lecture 15: digital to analog converters lecturers: professor john devlin mr robert ross

Lecture 15: Digital to Analog Converters

Lecturers:Professor John Devlin

Mr Robert Ross

Overview

• Introduction to DACs

• Types of DACs

• Applications of DACs

• Further Reading:– R.J. Tocci, Digital Systems, Principles and

Applications, Prentice Hall (Chapter 10)

Interfacing with the analog world

Introduction DACs

• The real world is full of analog, continuous signals

• Microprocessors use digital electronics (discrete binary values) for processing

• Digital to Analog Converters (DAC or D/A) convert discrete digital numbers into continuous-like analog signals – allowing digital electronics to output real world analog signals

• DAC’s are ‘Mixed Signal Devices’ as they combine analog circuits with DSP

• Reverse of the operation of the ADC (Analog to Digital Converter)

Digital to analog conversion

• Convert a digital value to a proportional current or voltage.

• Vref is used to set the full scale output.

DAC Specifications

• Resolution: The smallest possible change that can occur in the analog output due to a change in the digital input (Step Size)

• Offset Error: Signal may be artificially offset, yet remain linear

• Linearity: How much two adjacent analog values deviate from the ideal 1LSB step

DAC Specifications

• Monotonicity: Direction of change the same – input increases = output increases

Monotonic Function Non-Monotonic Function

Resolution

Calculating the Resolution

12

n

fsAKResolution = Afs: Analog full scale voltage

n: Number of bits

Calculations

Analog Output = K X Digital Input

12

n

fsAKResolution = Afs: Analog full scale voltage

n: Number of bits

Digital Input = Analog Output / K

Types of DACs

• R-2R Ladder

• Pulse Width Modulation (PWM)

• Binary Weighted

• Thermometer coded

Pulse Width Modulation DAC

• Pulse Width Modulation (PWM)

• The duty cycle of a square wave is modulated, thereby altering the average voltage of the waveform

• Period remains constant

R-2R Ladder

• Resistor Ladders (or R-2R Ladders) is the simplest DAC

• Operates as an array of voltage dividers

• Requires one output pin for each bit of resolution

• Requires well matched resistors

• Voltage spikes at major crossings (eg. 01111->10000)

Binary Weighted

• Contains a resistor for each bit of the DAC

• Resistors are arranged in binary decades

• All resistors fed into a summing point

• Difficult to produce – with accurate resistors for each binary bit

Binary Weighted

Thermometer coded

• A resistor or current source for each possible value of the DAC Output

• 8 bit DAC would have 256 resistors

• Fast and high precision, but very expensive

DAC Applications

• Audio– CD Players– MP3 Players

• Video– DVD – Analog TV

• Signal Generators– Ramp Function– Sine Wave

Waveform Generation

• Waveforms can be generated by supplying digital representations of the desired analog output

Summary

• Digital to Analog converters allow digital electronics to output signals which are similar to real world continuous signals

• Pulse Width Modulation is a simple and widely used high resolution technique for implementing DACs