AD/DA CONVERTER Most of the physical variables is in analog signals. Analog signal can

be measured on a continuous limit for the signal values . Examples of this signal is the temperature, pressure, flow rate and other.

If an analog signals is serve as the input to digital system or otherwise, an interface devices such as as digital to analog converter (DAC) and analog to digital converter (ADC) is need to be used.

The circuit that is capable to convert analog signals to digital signals is an analog to digital converter (ADC - Analog-to-Digital Converter)

Digital to analog converter (DAC - Digital-to-Analog Converter) is used to convert digital signals to analog signals.

ADC and DAC use as an interface between a computer with an

analog world

driver

(e.g. valve)

phyiscal quantity

Analog output

Digital output

TRANSDUCER

Digital system

(eg. computer)

DAC

.

.

.

.

.

.

Analog input

Physical quantity control

ADC

Digital input

DIFFERENCES BETWEEN ANALOG AND DIGITAL

SIGNALS

Digital Signals Analog Signals

-A digital to analog converter (DAC) is a device that converts digital signals numbers (binary) to an analog signal such as voltage or current output.

Basic DAC Block diagram

Analog outputDigital input

A

B

C

D DAC 4-bitV

1s2s4s8s

D/A CONVERTER

DAC Block Diagram

DAC

ABCD

Resistor Network

1s2s4s8s

Summing Amplifier

VoutV0ut

- In DAC block diagram it include resistor network and summing amplifier

circuit.

- There are two part in DACi) Resistor Networkii) Summing Amplifier

RESISTOR NETWORK The circuit is consists switches and resistors.

Binary or digital input switches was label with 20, 21 and so on.

Two types of circuits the resistor network

Weighted binary resistance network - where the value of the resistor is follow by weight of the binary number

R/2R- where the value of the resistor used is R and 2R only.

SUMMING AMPLIFIER Consists of operational amplifier (op-amp) which is designed

to operate as a summing amplifier circuit

Produce the total weight of the input voltages, where the output is an analog voltage or current that can be measured by the meter

WEIGHTED BINARY RESISTANCE NETWORK

20K

RF

18.7K 150K37.5K 75K

R4 R3 R2R1

3V

ABCD

VVVO

UT

-

+Vout

-

+Vout

Weighted Binary Resistance Network Circuit

The circuit shown is a digital to analog converter 4-bits weighted binary resistance network circuit types.

Resistor values can be calculated using the weight of the binary number.

For example;

Referring to the circuit as shown, the highest value resistor (150KΩ) is a digital input resistor. The smallest bit (least significant bit), and the values of other resistor is;

Circuit analysis to find Vout

i. If binary input is 0001

R1 = 150KΩ, RF = 20KΩ, Vref = 3V

Voltage Gain (AV) = RF = 20KΩ = 0.133

R1 150KΩ

Vout = Vref X AV

= 3V X 0.1333

= 0.4V

ii. If binary input is 0110

R2 = 75KΩ, R3 = 37.5KΩ, RF = 20KΩ, Vref = 3V

RT = R2//R3 = 25KΩ

Voltage Gain (AV) = RF = 20KΩ = 0.8

RT 25KΩ

Vout = Vref X AV

= 3V X 0.8

= 2.4VOr;

Rin = 1 + 1 Vout = Vref X RF X Rin

R2 R3 = 3V X 20KΩ X 40µΩ = 1 + 1 = 2.4V 75KΩ 37.5KΩ = 40µΩ

iii. If binary input is 1100

Simply that we can see the resulting output is shown in the table below

Bil. Desimal Masukan binariVout (V)D C B A

0 0 0 0 0 01 0 0 0 1 0.42 0 0 1 0 0.83 0 0 1 1 1.24 0 1 0 0 1.65 0 1 0 1 2.06 0 1 1 0 2.47 0 1 1 1 2.88 1 0 0 0 3.29 1 0 0 1 3.6

10 1 0 1 0 4.011 1 0 1 1 4.412 1 1 0 0 4.813 1 1 0 1 5.214 1 1 1 0 5.615 1 1 1 1 6.0

R-2R The circuit is different from the DAC circuit weighted binary

resistance network because it only uses two resistor values , R and 2R.

Disadvantage of weighted binary resistance network is we can see on the circuit was too much of the resistor to be provided. For example, if 12-bit DAC with resistor value MSB (most significant bit) is 1K then LSB resistor will exceed 2M. By fabrication technology circuit, it is difficult to produce a large resistance range values with small values of current and can set the exact ratio in the range of temperatures.

This is why R/2R DAC circuits are frequently used to obtain high accuracy and precision.

Where;n = number of bits Bin = digital input is converted to decimal

numbers

R-2R 2 bit circuit

Vout

+

-

2R

2R

Rf

Vref

2R

R

A B

Examples 1:

i. When input 012

First convert 012 to decimal number 012 110

Vout = Vref X Bin X RF

2n R

Vout = Vref X 1 X RF

2n R

ii. When input 1112

First convert 112 to decimal number 1112 710

Vout = Vref X Bin X RF

2n R

Vout = Vref X 7X RF

2n R

Examples 2:

VOUT

+

-

Rf

5V

2R

R R

2R

C D

2R

2R

A

R

2R

B

Input Output, VoutD C B A

0 0 0 0 0

0 0 0 1 0.3125

0 0 1 0

0 0 1 1

0 1 0 0

Input Output, VoutD C B A

0 1 0 1

0 1 1 0

0 1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1

SPECIFICATIONS DIGITAL TO ANALOG CONVERTER

1001 ………..0000 …

Bin

1V

0V

4-BIT COUNTER

DAC

Resolution(1 V)

A

B

D

C

CLK

VOUT

Full Scale = 15V

4-Bit DAC Output Waveform

The figure above shows the DAC receives digital input from the counter mode-16. 4-bit DAC has a resolution 1V and the output voltage maximum or full-scale voltage of 15 V

There are five specifications for the DAC

i. Resolutionii. Accuracy iii. Time Setting @ sedimentation iv. Offset Voltagev. Monotonicinity

RESOLUTION Defined as the smallest change that can occur in the analog output

when digital input changes

resolution for DAC is in bits numberexamples10-bit DAC have 10 bits resolution.10-bit DAC has a resolution smaller than 8-bits DAC

Resolution can be expressed in two cases, either the voltage or Ampere and also percentages.

Resolution is usually referred to the step size since it was a total change in Vout when the digital input changes from one step to the next step.

Its value is equal to the LSB wheighted

Resolution = Step Size = Input bit for LSB

Vout (analog output)= K x Digital Input

K = Total Voltage/Current Or Analog Output Number Of Step Digital Input

Formula

* K = the factor of proportionality and is a fixed value for a DAC

Digital Input = Number of Step

Number of Step = 2n – 1

Where;

n = Number of input bits

Examples 1

If digital input 10102 and K = 3V, what is the output voltage (Vout).

10102 1010

Vout = 3V x 1010

= 30V

Examples 2Calculate full scale Vout for digital input 11112 and K = 0.2V

11112 1510

Vout = 0.2V x 1510

= 3V

Examples 3

If 5-bits DAC have an output in current for digital input 101002, output

current 10mA is produced. What is Iout value for digital input of 111012?

Digital Input = 111012 2910

Digital Input = 101002 2010

K = Analog Output Digital Input

= 10mA 2010

= 0.5mA Iout = 0.5mA x 2910

= 14.5mA

Examples 3

What is the largest output value 8-bits DAC that produces 1V for digital input

001100102

Resolution Percentages (%)

% Resolution = Step Size X 100% Full Scale

Full Scale = Number Of Step x Step Size

Step Size = Full Scale Number Of Step

% Resolusi = 1 x 100% Number Of Step

= 1 x 100% 2n - 1

Formula

Examples 1

A 4-bits DAC has a step size 10mV. Determine the full scale output voltage and

the resolution percentages.

Method 1 Number of step = 2n – 1

= 24– 1 = 16– 1 = 15 Full scale output = number of step X step size

= 15 x 10mV= 150mV

% resolusi = Saiz Langkah x 100% Skil Penuh

= 10mV x 100% 150mV

= 6.67%

Method 2

% resolusi = 1 x 100% Number Of Step

= 1 x 100% 2n – 1

= 1 x 100% 24 - 1

= 1 x 100% 15

= 6.67%

Examples 2

Digital to analog converter 10 bits have step size 10mV. Find full scale voltage

and % resolution

ACCURACY Manufacturer of digital to analog converter has a several ways

to define accuracy.Two of them are often referred to Linearity Error and Full-scale error

Full Scale Error The maximum deviation from the ideal DAC output value.

Examples

4-bit DAC has +0.01%FS accuracy and DAC full-scale is15V. So +0.01% x 15 = +1.5mV.

This means that the DAC output will be different from the ideal value 1.5mV

Linearity Error

The maximum deviation of the step size from ideal step size. Example 1:

4-bit DAC with 1V step size. If the converter has linearity error +0.01% FS.

This means that the actual value of the step size will be different from the ideals value1.5mV.

Example 2:

An 8-bit DAC has 2mA full-scale value and +0.5% FS accuracy. What is the output range for input 10000000?

10000000 12810

Step Size = 2mA = 7.84µA 255

Ideal ouput for input 12810 = 12810 X 7.84µA= 1004µA

Error = +0.5% FS X 2mA= 10µA

Actual output will deviate as much as 1004 The actual range is 994µA-1014µA after + with error.

SETTLING TIME The speed of digital to analog converter is usually referred to the settling time,

which is the time required by a digital to analog converter output for change from zero to full-scale during binary input change from all zero to all one.

Actually, this settling time measured at the time of digital to analog converter

output was completed in the range of 1/2 step size full-scale.

Usually the settling time for current digital to analog converter is shorter than the settling time voltage digital to analog converter.

This is because the op-amp feedback is used as current to voltage converter.

ExamplesIf the digital to analog converter has 10mV resolution. The settling time is measured at fixed output time at 5mV full-scale range.

OFFSET VOLTAGE Digital to analog converter ideal output is 0V when the binary input is all '0 '.

In practical there is usually a small voltage value at this time.

Most of DAC has external offset adjustment that will adjust to 0V as required.

Examples 4-bit digital to analog converter has an offset error +2 mV and 100mV step size.

Input Ideal Output (mV) Actual Output (mV)0000 0 20001 100 1021000 800 8021111 1500 1502

The above table shows a difference between ideal and actual output value, which is actual value increases 2mV from the ideals value.

MONOTONIC Digital to Analog Converter is monotonic if the output either increases

or same if binary input increases from one values to other values .

Monotonic is important in closed-loop system to avoid oscillation.

Examples

BinBin

Vout

a and b is Monotonic but c is not Monotonic

Bin

Vout

Vout

b ca

DAC USAGE CONTROL

Digital output from a computer can be converted to an analog control signal to adjust the motor speed or furnace temperature or any physical variable.

AUTOMOTIC TESTING Computer can be programmed to generate an analog signal (through DAC) needed to test analog circuits which testing results will be converted into a digital value by DAC and loaded to a PC to be stored, displayed or analyzed.

THE SIGNAL RECONSTRUCTION

In most applications,analog signal is been digitized which is some sequence point at signal is converted into an equivalent digital value and stored in memory.

The conversion is done by the ADC. DAC is then used to convert digitized data into an analog at one point in a time to reconstruct the original signal.

This usages can be seen in the 'digital storage oscilloscope "or digital audio tape recording

A / D CONVERSION

DAC are used as part of the ADC circuit