Digital To Analog Converter (DAC) in Microprocessor

YASH PAL,

Digital to Analog Converter (DAC) in Microprocessor – The electronic circuit that translates a digital signal into an analog signal is called a Digital to Analog Converter (DAC). Most of the information-carrying signals, such as voltage, current, temperature, pressure, charge, time, etc., are available in analog form. These are known as analog signals. Although an analog signal represents a real physical parameter with accuracy, it is difficult to store and process the signal without introducing a considerable error. For sorting, processing, and transmitting purposes, it is often more convenient to express such signals in digital form. The digital signals show better accuracy and reduce the effect of the noise signal.

In the microprocessor-based system, it is necessary to convert the analog signal to a digital signal. The electronic circuit that translates an analog signal into a digital signal is called an analog-to-digital (A/D) converter (ADC). Similarly, a digital-to-analog (D/A) converter (DAC) is used when a digital signal is to be translated into an analog signal. Both ADC and DAC are also known as data converters and are now available as integrated circuits (ICs).

Digital to Analog Converter (DAC)

A digital-to-analog converter accepts an n-bit input word (b1, b2, b3, b4,… bn) in binary form and produces an analog signal proportional to it. This analog form may be sent to the real world, which deals with the analog form. Depending on the output, DACs can be broadly classified into three categories:

  1. Current Output DAC
  2. Voltage Output DAC
  3. Multiplying type DAC

The current output DAC provides current as the output signal, as its name suggests. The voltage output DAC internally converts the current signal into a voltage signal. It requires some additional time to convert the current signal into a voltage signal, hence slower than the current output DAC. The multiplying type DAC output represents the product of the input signal and the reference source. The symbol for DAC is shown in the figure below.

Digital to circuit symbol in microprocessor
Digital to circuit symbol in a microprocessor

If there are four digital inputs, the DAC is known as a 4-bit DAC. Each digital input requires an electrical signal representing either a logic ‘1’ or a logic ‘0’.

Parameters of (DAC)

Resolution – Resolution is defined as the ratio of change in output voltage (analog) resulting from a change of one least significant bit (LSB) at the input (digital). For an n-bit DAC, the resolution is given as

Resolution=Vof(2n−1)Volts/LSBResolution = \frac {V_{of}}{(2^n – 1)} Volts/LSB

Where Vof is the full-scale output voltage.

Accuracy – Accuracy shows the relation between the actual value and the theoretical value. Ideally, the accuracy of the DAC should not be less than ± 1/2 LSB. Mathematically

Minimum Accuracy=Resolution2Minimum \space Accuracy = \frac {Resolution}{2}
Minimum Accuracy=Vof2(2n−1)VoltsMinimum \space Accuracy = \frac {V_{of}} {2(2^n – 1)} Volts

Conversion Time – It is the time required to convert the digital input into an equivalent analog output. It is also known as the setting time of the DAC. Minimum conversion time is desired to speed up the digital-to-analog conversion. It depends on the response time of the switches used in the design of the DAC.

Stability – The performance of DAC changes according to age, temperature, and power supply variations. So all the relevant parameters must be specified over the full temperature and power supply ranges. The stability factor shows the consistency in the analog output signal with the change in age, temperature, and power supply conditions.

Digital to Analog Conversion Techniques

There are mainly two techniques used for digital-to-analog conversion.

  1. Binary weighted resistor network.
  2. R/2R ladder network.

In both techniques, an op-amp circuit is used. The network (Binary weighted resistor or R/2R ladder) generates the weighted current according to the digital input, and the op-amp circuit converts this current into a proportional voltage. Therefore, such DACs are known as current-driven DACs.

Binary Weighted Resistor DAC

The binary-weighted resistor DAC uses current-scaling resistors 2R, 4R, 8R, … 2nR. For an n-bit DAC, n binary-weighted currents are derived from a reference voltage Vref via current-scaling registers. These currents are summed with the help of an op-amp. The circuit for the binary weighted resistor DAC is shown in the figure below.

Binary weighted resistor DAC
Binary weighted resistor in DAC

As shown in the above figure, the binary inputs control the switches of the circuit. When digital input is logic ‘1’, it connects the corresponding resistor to the reference voltage Vref; otherwise, it leaves the resistor open.

For the ON switch, current I=VrefRFor\space the\space ON\space switch,\space current\space I = \frac {V_{ref}}{R}

And for the OFF switch, current I = 0. Therefore, the total current from current scaling resistors is given as

IT=I1+I2+I3+...+InI_T = I_1 + I_2 + I_3 + … + I_n

The output voltage is the voltage across Rf, and it is given as

V0=−ITRf=−(I1+I2+I3+...+In)RfV_0 = -I_TR_f = – (I_1 + I_2 + I_3 + … + I_n)R_f
=−(D1Vref2R+D2Vref4R+D3Vref8R+...+DnVref2nR)Rf= -\left( D_1\frac{V_{ref}}{2R} +D_2\frac{V_{ref}}{4R}+D_3\frac{V_{ref}}{8R}+…+D_n\frac{V_{ref}}{2^nR} \right)R_f
=−VrefRRf(D12+D24+D38+...+Dn2n)= -\frac{V_{ref}}{R}R_f\left(\frac{D_1}{2}+\frac{D_2}{4}+\frac{D_3}{8}+…+\frac{D_n}{2^n} \right)

If Rf = R, then V0 is given as

V0=−Vref(D12+D24+D38+...+Dn2n)V_0= -V_{ref}\left(\frac{D_1}{2}+\frac{D_2}{4}+\frac{D_3}{8}+…+\frac{D_n}{2^n} \right)

This equation gives the analog output voltage, which is proportional to the input digital signal.

Limitations:

  1. A wide range of resistor values is required (2R, 4R, 8R, … 2nR)
  2. Resistor values have restrictions on both higher and lower ends. High-value resistors can not be fabricated in ICs, whereas low-value resistors have a loading effect.
  3. The finite resistance of the switches becomes significant for small current scaling resistors, and there may be an error in the output analog voltage.

R/2R Ladder Network DAC

The limitations of the binary weighted resistor DAC are overcome by the R/2R ladder network DAC. The circuit for the R/2R ladder network DAC is shown in the figure below. This includes the resistance of only two values, R and 2R. Each bit of the digital input connects the corresponding switch either to ground or to the inverting terminal of the op-amp, which is at the virtual ground.

R/2R ladder network digital to analog converter
R/2R ladder network DAC

Note – The number of bits can be expanded for the R/2R ladder network DAC by adding more sections of the same R/2R values.

The currents flowing through the R/2R ladder networks are given as

I1=Vref2RI_1 = \frac{V_{ref}}{2R}
I2=Vref/22R=Vref4RI_2 = \frac{V_{ref}/2}{2R} = \frac{V_{ref}}{4R}
I3=Vref/42R=Vref8RI_3 = \frac{V_{ref}/4}{2R} = \frac{V_{ref}}{8R}

… …..

In=Vref/(2n−1)2R=Vref2nRI_n = \frac{V_{ref}/(2^n-1)}{2R} = \frac{V_{ref}}{2^nR}

The output voltage is

V0=−RfITV_0 = -R_fI_T
=−Rf(I1+I2+I3+...+In)= -R_f(I_1 + I_2 + I_3 + … + I_n)
=−Rf(D1Vref2R+D2Vref4R+D3Vref8R+...+DnVref2R)= -R_f\left( D_1\frac{V_{ref}}{2R} +D_2\frac{V_{ref}}{4R}+D_3\frac{V_{ref}}{8R}+…+D_n\frac{V_{ref}}{2R} \right)

When Rf = R, the output voltage is given as

V0=−Vref(D12+D24+D38+...+Dn2n)V_0= -V_{ref}\left(\frac{D_1}{2}+\frac{D_2}{4}+\frac{D_3}{8}+…+\frac{D_n}{2^n} \right)

This equation gives the analog output voltage, which is proportional to the input digital signal.

Note: Since each digital signal connects the corresponding switch to the ground or virtual ground (Inverting terminal of the op-amp), all ladder node voltages remain constant with changing input signal.

Interfacing of the D/A Converter

The microprocessor processes the data in digital format. But in the real world, the analog signals are required. In response to this need, interfacing of the DAC to the microprocessor is a must. There are several DACs available that are compatible with the microprocessors.

Interfacing of 1408 DAC with the 8085 microprocessor

The 1408 is an 8-bit R/2R ladder-type DAC. The output of the 1408 DAC is a current that is the linear product of an eight-bit digital input. The settling time for this DAC is 300n sec. The figure below shows the pin diagram for the 1408 DAC.

Pin Diagram for DAC 1408
Pin Diagram for DAC 1408

The DAC 1408 has eight input lines (A1 – A8). The input line A1 is MSB, and A8 is LSB; the convention of labelling MSB to LSB is opposite to that of what is normally used for the data bus in a microprocessor. It requires 2mA reference current for full-scale input and two power supplies, Vcc = +5V and VEE = -15V. The DAC 1408 consists of eight high-speed current switches, a R/2R ladder network, and a reference current amplifier. The block diagram for DAC 1408 is shown in the figure below.

Block diagram of DAC 1408
Block diagram of DAC 1408

The voltage Vref and the resistor at pin 14 (R14) determine the total reference current source. Generally, the resistor connected at pin 15 is equal to the resistor connected at pin 14. It is used to match the input impedance of the reference current amplifier. The output current is given as

I0=VrefR14(A12+A24+A38+A416+A532+A664+A7128+A8256)I_0 = \frac{V_{ref}}{R_{14}}\left( \frac {A_1}{2} + \frac {A_2}{4} + \frac {A_3}{8}+\frac {A_4}{16}+\frac {A_5}{32}+\frac {A_6}{64}+\frac {A_7}{128}+\frac {A_8}{256}\right)

Where input A1 through A8 can be either 0 or 1. The direction of the output current is inward. It means that DAC 1408 sinks current. The 8085 microprocessor provides the data on the data bus for a few microseconds. There is no internal latch in DAC 1408; an additional latch is required with the input of the DAC 1408. The chip select logic of the latch IC is used to determine the address of the system being designed. Since the output of DAC 1408 is in current, we need an op-amp circuit that converts the analog current signal to an analog voltage signal. The interfacing of DAC 1408 with the 8085 microprocessor is shown in the figure below.

Interfacing of DAC 1408 with the 8085 microprocessor
Interfacing of DAC 1408 with the 8085 microprocessor

Interfacing of the AD558 DAC with the 8085 Microprocessor

The Ad 558 DAC is a 16-pin IC that has an internal latch and an op-amp circuit to convert the analog current to the analog voltage. These are the two main limitations of DAC 1408, which are overcome by AD558 DAC. Another advantage of the AD558 DAC over the DAC 1408 is that it requires only one power supply between +4.5V and +16.5V. In the AD558 DAC, there are two pins (CS and CE) that are used to select the IC. When both CE and CS are at logic ‘0’. The latch is transparent, as shown in the figure below. It means the input digital signal coming from the microprocessor is transferred to the DAC section. When either CS or CE goes to logic ‘1’, the input is latched in the register and held until both signals go to logic ‘0’.

Block diagram of DAC AD558
Block diagram of DAC AD558
engineering subjects Microprocessor