Digital Electronics and Computer Interfacing

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Digital Electronics and Computer Interfacing

• Tim Mewes
• 5. Computer Interfacing DAQ cards

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5.4 Digital to Analog conversion

• 5.4.1 Operational Amplifiers
• Short Op-Amp
• DC coupled amplifier withtwo inputs and one
  output
• Feedback network determines gain

Golden rules (Horowitz Hill)
Voltage Rule The output attempts to do whatever
is necessary to make the voltage difference
between the inputs zero.
Current RuleThe inputs draw no current.
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5.4.1 Operational Amplifiers

• Summing amplifier

Current Rule ? non-inverting input draws no
current thus it is at ground potential
Voltage Rule ? inverting input - (and thus A)
is at virtual ground potential
Current Rule
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5.4.2 DAC using scaled resistors
4-Bit Digital to Analog converter
R
MSB
3
For n bits the largest resistor needs to be 2n-1
times as large as the smallest one!
2R
2
R
4R
Resistors need to be veryprecise!
1
8R
0
LSB
VOut
V
Impractical for large numberof bits n
5
5.4.2 DAC using scaled resistors
4-Bit Digital to Analog converter
R
1
MSB
3
How does it work?!
2R
Voltage rule Inverting input - is at ground
0
2
R
4R
Current rule
0
1
8R
1
0
LSB
VOut
V-8 V
100121?80?40?21?1910
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5.4.2 DAC using scaled resistors
4-Bit Digital to Analog converter
R
0
MSB
3
How does it work?!
2R
Voltage rule Inverting input - is at ground
0
2
R
4R
Current rule
1
1
8R
1
0
LSB
VOut
V-8 V
001120?80?41?21?1310
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5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
2R
2R
Only requires resistance values R and 2R
LSB
0
R
2R
1
Resistors still need to be precise!
R
2R
R
2
R
VSupl.
2R
3
MSB
VOut
V
VSupl. -
Can be used for arbitrarynumber of bits
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5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
2R
2R
How does it work?!
0
LSB
0
R
Voltage rule Inverting input - is at ground
2R
0
1
R
Current rule
Why?!
2R
R
1
2
R
VSupl.
2R
1
3
MSB
VOut
VSupl. -
V-16 Volts
110021?81?40?20?11210
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5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
How does it work?!
0
LSB
0
Why?!
R
2R
0
1
R
2R
2R
R
1
2
R
VSupl.
2R
1
3
MSB
VOut
VSupl. -
V-16 Volts
10
5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
How does it work?!
0
LSB
0
Why?!
0
1
2R
2R
R
1
2
R
VSupl.
2R
1
3
MSB
VOut
VSupl. -
V-16 Volts
11
5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
How does it work?!
Why?!
2R
2R
V-16 Volts
R
12
5.4.2 R-2R ladder DAC
4-Bit Digital to Analog converter
2R
2R
Summary
0
LSB
0
R
2R
1
1
R
2R
R
0
2
R
VSupl.
2R
1
3
MSB
VOut
VSupl. -
V-16 Volts
101021?80?41?20?11010
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5.4.3 Definitions

• Voltage resolution ?V smallest voltage
  difference possible with DACdepends on the
  number n of bits used