Digital to Analog Converters Andrew Gardner Muhammad Salman David Fernandes Jevawn Roberts Introduction to Mechatronics Student Lecture – 10/23/06

Outline What is a DAC? Different Types of DACs Binary Weighted Resistor R-2R Ladder Specifications Commonly used DACs Application Introduction to Mechatronics Student Lecture – 10/23/06

Introduction A DAC is a Digital to Analog converter. It converts a binary digital number into an analog representation, most commonly voltage though current is also used sometimes. 1001 0101 0011 0111 1001 1010 1011 DAC Introduction to Mechatronics Student Lecture – 10/23/06

Introduction Each binary number sampled by the DAC corresponds to a different output level. Digital Input Signal Analog Output Signal Introduction to Mechatronics Student Lecture – 10/23/06

Ideally Sampled Signal Typical Output DACs capture and hold a number, convert it to a physical signal, and hold that value for a given sample interval. This is known as a zero-order hold and results in a piecewise constant output. Output typical of a real, practical DAC due to sample & hold Ideally Sampled Signal DAC Introduction to Mechatronics Student Lecture – 10/23/06

Binary Weighted Resistor DAC Utilizes a summing op-amp circuit Weighted resistors are used to distinguish each bit from the most significant to the least significant Transistors are used to switch between Vref and ground (bit high or low) Introduction to Mechatronics Student Lecture – 10/23/06

Summing OP-Amps Inverting summer circuit used in Binary Weighted Resistor DAC. V(out) is 180° out of phase from V(in) Introduction to Mechatronics Student Lecture – 10/23/06

Binary Weighted Input DAC - + R 2R 4R 2n-1R Rf Vout Vref V1 V2 V3 Vn Ideal Op-amp No current into op-amp Virtual ground at inverting input Vout= -IRf I - + R 2R 4R 2n-1R Rf Vout Vref V1 V2 V3 Vn MSB LSB Introduction to Mechatronics Student Lecture – 10/23/06

Calculation Introduction to Mechatronics Student Lecture – 10/23/06

Cont’d Example: n = totalbits Introduction to Mechatronics Student Lecture – 10/23/06

Advantages and Disadvantages Easy principle/construction Fast conversion Disadvantages Requirement of several different precise input resistor values: Requires large range of resistors (2048:1 for 12-bit DAC) with necessary high precision for low resistors one unique value per binary input bit. (High bit DACs) Larger resistors ~ more error. Precise large resistors – expensive. Introduction to Mechatronics Student Lecture – 10/23/06

R-2R Resistor Ladder DAC Vref MSB LSB Bit: 0 0 0 0 Vout 4-Bit Converter Introduction to Mechatronics Student Lecture – 10/23/06

R-2R DAC Example Convert 0001 to analog V2 V1 V0 Vref Introduction to Mechatronics Student Lecture – 10/23/06

R-2R DAC Example (cont.) = Nodal Analysis Likewise, Voltage Divider V1 Introduction to Mechatronics Student Lecture – 10/23/06

Conversion Equation For a 4-Bit R-2R Ladder For general n-Bit R-2R Ladder Binary Weighted Resister DAC Introduction to Mechatronics Student Lecture – 10/23/06

R-2R DAC Summary Advantages Disadvantages Only two resistor values Does not need as precision resistors as Binary weighted DACs Cheap and Easy to manufacture Disadvantages Slower conversion rate Introduction to Mechatronics Student Lecture – 10/23/06

DAC Specification Resolution Reference Voltage Speed Settling Time Linearity Introduction to Mechatronics Student Lecture – 10/23/06

Resolution The change in output voltage for a change of the LSB. Related to the size of the binary representation of the voltage. (8-bit) Higher resolution results in smaller steps between voltage values Introduction to Mechatronics Student Lecture – 10/23/06

Reference Voltage Multiplier DAC Reference voltage is a constant set by the manufacturer Non-Multiplier DAC Reference voltage is variable Full scale Voltage Slightly less than the reference voltage (Vref-VLSB) Introduction to Mechatronics Student Lecture – 10/23/06

Speed Also called the conversion rate or sampling rate rate at which the register value is updated For sampling rates of over 1 MHz a DAC is designated as high speed. Speed is limited by the clock speed of the microcontroller and the settling time of the DAC Introduction to Mechatronics Student Lecture – 10/23/06

Settling Time Time in which the DAC output settles at the desired value ± ½ VLSB. Faster DACs decrease the settling time Introduction to Mechatronics Student Lecture – 10/23/06

Linearity Represents the relationship between digital values and analog outputs. Should be related by a single proportionality constant. (constant slope) Introduction to Mechatronics Student Lecture – 10/23/06

DAC Error Non-Linearity Differential Integral Gain Error Offset Error Monotonicity Resolution Introduction to Mechatronics Student Lecture – 10/23/06

Non-linearity Deviation from a linear relationship between digital input and analog output. Analog Output Voltage Digital Input Desired Output Introduction to Mechatronics Student Lecture – 10/23/06

Non-Linearity Differential Worst case deviation from the ideal VLSB step for an increment of LSB Integral Worst case deviation from the line between the endpoint (zero and full scale) voltages Digital Input Analog Output Voltage VLSB 2VLSB Digital Input Analog Output Voltage Integral Non-linearity Introduction to Mechatronics Student Lecture – 10/23/06

Gain Error Also called Full-Scale Error Deviation from the ideal full scale voltage due to a higher or lower gain than expected. High Gain Desired/Ideal Output Analog Output Voltage Low Gain Introduction to Mechatronics Student Lecture – 10/23/06 Digital Input

Offset Error Also called Zero Error Difference between ideal voltage output and actual voltage output for a digital input of zero. Digital Input Ideal Output Output Voltage Introduction to Mechatronics Student Lecture – 10/23/06

Monotonicity Increases or decreases of the digital value must correspond to increases or decreases of the voltage output. Analog Output Voltage Digital Input Desired Output Non-monotonic behavior Introduction to Mechatronics Student Lecture – 10/23/06

Resolution Error For matching curves over time or simply outputting accurate values a proper resolution must be selected Resolution must be high enough for the desired precision (½ VLSB) Vout Desired Analog signal 11 10 01 00 Introduction to Mechatronics Student Lecture – 10/23/06 Time

Applications – Audio Many audio signals are stored as binary numbers (on media such as CDs and in computer files such as MP3s). Therefore computer sound cards, stereo systems, digital cell phones, and portable music players contain DAC to convert the digital representation to an analog signal. Introduction to Mechatronics Student Lecture – 10/23/06

Example DAC AD 7224 – Manufactured by Analog Devices Type: R-2R Voltage Output Reference voltage: Non-Multiplier 2 – 12.5 Volts 8-bit Input Settling Time: 7 μs Cost: about $4.00 Introduction to Mechatronics Student Lecture – 10/23/06

Example DAC 18 Pin integrated circuit including output amplifier Introduction to Mechatronics Student Lecture – 10/23/06

Applications – Video Video signals from digital sources, such as a computer or DVD must be converted to analog signals before being displayed on an analog monitor. Beginning on February 18th, 2009 all television broadcasts in the United States will be in a digital format, requiring ATSC tuners (either internal or set-top box) to convert the signal to analog. Introduction to Mechatronics Student Lecture – 10/23/06

References Previous Student Lectures http://en.wikipedia.org/ http://allaboutcircuits.com Introduction to Mechatronics Student Lecture – 10/23/06

Questions Introduction to Mechatronics Student Lecture – 10/23/06