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 Digital Digital Analog input output output Analog input Digital system TRANSDUCER . . driver (eg. computer) (e.g. valve) ADC . DAC . Physical quantity phyiscal quantity control . .
DIFFERENCES BETWEENANALOG AND DIGITAL SIGNALS Digital Signals Analog Signals
D/A CONVERTER-A digital to analog converter (DAC) is a device that convertsdigital signals numbers (binary) to an analog signal such as voltageor current output.Basic DAC Block diagram Digital input Analog output A 1s B 2s 4s C V 8s D DAC 4-bit
DAC Block Diagram DAC 1s A 2s B VoutV0ut 4s C Resistor Summing 8s D Network Amplifier- In DAC block diagram it include resistor network and summing amplifier circuit.- There are two part in DAC i) Resistor Network ii) Summing Amplifier
RESISTOR NETWORK The circuit is consists switches and resistors. Binary or digital input switches was label with 2 0, 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 Weighted Binary Resistance Network Circuit D C B A3V 18.7K 37.5K 75K 150K RF R4 R3 R2 R1 20K - - Vout O VVV Vout ++ UT
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 Vouti. 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
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 1KΩ then LSB resistor will exceed 2MΩ. 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.
R-2R 2 bit circuit Vref A B Rf 2R 2R - R + 2R Vout Where; n = number of bits Bin = digital input is converted to decimal numbers
Examples 1:i. When input 012 ii. When input 1112 First convert 012 to decimal First convert 112 to decimal number number 012 110 1112 710 Vout = Vref X Bin X RF Vout = Vref X Bin X RF 2n R 2n R Vout = Vref X 1 X RF Vout = Vref X 7X RF 2n R 2n R
Examples 2: 5V A B C D Rf 2R 2R 2R 2R - R R R + 2R VOUT Input Output, Vout D 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
SPECIFICATIONS DIGITAL TO ANALOG CONVERTER 4-BIT COUNTER Full Scale = 15V D C DAC VOUT 1V B Resolution(1 V) A 0V CLK Bin 0000 … 1001 ……….. 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. Resolution ii. Accuracy iii. Time Setting @ sedimentation iv. Offset Voltage v. Monotonicinity
RESOLUTION Defined as the smallest change that can occur in the analog output when digital input changes resolution for DAC is in bits number examples 10-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
Formula 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* 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 1If digital input 10102 and K = 3V, what is the output voltage (Vout).10102 1010 Vout = 3V x 1010 = 30VExamples 2Calculate full scale Vout for digital input 11112 and K = 0.2V11112 1510 Vout = 0.2V x 1510 = 3V
Examples 3If 5-bits DAC have an output in current for digital input 10100 2, outputcurrent 10mA is produced. What is Iout value for digital input of 11101 2? 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 3What is the largest output value 8-bits DAC that produces 1V for digital input001100102
Resolution Percentages (%)Formula % 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
Examples 1A 4-bits DAC has a step size 10mV. Determine the full scale output voltage andthe 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 2Digital to analog converter 10 bits have step size 10mV. Find full scale voltageand % 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 errorFull 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.
SETTLINGTIME 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. Examples If 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 2 0001 100 102 1000 800 802 1111 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 Vout Vout Vout Bin Bin Bin a b c a and b is Monotonic but c is not Monotonic
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