Digital to Analog Converters (DAC) 15 March 2006 Doug Hinckley Lee Huynh Dooroo Kim

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1 Digital to Analog Converters (DAC) 5 March 006 Doug Hinckley Lee Huynh Dooroo Kim

2 What is a DAC? A digital to analog converter (DAC) converts a digital signal to an analog voltage or current output. 000 DAC

3 Analog Output Signal What is a DAC? Digital Input Signal

4 Types of DACs Many types of DACs available. Usually switches, resistors, and opamps used to implement conversion Two Types: Binary Weighted Resistor R-R Ladder

5 Binary Weighted Resistor 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 ref and ground (bit high or low)

6 Binary Weighted Resistor Assume Ideal Op-amp ref No current into op-amp R R I Rf irtual ground at inverting input 4R - + out out = -IR f n R

7 Binary Weighted Resistor oltages through n are either ref if corresponding bit is high or ground if corresponding bit is low ref R R I Rf is most significant bit n is least significant bit 3 4R - + out n n- R MSB 3 n out IRf Rf n- R R 4R R LSB

8 Binary Weighted Resistor If R f =R/ out IR f 4 8 For example, a 4-Bit converter yields out ref b 3 b 4 3 b 8 b 0 n n 6 Where b 3 corresponds to Bit-3, b to Bit-, etc.

9 Binary Weighted Resistor Advantages Simple Construction/Analysis Fast Conversion Disadvantages Requires large range of resistors (000: for -bit DAC) with necessary high precision for low resistors Requires low switch resistances in transistors Can be expensive. Therefore, usually limited to 8-bit resolution.

10 R-R Ladder ref Each bit corresponds to a switch: Bit: Bit Converter out If the bit is high, the corresponding switch is connected to the inverting input of the op-amp. If the bit is low, the corresponding switch is connected to ground.

11 R-R Ladder 3 ref 3 Ideal Op-amp R R R eq R R R R R

12 R-R Ladder ref 3 3 R R I 3 Likewise, R R R out out ref IR

13 R-R Ladder Results: ref ref, 4 ref, ref out R b 3 ref R b ref 4R b ref 8R b 0 ref 6R Where b 3 corresponds to bit 3, b to bit, etc. out If bit n is set, b n = If bit n is clear, b n =0

14 R-R Ladder For a 4-Bit R-R Ladder out ref b 3 b 4 b 8 b 0 6 For general n-bit R-R Ladder or Binary Weighted Resister DAC out ref n b n i i i

15 R-R Ladder Advantages Only two resistor values (R and R) Does not require high precision resistors Disadvantage Lower conversion speed than binary weighted DAC

16 Specifications of DACs Resolution Speed Linearity Settling Time Reference oltages Errors

17 Resolution Smallest analog increment corresponding to LSB change An N-bit resolution can resolve N distinct analog levels Common DAC has a 8-6 bit resolution ref Resolution LSB N where N numberof bits

18 Speed Rate of conversion of a single digital input to its analog equivalent Conversion rate depends on clock speed of input signal settling time of converter When the input changes rapidly, the DAC conversion speed must be high.

19 Analog Output Signal Linearity The difference between the desired analog output and the actual output over the full range of expected values Digital Input Signal

20 Analog Output Signal Analog Output Signal Linearity Ideally, a DAC should produce a linear relationship between the digital input and analog output Linearity (Ideal) Non-Linearity Digital Input Signal Digital Input Signal

21 Settling Time Time required for the output signal to settle within +/- ½ LSB of its final value after a given change in input scale Limited by slew rate of output amplifier Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into DAC

22 Reference oltages Used to determine how each digital input will be assigned to each voltage division Types: Non-multiplier DAC: ref is fixed Multiplier DAC: ref provided by external source

23 Types of Errors Associated with DACs Gain Offset Full Scale Resolution Non-Linearity Non-Monotonic Settling Time and Overshoot

24 Analog Output Gain Error Occurs when the slope of the actual output deviates from the ideal output Digital Input Ideal Output Positive Offset Errorr Negative Offset Error

25 Analog Output Offset Error Occurs when there is a constant offset between the actual output and the ideal output Digital Input Ideal Output Positive Offset Errorr Negative Offset Error

26 Analog Output Full Scale Error Occurs when the actual signal has both gain and offset errors Digital Input Ideal Output Full Scale Error Error

27 Resolution Error Poor representation of ideal output due to poor resolution Size of voltage divisions affect the resolution

28 Non-Linearity Error Occurs when analog output of signal is non-linear Two Types Differential analog step-sizes changes with increasing digital input (measure of largest deviation; between successive bits Integral amount of deviation from a straight line after offset and gain errors removed; on concurrent bits

29 Non-Linearity Error, cont.

30 Non-Monotonic Error Occurs when an increase in digital input results in a decrease in the analog output

31 Settling Time and Overshoot Error Settling Time time required for the output to fall with in +/- ½ LSB Overshoot occurs when analog output overshoots the ideal output Analog Output Ideal Output -/* LSB +/* LSB Settling Time Time

32 Applications Digital Motor Control Computer Printers Sound Equipment (e.g. CD/MP3 Players, etc.) Electronic Cruise Control Digital Thermostat

33 References Callis, J. B. The Digital to Analog Converter c5_sp-0.pdf. 4 March 006 DAC March 006. Johns, David and Ken Martin. Data Converter Fundamentals _slides.pdf. 4 March 006 Goericke, Fabian, Keunhan Park and Geoffrey Williams. Digital to Analog Converter ppt. 4 March 006

34 QUESTIONS?

A-D and D-A Converters

Chapter 5 A-D and D-A Converters (No mathematical derivations) 04 Hours 08 Marks When digital devices are to be interfaced with analog devices (or vice a versa), Digital to Analog converter and Analog