Transcript Digital to Analog Converters (DAC)

Digital to Analog Converters
(DAC)
1
Technician Series
©Paul Godin
[email protected]
March 2015
Digital and Analog
◊
Digital systems are discrete, meaning they have a finite
numerical value. Sometimes referred to as “fixed” or
“stepped” values.
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Analog values are continuous, meaning they have a value
that can vary continuously. The values can be to a great
degree of precision and may contain more information such
as frequency, phase, etc…
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Analog values make up real-world values that can be
measured.
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This presentation describes methods for converting digital
values to analog values.
DAC 1.2
Digital to Analog
◊ Digital electronics offers advantages over analog
in processing, data manipulation, storage and
analysis of values.
◊ Often these digital circuits must interface with the
real world:
◊ as inputs to analyze, process and manipulate
◊ as outputs to control the physical environment
◊ It is important to establish a means of converting
between digital systems and the real world.
DAC 1.3
Transducers
◊ Transducers are devices that convert physical
quantities into electrical quantities. There are
many possible physical measurements requiring
many types of transducers:
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Light
Pressure
Speed
Flow
Angle
Temperature
Rotation
Vibration
Sound, …
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DAC 1.4
Actuators
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Actuators are electrically controlled devices that control the
physical environment. There are many types of actuators
available. These include:
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motors
solenoids (electromagnetic non-rotational motion)
relays
pumps
valves
lifts
heaters
lights
acoustic devices, …
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DAC 1.5
Analog versus Digital
Distorted Analog signal
Original Analog signal
000000100000010000101000
101000011010010011001110
101000100000101000101000
011010010011001110101000
100000001000010100000010
000101000101000011010010
011001110101000100001010
000110100100110011101010
001010111011011010001001
Binary signal
DAC 1.6
Analog to Digital
Original Analog signal
A to D Conversion
The voltage is converted to a
binary value at regular intervals.
Animated
000100110111101010001
000111000000100000010
011100101001001011101
011110010101010010101
010101001001010101001
000101001010101111010
000001001011101011101
000000010101110101010
000000000001001111010
000000000000111111010
000000000001010101010
000000000001011011101
000000000001101101100
000000001100010111010
000000100011111010110
000001001010101000100
000001010111101111000
000011001101010100101
000110111000010100101
…
Binary signal
DAC 1.7
Digital to Analog
000100110111101010001
000111000000100000010
011100101001001011101
011110010101010010101
010101001001010101001
000101001010101111010
000001001011101011101
000000010101110101010
000000000001001111010
000000000000111111010
000000000001010101010
000000000001011011101
000000000001101101100
000000001100010111010
000000100011111010110
000001001010101000100
000001010111101111000
000011001101010100101
000110111000010100101
…
Digital signal
Animated
D to A Conversion
Analog signal
The binary value is converted to
a voltage at regular intervals.
DAC 1.8
Digital to Analog
◊ We will begin looking at converting binary and
analog values from the perspective of the
actuator; we will look at digital to analog
converters.
◊ There are several ways to implement such a
system. This presentation will look at several of
these systems.
◊ It is important to understand their basic operation
to determine a circuit fault.
DAC 1.9
DAC Challenges
◊ Digital to Analog Converters take a digital value
and convert it to voltage or current over time.
◊ Converting discrete (digital) values to analog
values has some challenges.
◊ Since the digital values have discrete steps, the steps
and the values between the steps cannot always be
completely and accurately represented in analog.
◊ How well a digital value creates an analog value depends
on the number of bits that are used. Fewer bits means
less resolution.
DAC 1.10
Scaling
◊ The range of the available digital values
represents the scale. It is based on the
number of bits in the binary number.
◊ Scale is referred to as Resolution in DACs.
◊ DACs have two extremes in output values:
zero and full-scale output. Knowing these two
extremes and the number of unique digital
outputs in between, the resolution of a circuit
can therefore be determined.
DAC 1.11
Resolution Example
C
B
A
VOUT
0
0
0
0
0.0
0
0
0
1
0.5
0
0
1
0
1.0
0
0
1
1
1.5
0
1
0
0
2.0
0
1
0
1
2.5
0
1
1
0
3.0
There are 16 values from 0000 to
1111, but the first step (0000) equals
0V. Therefore there are 15 steps.
0
1
1
1
3.5
1
0
0
0
4.0
1
0
0
1
4.5
1
0
1
0
5.0
If the maximum output is 7.5 Volts
(input 1111), the calculated scale will
be 0.5 Volts per binary increment.
1
0
1
1
5.5
1
1
0
0
6.0
1
1
0
1
6.5
1
1
1
0
7.0
1
1
1
1
7.5
Min binary = 0000
Max binary = 1111
D
MSB
LSB
D
C
B
A
VOUT
DAC
Min VOUT = 0V
Max VOUT = 7.5V
DAC 1.12
Resolution Example
◊ Analyzing the voltage output from the example it
becomes evident that the output voltage, although
analog, still follows a pattern of discrete values.
DAC 1.13
Resolution
◊ The resolution represents the smallest change, or
step, in the analog output. The greater the
resolution, the smaller the steps.
◊ To increase resolution increase the number of bits
in the binary value.
◊ In our example, a 4-bit number represented a 0.5
volt change per step. By increasing the number
to 5 bits, each change would represent
approximately 0.25 volt change per step,
increasing the resolution.
DAC 1.14
Improved Resolution
◊ By increasing the binary number size
by one bit the voltage between steps
decreases.
4-bit resolution
5-bit resolution
DAC 1.15
Resolution
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Volts per step is calculated as the full scale voltage divided
by the number of steps.
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A percent resolution is the percent of output voltage change
with one step. It is simply calculated as 1/(2N -1) where N
represents how many bits in the binary number.
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Discussion: assuming 12V out on a full scale, what is the
resolution of:
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8-bit value
16-bit value
20-bit value
DAC 1.16
Bipolar DAC
◊ The examples shown so far represented positive
digital values. Analog values can be negative or
positive.
◊ To represent a negative value two popular
numbering systems are used:
◊ signed magnitudes
◊ 2’s compliment values
DAC 1.17
Signed Magnitude
◊ Binary systems utilize only 1’s and 0’s. The
negative symbol cannot be used.
◊ In a signed magnitude value, the bit in the
leftmost position of a binary number is used to
indicate if the value is positive or negative. This is
the sign bit. The value following the sign bit is
the magnitude.
01001101 = positive value, 10011012
11001101 = negative value, 10011012
The leftmost bit is the sign bit.
DAC 1.18
2’s Compliment
◊ In Binary there is an interesting principle.
◊ If each digit of a binary number is inverted and a 1 is
added to the number, the new value is the “negative
equivalent” of it.
◊ 2’s compliment example:
12
-3
9
1100 is 12
0011 is 3
1100 is 1’s compliment
1101 is 2’s compliment
1100 (12)
+1101 (-3)
11001 (9)
Note the extra bit is always disregarded
DAC 1.19
DAC DEVICES
DAC 1.20
DAC Devices
◊ DACs require an input that can scale the binary
values and an output circuit in the form of an
amplifier.
◊ There are several different ways of building DACs.
◊ Each has advantages and disadvantages. They are
chosen based on the required circuit parameters.
DAC 2.21
Operational Amplifiers (Op-Amps)
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The Operational Amplifier (Op-Amp) is one of the basic
building blocks of electronics.
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Its basic form has two inputs, one inverting and the other
non-inverting.
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Op-Amps can be configured in many different ways:
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Compare voltages
Amplify signals
Invert signals
Oscillate
Filter, …
VDD
VEE
Op Amps typically require a positive (VDD) and negative (VEE)
supply, and a ground reference (VSS).
DAC 1.22
Op-Amp as an Amplifier
◊ This Operational Amplifier configuration operates
in this general manner:
◊ Gain (voltage increase) equals the input voltage times
the ratio of the feedback resistor Rf to the input resistor.
◊ In this configuration the output is inverted (goes
negative)
Rf
Vin
Vout = Vin●(Rf/RIN)
Rin
VDD
VOUT
VEE
DAC 2.23
Binary-Weighted Resistor DAC
◊ The Summing Op-Amp output will be the sum of
the input voltages times the ratio of Rf over each
Rin.
Rf
Rin1
VDD
Rin2
Rin3
Rin4
VEE
DAC 2.24
Binary-Weighted Resistor DAC
◊ The first resistor has no attenuation therefore the
voltage is passed. The second R has a ½ ratio so
will attenuate by 50%. The 3rd R attenuates by ¼,
and the last by 1/8.
◊ This is an inverting amplifier (output voltage is
negative)
1 kΩ
1 kΩ
VDD
2 kΩ
4 kΩ
8 kΩ
VEE
DAC 2.25
Binary-Weighted Resistor DAC
◊ A 4-bit binary input is applied to the input
resistors, with the 1 kΩ resistor considered the
MSB.
1 kΩ
MSB
1 kΩ
VDD
2 kΩ
4 kΩ
LSB
8 kΩ
VEE
◊ The resistor ratio for the MSB is 1:1...if the input
voltage is 5V, the output is 5V.
DAC 2.26
Binary-Weighted R DAC - Table
◊ Based on an input of 5V for the
MSB, the resolution can be
calculated:
◊ If just the MSB is active, the output
voltage equals the MSB input
voltage (gain =1)
◊ 10002 = 810, therefore each step =
5V/8 = 0.625V per step
◊ Note the amplifier inverts,
therefore the output voltage is
negative
D
C
B
A
VOUT
0
0
0
0
-0.000
0
0
0
1
-0.625
0
0
1
0
-1.250
0
0
1
1
-1.875
0
1
0
0
-2.500
0
1
0
1
-3.125
0
1
1
0
-3.750
0
1
1
1
-4.375
1
0
0
0
-5.000
1
0
0
1
-5.625
1
0
1
0
-6.250
1
0
1
1
-6.875
1
1
0
0
-7.500
1
1
0
1
-8.125
1
1
1
0
-8.750
1
1
1
1
-9.375
DAC 2.27
Limitations
◊ The Binary-Weighted DAC can be difficult to
implement:
◊ The resistors must be precise, otherwise the scale steps
will be uneven.
◊ The output of logic devices such as gates or flip-flops are
not always at 5 volts and will therefore affect the scale.
◊ If switches are used, pull-up resistors will affect the
operation of the device.
◊ Larger binary values require progressively larger
resistors for the LSB. For our example:
◊ 5 bit = 16kΩ
◊ 8 bit = 128kΩ
◊ 12 bit = 2.048MΩ
DAC 2.28
Conclusion
◊ There are other configurations for DACs.
◊ Next presentation will look at other methods.
DAC 2.29
End of Part 1
©Paul R. Godin
prgodin°@ gmail.com
DAC 1.30