
corner frequency set to 2fs.
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Filtering
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ADC0808 IC ADC – 1
• Successive approximation ADC.
• Able to convert analog information from
up to 8 (multiplexed) channels.
• Can form the basis of a data acquisition
network.
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ADC0808 IC ADC – 2
• START conversion with HIGH pulse.
• Conversion process driven by the clock.
• End-of-conversion indicated by a HIGH on
EOC.
• Making OE HIGH allows the digital output to
be read.
• When OE inactive, outputs in Hi-Z state.
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ADC0808 IC ADC – 3
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ADC0808 IC ADC – 4
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