![Page 1: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/1.jpg)
Lecture 15: Digital to Analog Converters
Lecturers:Professor John Devlin
Mr Robert Ross
![Page 2: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/2.jpg)
Overview
• Introduction to DACs
• Types of DACs
• Applications of DACs
• Further Reading:– R.J. Tocci, Digital Systems, Principles and
Applications, Prentice Hall (Chapter 10)
![Page 3: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/3.jpg)
Interfacing with the analog world
![Page 4: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/4.jpg)
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)
![Page 5: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/5.jpg)
Digital to analog conversion
• Convert a digital value to a proportional current or voltage.
• Vref is used to set the full scale output.
![Page 6: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/6.jpg)
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
![Page 7: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/7.jpg)
DAC Specifications
• Monotonicity: Direction of change the same – input increases = output increases
Monotonic Function Non-Monotonic Function
![Page 8: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/8.jpg)
Resolution
Calculating the Resolution
12
n
fsAKResolution = Afs: Analog full scale voltage
n: Number of bits
![Page 9: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/9.jpg)
Calculations
Analog Output = K X Digital Input
12
n
fsAKResolution = Afs: Analog full scale voltage
n: Number of bits
Digital Input = Analog Output / K
![Page 10: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/10.jpg)
Types of DACs
• R-2R Ladder
• Pulse Width Modulation (PWM)
• Binary Weighted
• Thermometer coded
![Page 11: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/11.jpg)
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
![Page 12: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/12.jpg)
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)
![Page 13: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/13.jpg)
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
![Page 14: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/14.jpg)
Binary Weighted
![Page 15: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/15.jpg)
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
![Page 16: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/16.jpg)
DAC Applications
• Audio– CD Players– MP3 Players
• Video– DVD – Analog TV
• Signal Generators– Ramp Function– Sine Wave
![Page 17: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/17.jpg)
Waveform Generation
• Waveforms can be generated by supplying digital representations of the desired analog output
![Page 18: Lecture 15: Digital to Analog Converters Lecturers: Professor John Devlin Mr Robert Ross](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649eda5503460f94be9b4f/html5/thumbnails/18.jpg)
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