LEARNING OBJECTIVES « Introduction, Weighted-Register D/A Converter, R-2R Ladder D/A Converter, Accuracy and Resolution, Successive Approximation converter 10.0. INTRODUCTION 7 ; A device that produces an analog output from a digital input is known as Digital-to- analog (D/A) converter. A device that produces a digital output from an analog input is nown as analog-to-digital (A/D) converter. Digital-to-analog and analog-to-digital Conversions are the important aspects of digital data processing. Digital-to-analog conversion involves translation of digital information into equivalent analog information. For example the output of a digital system might be changed to analog form to drive a pen recorder. Hence D/A converter is referred to as a decoding device. Analog-to-digital conversion involves changing an analog signal to an equivalent digital signal. A/D conversion is accomplished by the use of an A/D converter. For example A/D converter is used to change the analog signals from the transducers into equivalent digital signal. A/D converter is referred to as an encoding device because it is used to encode signals for entry into a digital system. D/A conversion is a straight forward process and it is easier than A/D conversion. 10.1. WEIGHTED-REGISTER D/A CONVERTER The circuit diagram of a weighted-register digital-to-analog converter is shown in the figure 10.1. The operational amplifier is used to produce a weighted sum of the digital inputs applied to the inverting input terminal. The weights are proportional to the weights of the bit positions of the inputs, The point G at virtual ground. MSB R,‘The output voltage of the OPAMP adder is given by, Dye De Deed, at Ree rere R 2R 4k 8R Se ‘ Where the MSB D, is applied through R, D, is applied through 2R, D, is applied through 4R and the LSB D, is applied through 8R to the inverting terminal of OP AMP and R, is the feedback resistance (2) Re R, Its clear that MSB D, is amplified by —°, D, is amplified by FR: Di is amplified R R by a and LSB D, is amplified by ra _ From equation (2) it is clear that the output voltage is proportional to the numerical value of binary input The accuracy and stability of weighted registor digital-to-analog converter depend on the resistance ratios and on their ability to track each other during the change of temperature. Disadvantages = The weighted-resistor for digital-to-analog conver {i) It requires a different values precision resistor input. (ii) It requires resistances over a wide range for the constr the binary input has a large number of bits. (iii) It is difficult to accommodate a large resistance in IC form because a large resistance has a large shape. 10.2. R-2R LADDER D/A CONVERTER The R -2R ladder digital -to - analog converter is a resistive network whose output voltage is a properly weighted sum of the digital inputs. The circuit diagram of a R = 2R ladder digital - to -analog converter designed for 4 -bits, is shown in the figure - 10. 2 ai Analog output = V,, ter has the following disadvantages: for each bit position of the digital uction of D/A converter if Input m of R - 2R ladder D/A converterThe R -2R ladder D/A converter is the most popular D/A converter.It consist g ladder network of series parallel combination of two resistors of resistance R and 2p a an operational amplifier operating as a voltage follower to prevent loading. If a gig signal D, D, D,D, is applied at the input terminals of the R ah ladder D/A converter equivalent analog signal V, is produced at the output termi If the digital input is 1000, the input terminal D, is connectecetd to + y 4, minals are grounded. With this input signal the binary ladge, all other input ter shown in the figure - 10.3 Bey, OR Fig - 10.3- Binary ladder with a digital input of 1000 There are no voltage sources to the left of node b,. Hence the entire network to the left of node b, can be replaced by a resistance of 2R to form the equivalent circuit with digital input of 1000. 2R b, 2R if +VOD, Fig - 10.4- Equivalent circuit with a digital input of 1000 a ‘The output voltage for digital input 1000 is given by -275 There are no voltage sources to the left of node b,. Hence the entire network to the left of node b, can be replaced by a resistance of 2R to form the partially reduced equivalent circuit. 2k 4, R b, ¢ +V% D, Fig - 10.6- Partially reduced equivalent circuit with a digital input of 1000 The network to the left of node b, can be replaced by Thevenin equivalent circuit. The final equivalent circuit using Thevenin equivalent circuit for digital input 0100, is shown in the figure 10.7. { D, Fig - 10.7- Final equivalent circuit with a digital input of 0010 ©, The output voltage for digital input 0100 is given by ay the input terminal D, is connected +V and all other input terminals Ifthe digital input is 0010, ae grounded with this input signal the binary ladder is shown in the figure 108: : *Vop, 1 D, Fig - 10.11 - Equivalent circuit with a digital input of 0001 The network to the left of b, can be replaced by Thevenin equivalent circuit. The equivalent circuit using Thevenin equivalent circuit for digital input 0001 is shown in the figure 10.12 Re pe uR ie 9 V, +V/8 D. J Fig - 10.12 - Binary ladder with a digital input of 0001 ~. The output voltage for digital input 0001 is given by ed ( 2R ~ (R+R42R 2R V = — — PGR = (4) or V= — e156 This process can be continued to determine the output voltages of an n-bit binary R -2R ladder D/A converter. The output voltages for different bit position of an n -bit R - 2R ladder D/A converter are shown in the figure — 10.13. Ingeneral if, input is 1 and all other inputs are grounded then the output voltage is given by ys aS ee Where N is the total number of binary inputSRE oe 10.3 ACCURACY AND RESOLUTION The accuracy analog converters. The accuracy of the digital -to . accuracy of the precision of the voltage close the actual output voltage Se and the resolution are muon @re the most importam aspects of the digitalto. analog converter ig ee pie 'S Primarily a function of the Supply used. The acura enue © Accuracy is a measure of how 41 Output value of ov Ecnureey ofS pone sa StDt volage fora para ne idb cl yo cent mez a te ea +20V. An accuracy of 5 percent means that the acinar Output voltage must be between 4 19V and +21V. Similarly an accuracy of 2 'e cout vetla 2 percent means tha must be between + 19.6V and + 20.4, q The resolution of the digital to -analog conve of bits in the digital input signal. The resolution voltage. The smallest increment in output volt the actual output voltage Tetd is primarily a function of the number defines the smallest increment i ‘age is determined by the LSB of n output of input . , 1 For example, in a 3 bit R ~ 2R ladder D/A, Converter the LSB has a weight of gc This 1 g of the input voltage.Let us assume that the D/A converter has voltage levels of + 8V.A chang ans that the smallest increment in output voltage is in LSB will produce a change 1 of IV in the output voltage because the LSB has a weight of g- Hence the analog voltage ranges for this digital - to -analog converter are from 0 to + 7V in | V increments. This D/A converter can be used to represent analog voltages from 0 to + 7 V but it so not resolve voltages into increments smaller than 1V, Hence the resolution of the D/A converter is 1V. 1 Similarly in a 10 — bit, R — 2R ladder D/A converter, the LSB has a weight of Tou 1 ii f this converte —— of the full scale Hence the smallest increment is the output of this converter is 7954 f e res of the converter voltage. If this converter has a full scale output of + 20V then the resolution ' resenting is ole 20V = 20mV. This converter has finer resolution and it is capable of repr: 1024 i finer than 20mV. ges to withil i f distinguishing voltages voltages to within 20 mV. It is not capable o aa t 10.3 SUCCESSIVE RUPE ORIMATION ere Bees wie eon lodigat oe 4 Pee tijcimole 4- bit SAC is shown i the figure converters.281. Conversion The voltage comparator determines that 6V is greater than the analog input 5.8 V. Hence the comparator goes low. The control logic clears that bit and the output of SAC goes back to 100 which is the nearest integer value to input 5.8 V. At this point all the register bits have been processed and the conversion is complete. Thus the control logic activates its (end of conversion) EOC output to signal that the digital equivalent of V, is now in the output register. [SOLVED EXAMPLES 1. Determine the weight of each input bit for a 4 - bit weighted -register D/A converter if the inputs are OV and 8V. Ans. The MSB D, passes with a gain of 1 => Weight of MSB D, = 8 x 1 = 8V 1 The next bit D, passes with a gain of > ae 1 = Weight of D, = 8 x > = 4V 1 The next bit D, passes with a gain of 3 1 = Weight of D, = 8 « 7 = 2¥. 1 The LSB D, passes with a gain of § : 1 => Weight of LSB D, = a =1V. inputs are OV and 10V and R, = 4 kQ and R = 2kQ. Aus. 10V 10V_ 10V)R, (aos to A0¥ «tt Aiele J \4 =-| =—+-+-|-V or V, mo(tst+t+5}s 84+44+2+1)4 oie | V or Vy i 3 \s et Yoni grsy a Determine the full-scale output of a 4 — bit weight register D/A converter if theWhat are the output voltages caused by logic 1 in each bit position in a 6 -bit R -2R ladder D/A converter if the input level of 0 is OV and for 1 is 8V. Ans. V, caused by D, bit = Now N=6,V=8v Vv V, caused by MSB D,= — V, caused by MSB D, bit = = vas V, caused by MSB D, bit ==> =—= V, caused by MSB D, bit = sr=5V A eet, V, caused by MSB D, bit = >27=35= Vv V, caused by MSB D, bit= 5-5 -35=5 Determine the resolution of a 7 bit R - 2R ladder D/A converter. What is its resolution expressed in percentages ? If the full scale output voltage of this D/A converter is +10V, what is its resolution in volts ? Ans. Weight of the LSB in a 6 ~ bit converter 1 ~. Resolution of the D/A converter = heConversion % ~ 288, + A device that produces an analo analog (D/A) converter. + A device that produces a digital out digital (A/D) converter. Output from a digital input is known as digital-to- ‘put from an analog input is known as analog-to- eee ; igital-to-analog and analog-to-digital conversions are the important aspects of digital data processing. Digital-to-analog conversion involves translation of digital information into equivalent analog information. Analog-to-digital conversion involves changing an analog signal to an equivalent digital signal A/D converter is referred to as an encoding device because it is used to encode signals for entry into a digital system. D/A conversion is a straight forward process and it is easier than A/D conversion. + The accuracy and the resolution are the most important aspects of the digital-to- analog converters. The accuracy of the digital to analog converter is primarily a function of the accuracy of the precision of the voltage supply used. « The accuracy is a measure of how close the actual output voltage to the theoretical output value of output voltage. « The resolution of the digital to analog converetd is primarily a function of the number of bits in the digital input signal » The resolution defines the smallest increment in output voltage. The smallest increment in output voltage is determined by the LSB of of input. « The successive Approximation converter (SAC) is one of the most widely used analog- to-digital converters. 1. What is digital -to -analog conversion ? With a neat circuit diagram describe the operation of a weighted-resister D/A converter. 2. With a neat circuit diagram describe the operation of a 4-bit R-2R ladder D/A converter. 3. Write a note on accuracy and resolution. 4. What is analog-to-digital conversion ? With a neat block ie operation of a successive approximation converter. diagram describe theANALOG SYSTEMS AND APPLICATIONS