1. EET 252 Unit 7 Digital-to-Analog Conversion
Read Floyd, Sections 12-3 to 12-5 (through page 707).
Study Unit 7 e-Lesson.
Do Lab #7.
Homework #7 and Lab #7 due next week.
Quiz next week.
-Handout: slide 5, practiceOpAmp
-Take Quiz 6.
-Fire up Multisim.

2. The Big Picture
An analog-to-digital converter (ADC) takes an analog voltage or current as its input and produces a digital code as its output. This digital code is proportional to the analog input.
A digital-to-analog converter (DAC) takes a digital code as its input and produces an analog voltage or current as its output. This analog output is proportional to the digital input.
-Recall that many ADC’s contain a DAC as a component.

3. Review . . Digital inputs Digital outputs Analog input (voltage or
current)
Analog output
(voltage or
current)
ADC
Computer
DAC . .
Control
physical
variable
-Recall that the ADC block typically includes an anti-aliasing filter and a sample-and-hold circuit, in addition to the circuit the performs that actual quantization.
Physical
variable
Transducer
Actuator

4. Review: Resolution
Just as with ADCs, there are several common ways of specifying a DAC’s resolution:
Number of bits, n
Number of output codes, = 2n, or number of steps in the output, = 2n − 1
Percentage resolution, = 1 / (2n − 1), expressed as a percentage
Step size, = Vref / 2n

5. Resolution: Examples n 2n 2n−1 1 / (2n−1) Vref / 2n Formula 4-bit DAC
Number of bits n
Number of output codes 2n
Number of steps in the output
2n−1
Percentage resolution
1 / (2n−1)
Step size (assuming 5 V reference voltage)
Vref / 2n

6. An 8-Bit DAC in Multisim
Note 8 digital inputs, 1 analog output, and input reference voltage.
-Demo this file (dac_meter.ms10) in Multisim. Have them predict output voltage when digital input = , when digital input = (“full-scale voltage”), and when digital input =
-What digital input would be needed to produce an output of roughly 1.2 V?

7. Calculating the Output Voltage
For an 8-bit multiplying DAC like the one in previous slide, the output voltage is given by the following equation, where Din is the number (between 0 and 255) present on the digital inputs:
This gives the ideal value. In practice, various factors can cause the actual value to deviate from this predicted value.
-What number would be in the denominator for a 10-bit DAC?
-Don’t try to memorize this equation! Just think through it.
-Using file wordGenDemo.ms10, explain how to use Word Generator, which they’ll use in lab.
-Then run file dac_scope.ms10.

8. Voltage or Current?
Some DACs are designed to produce an output current (rather than an output voltage) that is proportional to the digital input.
For such a DAC, we’d simply change our equation to
The DAC chip that we’ll use in this week’s lab is a current chip.

9. How to Build a DAC
Two standard ways of building a digital-to-analog converter:
Binary-weighted input
R/2R Ladder
Both methods use operational amplifiers with negative feedback.
-Simpler and (generally) quicker than ADC’s.

10. Op Amp with Negative Feedback
In many applications, the op amp’s output is connected back to its inverting input directly or through a component (resistor or capacitor). This configuration is called negative feedback. For example:
Recall that an op amp with no feedback serves as a comparator.

11. “Golden Rules” of Op Amps with Negative Feedback
In The Art of Electronics, Horowitz and Hill give two “golden rules” for analyzing circuits that contain op amps with negative feedback:
The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.
The inputs draw no current.
Warning: These two rules apply only if the op amp has negative feedback.
Do practiceOpAmp handout.

12. Binary-weighted-input DAC
In a binary-weighted-input DAC, the input current in each resistor is proportional to the column weight in the binary numbering system. It requires very accurate resistors and identical HIGH level voltages.
LSB 8R Rf D0
The MSB is represented by the largest current, so it has the smallest resistor. To simplify analysis, assume all current goes through Rf and none into the op-amp. 4R D1 2R
Vout D2
Analog output R D3
MSB

13. Example Solution Binary-weighted-input DAC
A certain binary-weighted-input DAC has a binary input of If a HIGH = +3.0 V and a LOW = 0 V, what is Vout?
120 kW Rf
+3.0 V
60 kW
10 kW
0 V
30 kW
Vout
+3.0 V
15 kW
+3.0 V
-Have them find Vout when binary input is 0001 (step voltage) and 1111 (full-scale voltage).
-Note that Vout depends on the precise value of a HIGH at the binary inputs. This is undesirable, and we’ll return to this point later.
Solution
Vout = Iout Rf = (−0.325 mA)(10 kW) =
−3.25 V

14. R/R2 Ladder DAC
The R-2R ladder DAC requires only two values of resistors. By calculating a Thevenin equivalent circuit for each input, you can show that the output is proportional to the binary weight of inputs that are HIGH.
Each input that is HIGH contributes to the output:
where VS = input HIGH level voltage
n = number of bits
i = bit number
Inputs D0 D1 D2 D3
For accuracy, the resistors must be precise ratios, which is easily done in integrated circuits. R1 R3 R5 R7
Rf = 2R 2R 2R 2R 2R R2 R4 R6 R8 2R R R R
Vout

15. Example Solution R/R2 Ladder DAC
An R-2R ladder DAC has a binary input of If a HIGH = +5.0 V and a LOW = 0 V, what is Vout?
Example D0 D1 D2 D3
+5.0 V
+5.0 V
0 V
+5.0 V R1 R3 R5 R7
Rf = 50 kW
50 kW
50 kW
50 kW
50 kW R2 R4 R6 R8
50 kW
25 kW
25 kW
25 kW
Vout
-Have them find Vout when binary input is 0001 (step voltage) and 1111 (full-scale voltage).
-As in previous design, Vout depends on the precise value of a HIGH at the binary inputs. This is undesirable, and we’ll turn to this point next.
Solution
Apply to all HIGH inputs, then sum the results.
Applying superposition, Vout = −6.875 V

16. Using a Reference Voltage
In the previous circuits, the output voltage depended on the precise voltage present on the digital inputs. This is undesirable, since a digital HIGH on one of these pins could be anywhere from about 2.4 V to about 5 V.
We’d rather have the output voltage depend only on whether the inputs are HIGH or LOW, regardless of the precise voltage.
So most DAC chips use additional circuitry and a reference voltage that sets the full-scale output, independent of the precise voltages present on the digital inputs.

17. Binary-Weighted DAC, Using a Reference Voltage
-Similar idea applies to R/2R Ladder design.
-Shown is a Multisim schematic with voltage-controlled switches.
-The LM336 reference diode that they’ll use in lab is one way to provide a precision reference voltage.

18. A Popular DAC Chip MC1408 8-bit DAC (Datasheet on course website.)
It’s also known as a DAC0808.
This chip requires a ground connection and positive (VCC) & negative (VEE) supply voltages.
Its output current is given by
Io = Iref x Din / 256
where Iref is the current into pin 14 (typically 2 mA).
Note strange pin naming: A1 is MSB and A8 is LSB.

19. Digital Signal Processing
A digital signal processor (DSP) is optimized for speed and working in real time (as events happen). It is basically a specialized microprocessor with a reduced instruction set.
After filtering and converting the analog signal to digital, the DSP takes over. It may enhance the signal in some predetermined way (reducing noise or echoes, improving images, encrypting the signal, etc.). The signal can then be converted back to analog form if desired.