Dueck R.Digital design with CPLD applications and VHDL.2000

FIGURE 12.12

MC1408 Configured for

Unbuffered Analog Output

Va is positive because the voltage drop across RF is positive with respect to the virtual ground at the op amp ( ) input. This feedback voltage is in parallel with (i.e., the same as) the output voltage, since both are measured from output to ground.

We can develop the formula for the analog voltage, Va, in three stages:

1. Calculate the reference current:

Iref Vref( )/R14

2. Determine the binary-weighted fraction of reference current to get DAC output current:

3. Use Ohm’s law to calculate the op amp output voltage:

The resistor values in the above formulae are the total resistances for the correspond-

ing part of the circuit. That is, R14 R14A R14B and RF RFA RFB. These both consist of a fixed and a variable resistor, which has two advantages: (a) The reference current

and output voltage can be independently adjusted within a specified range by the variable resistors. (b) The resistances defining the reference and feedback currents cannot go below a specified minimum value, determined by the fixed resistance, ensuring that excessive current does not flow into the reference input or the DAC output terminal.

Va can, in theory, be any positive value less than the op amp positive supply ( 12 V in this case). Any attempt to exceed this voltage makes the op amp saturate. The actual maximum value, if not the same as the op amp’s saturation voltage, depends on the values of RF and R14.

FIGURE 12.14

Example 16.5

DAC Ramp Generator

Briefly explain the operation of the circuit and sketch the output waveform. Calculate the step size between analog outputs resulting from adjacent codes. Assume that the DAC is set for 6-V output when the input code is 10000000.

Calculate the output sawtooth frequency when the clock is running at 1 MHz.

Solution The 8-bit counter cycles from 00000000 to 11111111 and repeats continuously. This is a total of 256 states.

The DAC output is 0 V for an input code of 00000000 and (12 V 1 LSB) for a code of 11111111. We know this because a code of 10000000 always gives an output voltage of half the full-scale value (6 V 12 V/2), and the maximum code gives an output that is one step less than the full-scale voltage. The step size is 12 V/256 steps 46.9 mV/step. The DAC output advances linearly from 0 to (12 V 1 LSB) in 256 clock cycles.

Figure 12.15 shows the analog output plotted against the number of input clock cycles. The ramp looks smooth at the scale shown. A section enlarged 32 times shows the analog steps resulting from eight clock pulses.

One complete cycle of the sawtooth waveform requires 256 clock pulses. Thus, if

fCLK 1 MHz, fo 1 MHz/256 3.9 kHz.

(Note that if we do not use a high slew rate op amp, the sawtooth waveform will not have vertical sides.)

FIGURE 12.16

MC1408 as a Bipolar D/A Converter

The current sink, Io, is a variable element. The voltage source, Vref ( ), remains constant. To satisfy Kirchhoff’s current law, the feedback current, IF, must vary to the same degree as Io. Depending on the value of Io with respect to Is, IF can be positive or negative.

We can get some intuitive understanding of the circuit operation by examining several cases of the equation Va.

Case 1: Io 0. This corresponds to the digital input b7b6b5b4b3b2b1b0 00000000. The output voltage is:

Va = (Io − Is )RF = −Is RF = − RF Vref

R4

This is the maximum negative output voltage.

Case 2: 0 Io Is. The term (Io Is) is negative, so output voltage is also a negative value.

Case 3: Io Is. The output is given by:

(127/128)(RF/R4)(Vref) if R4 2R14.

To set the maximum negative value, set the input code to 00000000 and adjust RFB for12 V. RFB RF RFA. Solve the following equation for RF:

(Note: 12 V 2 LSB 12 V (12 V/128) 12 V 94 mV 11.906 V.)

SECTION 12.2E REVIEW PROBLEM

12.6Why is the actual maximum value of an 8-bit DAC less than its reference (i.e., its apparent maximum) voltage?

DAC Performance Specifications

A number of factors affect the performance of a digital-to-analog converter. The major factors are briefly described below.