ECEN 301Discussion #24 – DAC1 Conversion Luke 22:32 32 But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren.

ECEN 301Discussion #24 – DAC2 Lecture 24 – Digital to Analog Converters (DACs)

ECEN 301Discussion #24 – DAC3 ADC/DAC Power coming from the wall is analog, but most devices (appliances, computers, etc.) are digital thus there must be a conversion Analog to digital (ADC) – coming into a device Digital to analog (DAC) – going out of a device Device ADCDAC Digital Analog Actuator Sensor

ECEN 301Discussion #24 – DAC4 ADC/DAC ADCDAC Digital Analog … … Power coming from the wall is analog, but most devices (appliances, computers, etc.) are digital thus there must be a conversion Analog to digital (ADC) – coming into a device Digital to analog (DAC) – going out of a device

ECEN 301Discussion #24 – DAC5 Digital to Analog Converter (DAC) DAC: converts a binary word to an analog output voltage or current Word length (n): the number of bits in the sequence of 1s and 0s representing an output EX: 0110 – 4-bit word length – 6-bit word length Binary word (B): a sequence of n 1s and 0s B = b n-1 b n-2 …b 2 b 1 b 0 EX: B = (n = 8)

ECEN 301Discussion #24 – DAC6 Digital to Analog Converter (DAC) DAC: converts a binary word to an analog output voltage or current Resolution δv: minimum step size by which the output voltage (or current) can increment Output voltage v a : the analog value represented by the binary word B EX: let n=4 v a = (2 3 ·b ·b ·b ·b 0 )δv Max output voltage v aMax : the maximum analog value EX: let n=4 v aMax = ( )δv = (2 n – 1) δv Example: δv = 1V, B = (n = 5) Find v aMax and v a v aMax = (2 n – 1) δv = (2 5 – 1) ∙ 1 = 31 v a = (2 4 ·b ·b ·b ·b ·b 0 )δv = (16 ·1 + 8·0 + 4·1 + 2·1 + 1·0) · 1 = ( ) = 22

ECEN 301Discussion #24 – DAC7 Digital to Analog Converter (DAC) Building a DAC: use a summing amplifier – + +vo–+vo– +–+– +–+– +–+– R Sn R S2 R S1 v Sn v S2 v S1 RFRF – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0 Summing amplifierDAC

ECEN 301Discussion #24 – DAC8 Digital to Analog Converter (DAC) Building a DAC: the analog output (v a ) is proportional to the binary word B – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0 Choose THUS v si in summing amplifier

ECEN 301Discussion #24 – DAC9 Digital to Analog Converter (DAC) Example1: v in = 5V, B = 1011, R 0 = 32kΩ, R F = 64kΩ Find R n and v a – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC10 Digital to Analog Converter (DAC) Example1: v in = 5V, B = 1011, R 0 = 32kΩ, R F = 64kΩ Find R n and v a – + +va–+va– R1R1 R2R2 R3R3 RFRF R0R0 5 V b 3 = 1 b 2 = 0 b 1 = 1 b 0 = 1

ECEN 301Discussion #24 – DAC11 Digital to Analog Converter (DAC) Building a DAC: the analog output (v a ) has a step-like appearance because of the discrete nature of a binary signal The resolution (coarseness of the “staircase”) can be adjusted by changing the word length (the number of bits) Approximated using 2-bits Approximated using 3-bits δvδv δvδv

ECEN 301Discussion #24 – DAC12 Digital to Analog Converter (DAC) Example2: find the smallest resolution δv of an 8-bit DAC v aMax = 12V – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC13 Digital to Analog Converter (DAC) Example2: find the smallest resolution δv of an 8-bit DAC v aMax = 12V – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC14 Digital to Analog Converter (DAC) Example3: find an expression for the number of bits required in a DAC for a given range and resolution range = v aMax – v aMin resolution = δv – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC15 Digital to Analog Converter (DAC) Example3: find an expression for the number of bits required in a DAC for a given range and resolution range = v aMax – v aMin resolution = δv – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC16 Digital to Analog Converter (DAC) Example4: find the number of bits required in a DAC given that: range = 10V resolution = 10 mV – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC17 Digital to Analog Converter (DAC) Example4: find the number of bits required in a DAC given that: range = 10V resolution = 10 mV – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC18 Digital to Analog Converter (DAC) Example5: find the resistor values for a DAC with: range = 15V δv = 1V v in = 5V R F = 2kΩ – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC19 Digital to Analog Converter (DAC) Example5: find the resistor values for a DAC with: range = 15V δv = 1V v in = 5V R F = 2kΩ – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC20 Digital to Analog Converter (DAC) Example5: find the resistor values for a DAC with: range = 15V δv = 1V v in = 5V R F = 2kΩ – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0

ECEN 301Discussion #24 – DAC21 Digital to Analog Converter (DAC) Example5: find the resistor values for a DAC with: range = 15V δv = 1V v in = 5V R F = 2kΩ – + +va–+va– R1R1 R n-2 R n-1 RFRF R0R0 v in b n-1 b n-2 b1b1 b0b0