Digital to Analog Converters DAC Adam Fleming Mark

Digital to Analog Converters (DAC) Adam Fleming Mark Hunkele 3/11/2005

Outline Purpose n Types n Performance Characteristics n Applications n 2

n n To convert digital. Purpose values to analog voltages Performs inverse operation of the Analog-to. Digital Converter (ADC) n Reference Voltage Digital Value DAC Analog Voltage 3

DACs n Types ¨ Binary Weighted Resistor ¨ R-2 R Ladder ¨ Multiplier DAC n The reference voltage is constant and is set by the manufacturer. ¨ Non-Multiplier DAC n The reference voltage can be changed during operation. n Characteristics ¨ Comprised of switches, op-amps, and resistors ¨ Provides resistance inversely proportion to significance of bit 4

Binary Weighted Resistor Rf = R R 2 R 4 R Vo 8 R MSB LSB -VREF 5

Binary Representation Rf = R Most Significant Bit R 2 R 4 R Vo 8 R Least Significant Bit -VREF 6

Binary Representation SET CLEARED Most Significant Bit Least Significant Bit -VREF ( 1 1 )2 = ( 15 )10 7

Binary Weighted Resistor n n “Weighted Resistors” based on bit Reduces current by a factor of 2 for each bit Rf = R R 2 R 4 R Vo 8 R MSB LSB -VREF 8

Binary Weighted Resistor n Result: ¨ Bi = Value of Bit i 9

Binary Weighted Resistor n More Generally: ¨ Bi = Value of Bit i ¨ n = Number of Bits 10

R-2 R Ladder VREF MSB LSB 11

R-2 R Ladder Same input switch setup as Binary Weighted Resistor DAC n All bits pass through resistance of 2 R n MSB VREF LSB 12

R-2 R Ladder n n The less significant the bit, the more resistors the signal muss pass through before reaching the op-amp The current is divided by a factor of 2 at each node LSB MSB 13

R-2 R Ladder n n The current is divided by a factor of 2 at each node Analysis for current from (001)2 shown below R R VREF 2 R R B 1 2 R R B 2 2 R 2 R Op-Amp input “Ground” B 0 14

R-2 R Ladder n Result: ¨ Bi = Value of Bit i Rf 15

R-2 R Ladder n If Rf = 6 R, VOUT is same as Binary Weighted: ¨ Bi = Value of Bit i 16

R-2 R Ladder n R Example: ¨ Input = (101)2 ¨ VREF = 10 V ¨R = 2 Ω ¨ Rf = 2 R R VREF B 0 B 2 2 R 2 R Op-Amp input “Ground” 17

Pros & Cons Binary Weighted R-2 R Pros Easily understood Only 2 resistor values Easier implementation Easier to manufacture Faster response time Cons Limited to ~ 8 bits Large # of resistors Susceptible to noise Expensive Greater Error More confusing analysis 18

Digital to Analog Converters ¨ Performance ¨ Common Specifications Applications Presented by: Mark Hunkele 19

Digital to Analog Converters -Performance Specifications Resolution n Reference Voltages n Settling Time n Linearity n Speed n Errors n 20

Digital to Analog Converters -Performance Specifications -Resolution: is the amount of variance in output voltage for every change of the LSB in the digital input. n How closely can we approximate the desired output signal(Higher Res. = finer detail=smaller Voltage divisions) n A common DAC has a 8 - 12 bit Resolution n N = Number of bits 21

Digital to Analog Converters -Performance Specifications -Resolution Better Resolution(3 bit) Poor Resolution(1 bit) Vout Desired Analog signal 1 0 Approximate output 110 8 Volt. Levels 2 Volt. Levels 111 0 Digital Input 101 100 011 010 001 110 101 100 011 010 001 000 Approximate output Digital Input 22

Digital to Analog Converters -Performance Specifications -Reference Voltage: A specified voltage used to determine how each digital input will be assigned to each voltage division. n Types: n ¨ Non-multiplier: internal, fixed, and defined by manufacturer ¨ Multiplier: external, variable, user specified 23

Digital to Analog Converters -Performance Specifications -Reference Voltage Multiplier: (Vref = Asin(wt)) Non-Multiplier: (Vref = C) Voltage 11 11 10 10 10 01 01 0 0 00 00 Digital Input 00 Assume 2 bit DAC 00 Digital Input 24

Digital to Analog Converters -Performance Specifications -Settling Time: The time required for the input signal voltage to settle to the expected output voltage(within +/- VLSB). n Any change in the input state will not be reflected in the output state immediately. There is a time lag, between the two events. n 25

Digital to Analog Converters -Performance Specifications -Settling Time Analog Output Voltage Expected Voltage +VLSB -VLSB Settling time Time 26

Digital to Analog Converters -Performance Specifications -Linearity: is the difference between the desired analog output and the actual output over the full range of expected values. n Ideally, a DAC should produce a linear relationship between a digital input and the analog output, this is not always the case. n 27

Digital to Analog Converters -Performance Specifications -Linearity Desired/Approximate Output Digital Input Perfect Agreement NON-Linearity(Real World) Analog Output Voltage Linearity(Ideal Case) Desired Output Approximate output Digital Input Miss-alignment 28

Digital to Analog Converters -Performance Specifications -Speed: Rate of conversion of a single digital input to its analog equivalent n Conversion Rate n ¨ Depends on clock speed of input signal ¨ Depends on settling time of converter 29

Digital to Analog Converters -Performance Specifications -Errors n Non-linearity ¨ Differential ¨ Integral Gain n Offset n Non-monotonicity n 30

Digital to Analog Converters -Performance Specifications -Errors: Differential Non-Linearity: Difference in voltage step size from the previous DAC output (Ideally All DLN’s = 1 VLSB) Analog Output Voltage n Ideal Output 2 VLSB Diff. Non-Linearity = 2 VLSB Digital Input 31

Digital to Analog Converters -Performance Specifications -Errors: Integral Non-Linearity: Deviation of the actual DAC output from the ideal (Ideally all INL’s = 0) Analog Output Voltage n Ideal Output Int. Non-Linearity = 1 VLSB Digital Input 32

Digital to Analog Converters -Performance Specifications -Errors: Gain n Gain Error: Difference in slope of the ideal curve and the actual DAC output High Gain Desired/Ideal Output slope greater than ideal Low Gain Error: Actual slope less than ideal Analog Output Voltage High Gain Error: Actual Low Gain Digital Input 33

Digital to Analog Converters -Performance Specifications n -Errors: Offset Error: A constant voltage difference between the ideal DAC output and the actual. ¨ The voltage axis intercept of the DAC output curve is different than the ideal. Output Voltage Desired/Ideal Output Positive Offset Negative Offset Digital Input 34

Digital to Analog Converters -Performance Specifications -Errors: Non-Monotonicity Non-Monotonic: A decrease in output voltage with an increase in the digital input Analog Output Voltage n Desired Output Non-Monotonic Digital Input 35

Digital to Analog Converters -Common Applications Generic use n Circuit Components n Digital Audio n Function Generators/Oscilloscopes n Motor Controllers n 36

Digital to Analog Converters -Common Applications -Generic Used when a continuous analog signal is required. n Signal from DAC can be smoothed by a Low pass filter n Digital Input Piece-wise Continuous Output 0 bit 01101001010100101 10101011111100101 00001010111110011 01010101010 1110101111000 100101010001111 n bit DAC Analog Continuous Output Filter nth bit 37

Digital to Analog Converters -Common Applications -Circuit Components n Voltage controlled Amplifier ¨ digital n input, External Reference Voltage as control Digitally operated attenuator ¨ External n Reference Voltage as input, digital control Programmable Filters ¨ Digitally controlled cutoff frequencies 38

Digital to Analog Converters -Common Applications -Digital Audio CD Players n MP 3 Players n Digital Telephone/Answering Machines n 1 2 1. http: //electronics. howstuffworks. com/cd. htm 2. http: //accessories. us. dell. com/sna. aspx? c=us&cs=19&l=en&s=dhs&~topic=odg_dj 3. http: //www. toshiba. com/taistsd/pages/prd_dtc_digphones. html 3 39

Digital to Analog Converters -Common Applications -Function Generators n Digital Oscilloscopes n ¨ Digital Input ¨ Analog Ouput 1 Signal Generators Sine wave generation ¨ Square wave generation ¨ Triangle wave generation ¨ Random noise generation ¨ 2 1. http: //www. electrorent. com/products/search/General_Purpose_Oscilloscopes. html 2. http: //www. bkprecision. com/power_supplies_supply_generators. htm 40

Digital to Analog Converters -Common Applications -Motor Controllers Cruise Control n Valve Control n Motor Control n 1 2 1. http: //auto. howstuffworks. com/cruise-control. htm 2. http: //www. emersonprocess. com/fisher/products/fieldvue/dvc/ 3. http: //www. thermionics. com/smc. htm 3 41

References n n n Cogdell, J. R. Foundations of Electrical Engineering. 2 nd ed. Upper Saddle River, NJ: Prentice Hall, 1996. “Simplified DAC/ADC Lecture Notes, ” http: //www-personal. engin. umd. umich. edu/ ~fmeral/ELECTRONICS II/Electronic. II. html “Digital-Analog Conversion, ” http: //www. allaboutcircuits. com. Barton, Kim, and Neel. “Digital to Analog Converters. ” Lecture, March 21, 2001. http: //www. me. gatech. edu/charles. ume/me 4447 Spring 01/Class. Notes/dac. ppt. Chacko, Deliou, Holst, “ME 6465 DAC Lecture” Lecture, 10/ 23/2003, http: //www. me. gatech. edu/mechatronics_course/ Lee, Jeelani, Beckwith, “Digital to Analog Converter” Lecture, Spring 2004, http: //www. me. gatech. edu/mechatronics_course/ 42