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 FunctionNon-Monotonic Function

Resolution Calculating the Resolution Resolution = A fs : Analog full scale voltage n: Number of bits

Calculations Analog Output = K X Digital Input Resolution = A fs : 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 >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