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578

C H A P T E R

1 2 • Interfacing Analog and Digital Circuits

This model is easily expanded. The source for the most significant bit always has the

value Vref/2. Each source is half the value of the preceding bit. Thus, for a 5-bit circuit, the

source for the least significant bit has a value of Vref/32. An 8-bit circuit has an LSB equiv-

alent source of Vref/256.

EXAMPLE 12.3

A 4-bit DAC based on an R-2R ladder has a reference voltage of 10 volts. Calculate the

analog output voltage, Va, for the following input codes:

a.

0000

b.

1000

c.

0100

d.

1100

Solution

a. Va (0/16) Vref 0 V

b. Va (8/16) Vref (1/2) Vref 5 V

c. Va (4/16) Vref (1/4) Vref 2.5 V

d. Va (12/16) Vref (3/4) Vref 7.5 V

EXAMPLE 12.4

Calculate the output voltage of an 8-bit DAC based on an R-2R ladder for the following in-

put codes. What general conclusion can be drawn about each code when compared to the

solutions in Example 12.3?

a.

00000000

b.

10000000

c.

01000000

d.

11000000

Solution

a.Va (0/256) Vref 0 V

b.Va (128/256) Vref (1/2) Vref 5 V

c.Va (64/256) Vref (1/4) Vref 2.5 V

d.Va (192/256) Vref (3/4) Vref 7.5 V

In general, a DAC input code consisting of 1 followed by all 0s generates an output value of 1⁄2 full scale. A code of 01 followed by all 0s yields an output of 1⁄4 full scale. An

output of 11 followed by all 0s generates an output of 3⁄4 full scale.

SECTION 12.2C REVIEW PROBLEM

12.4Calculate Va for an 8-bit R-2R ladder DAC when the input code is 10100001. Assume that Vref is 10 V.

MC1408 Integrated Circuit D/A Converter

K E Y T E R M

Multiplying DAC A DAC whose output changes linearly with a change in DAC

reference voltage.


12.2 • Digital-to-Analog Conversion

579

A common and inexpensive DAC is the MC1408 8-bit multiplying digital-to-analog converter. This device also goes by the designation DAC0808. A logic symbol for this DAC is shown in Figure 12.11.

FIGURE 12.11

MC1408 DAC

The output current, Io, flows into pin 4. Io is a binary fraction of the current flowing into pin 14, as specified by the states of the digital inputs. Other inputs select the range of output voltage and allow for phase compensation.

Figure 12.12 shows the MC1408 in a simple D/A configuration. R14 and R15 are approximately equal. Pin 14 is approximately at ground potential. This implies:

1.That the DAC reference current can be calculated using only Vref ( ) and R14 (Iref

Vref ( )/R14)

2.That R15 is not strictly necessary in the circuit. (It is used primarily to stabilize the circuit against temperature drift.)

The reference voltage must be set up so that current flows into pin 14 and out of pin 15. Thus, Vref ( ) must be positive with respect to Vref ( ). (It is permissible to ground pin 14 if pin 15 is at a negative voltage.)

Io is given by:

b7

b6

b5

b4

b3

b2

b1

b0

Vref (+)

Io

=

+

+

+

+

+

+

+

2

4

8

16

32

64

128

256

R14

Since the output is proportional to Vref ( ), we refer to the MC1408 as a multiplying

DAC.

Io should not exceed 2 mA. We calculate the output voltage by Ohm’s law: VoIo RL. The output voltage is negative because current flows from ground into pin 4.

The open pin on the Range input allows the output voltage dropped across RL to range from 0.4 V to 5.0 V without damaging the output circuit of the DAC. If the Range input is grounded, the output can range from 0.4 to 0.55 V. The lower voltage range allows the output to switch about four times faster than it can in the higher range.


580

C H A P T E R 1 2 • Interfacing Analog and Digital Circuits

FIGURE 12.12

MC1408 Configured for

Unbuffered Analog Output

EXAMPLE 12.5

The DAC circuit in Figure 12.12 has the following component values: R14 R15

5.6 k ; RL 3.3 k . Vref ( ) is 8 V, and Vref ( ) is grounded.

Calculate the value of Vo for each of the following input codes: b7b6b5b4b3b2b1b0

00000000, 00000001, 10000000, 10100000, 11111111.

What is the resolution of this DAC?

Solution First, calculate the value of Iref.

Iref Vref ( )/R14

8 V/5.6 k 1.43 mA

Calculate the output current by using the binary fraction for each code. Multiply Io

by RL to get the output voltage.

b7b6b5b4b3b2b1b0 00000000

Io 0, Vo 0

b7b6b5b4b3b2b1b0 00000001

Io (1/256) (1.43 mA) 5.58 A

Vo (5.58 A)(3.3 k ) 18.4 mV

b7b6b5b4b3b2b1b0 10000000

Io (1/2) (1.43 mA) 714 A

Vo (714 A)(3.3 k ) 2.36 V


12.2 • Digital-to-Analog Conversion

581

b7b6b5b4b3b2b1b0 10100000

Io (1/2 1/8)(1.43 mA) (5/8)(1.43 mA) 893 A Vo (893 A)(3.3 k ) 2.95 V

b7b6b5b4b3b2b1b0 11111111

Io (255/256) (1.43 mA) 1.42 mA

Vo (1.42 mA)(3.3 k ) 4.70 V

Resolution is the same as the output resulting from the LSB: 18.4 mV/step

SECTION 12.2D REVIEW PROBLEM

12.5The output voltage range of an MC1408 DAC can be limited by grounding the Range pin. Why would we choose to do this?

Op Amp Buffering of MC1408

The MC1408 DAC will not drive much of a load on its own, particularly when the Range input is grounded. We can use an operational amplifier to increase the output voltage and current. This allows us to select the lower voltage range for faster switching while retaining the ability to drive a reasonable load. The output voltage is limited only by the op amp supply voltages. We use a 34071 high slew rate op amp for fast switching.

Figure 12.13 shows such a circuit. The 0.1- F capacitor decouples the 5-V supply. (The manufacturer actually recommends that the 5-V logic supply not be used as a reference voltage. It doesn’t matter for a demonstration circuit, but may introduce noise that is unacceptable in a commercial design.) The 75-pF capacitor is for phase compensation.

FIGURE 12.13

DAC With Op Amp Buffering

Vref 5 V

Va

RFA

4.7 k

0.1 F

R14A

RFB

12 V

2.7 k

10 k

R14B

I0

I0

5 k

(14)

(4)

Va

Vref( )

I0

12 V

(5)

(15)

1 k

b7

MSB

Vref( )

(6)

b6

R15

(7)

b5

(8)

b4

(9)

b3

MC1408

(10)

b2

(11)

(2)

b1

Range

(12)

(1)

b0

LSB

Ground

Comp

(16)

VCC

VEE

(13)

(3)

75 pF

5 V

12 V