Digital to Analog Converter Nov 1 2005 Fabian

Digital to Analog Converter Nov. 1, 2005 Fabian Goericke, Keunhan Park, Geoffrey Williams 1

Outline n What is a DAC? n Types of DAC Circuits ¨ Resistor-string DAC ¨ Binary weighted DAC ¨ R-2 R Ladder DAC n Specifications of DAC n Errors n Applications 2

What is a DAC? n A digital to analog converter (DAC) is a device that converts digital numbers (binary) into an analog voltage or current output. 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 DAC 3

Analog Output Signal What is a DAC? 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 Digital Input Signal 4

Types of DAC Circuits 1. Resistor String 2. Binary Weighted Resistor 3. R-2 R Ladder 5

Resistor String DAC Components of a String DAC • Resistor String supply discrete voltage levels • Selection Switches connect the right voltage level to op-amp according to input bits • Op-amp amplifies the discrete voltage levels to desired range, keeps the current low 6

Resistor String DAC Resistor String Example 7

Resistor String DAC Selection Switches 1 1 0 6 V 1 0 0 4 V 1 1 1 7 V 0 0 0 0 V 8

Resistor String DAC Advantages: • simple • fast for < 8 bits Disadvantages: • high element count for higher resolutions, reason: number of resistors: number of switches: • slow for > 10 bits 9

Binary Weighted Resistor DAC Basic Idea: • Use a summing op -amp circuit • Use transistors to switch between high and ground • Use resistors scaled by two to divide voltage on each branch by a power of two R Rf 2 R 4 R - Vout + 2 n R 10

Binary Weighted Resistor DAC • non-inverting input on ground virtual ground at inverting input • KIRCHHOFF’s current law and no input current into op-amp I 1 + I 2 = 0 • I 1 = V 1 / R + V 2 / (2 R) + V 3 / (4 R) + … 11

Binary Weighted Resistor DAC Most significant bit Least significant bit Rf = R / 2 Vn = Vref, if bit is set Terms have less influence Vn = 0, if bit is clear 12

Binary Weighted Resistor DAC n Advantages ¨ Simple ¨ Fast n Disadvantages ¨ Needs large range of resistor values (2000: 1 for 12 bit) with high precision in low resistor values ¨ Needs very small switch resistances 13

R-2 R Resistor Ladder DAC Vref Each bit controls a switch between ground and the inverting input of the op amp. The switch is connected to ground if the corresponding bit is zero. 0 0 4 bit converter n Simplest type of DAC n Requires only two precision resistance valuce (R and 2 R) 14

R-2 R DAC Example n Convert 0001 to analog V 1 Vref V 3 V 2 V 1 V 0 = V 1 V 0 15

R-2 R DAC Example n Convert 0001 to analog R Vref V 0 2 R 16

R-2 R DAC Summary n Conversion results for each bit Digital bit Analog Conversion 0001 0010 0100 1000 n for Conversion equation for N-bit DAC 17

R-2 R DAC Summary n Advantages ¨ Only two resistor values ¨ Does not need the kind of precision as Binary weighted DACs ¨ Easy to manufacture ¨ Faster response time n Disadvantages ¨ More confusing analysis 18

Specification of DAC n Resolution n Speed n Settling time n Linearity n Reference voltage 19

Specification - Resolution n The amount of variance in output voltage for every change of the LSB in the digital input. n How closely can we approximate the desired output signal(Higher Res. = finer detail=smaller Voltage divisions) n A common DAC has a 8 - 16 bit Resolution N = Number of bits 20

Specification - Speed n Rate of conversion of a single digital input to its analog equivalent n Conversion Rate depends on ¨ clock speed of input signal ¨ settling n time of converter When the input changes rapidly, the DAC conversion speed must be high. 21

Specification – Settling Time n The time required for the input signal voltage to settle to the expected output voltage (within +/- ½ of VLSB). n Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into DAC n Fast converters reduce slew time, but usually result in longer ring time. tslew tdelay tring 22

Specification – Linearity n The difference between the desired analog output and the actual output over the full range of expected values. 23

Specification – Linearity n Ideally, a DAC should produce a linear relationship between a digital input and the analog output, this is not always the case. Desired/Approximate Output Digital Input Perfect Agreement NON-Linearity(Real World) Analog Output Voltage Linearity(Ideal Case) Desired Output Approximate output Digital Input Miss-alignment 24

Specification – Reference Voltage n A specified voltage used to determine how each digital input will be assigned to each voltage division. n Types: ¨ Non-multiplier DAC: Vref is fixed (specified by the manufacturer) ¨ Multiplier DAC: Vref is provided via an external source 25

Specification – Reference Voltage n Full Scale Voltage ¨ Defined as the output when digital input is all 1’s. 26

Errors There a multiple sources of error associated with DAC Common DAC Errors: n Gain Error n Offset Error n Full Scale Error n Non Linearity n Non-Monotonic n Resolution Errors n Settling Time and Overshoot 27

Gain Error: Deviation in the slope of the ideal curve and with respect to the actual DAC output. High Gain Desired/Ideal Output amplitude is higher than the desired output Low Gain Error: Step amplitude is lower than the desired output Analog Output Voltage High Gain Error: Step Low Gain Digital Input 28

Offset Error: Occurs when there is an offset in the output voltage in reference to the ideal output. Output Voltage Desired/Ideal Output This error may be detected when all input bits are low (i. e. 0). Positive Offset Negative Offset Digital Input 29

Full Scale Error: occurs when there is an offset in voltage form the ideal output and a deviation in slope from the ideal gain. 30

Differential Non-Linearity Analog Output Voltage Differential Non-Linearity: Voltage step size changes vary with as digital input increases. Ideally each step should be equivalent. Ideal Output 2 VLSB Diff. Non-Linearity = 2 VLSB Digital Input 31

Integral Non-Linearity Analog Output Voltage Integral Non-Linearity: Occurs when the output voltage is non linear. Basically an inability to adhere to the ideal slope. Ideal Output 1 VLSB Int. Non-Linearity = 1 VLSB Digital Input 32

Non-Monotonic Output Error Analog Output Voltage Non-Monotonic Output Error: Occurs when the an increase in digital input results in a lower output voltage. Desired Output Non-Monotonic Digital Input 33

Resolution Errors Poor Resolution(1 bit) Vout Does not accurately approximate the desired output due large voltage divisions. 2 Volt. Levels Desired Analog signal 1 0 Approximate output 0 Digital Input 34

Resolution Errors Better Resolution(3 bit) Vout Desired Analog signal 111 8 Volt. Levels Better approximation of the desired output signal due to the smaller voltage divisions. 110 101 100 011 010 001 000 Approximate output Digital Input 35

Settling Time and Overshoot Settling Time: The time required for the voltage to settle within +/the voltage associated with the VLSB. Any change in the input time will not be reflected immediately due to the lag time. Overshoot: occurs when the output voltage overshoots the desired analog output voltage. Analog Output Voltage +VLSB Expecte d -VLSB Voltage Settling time Time 36

Common Applications n Audio: Most modern audio signals are stored in digital form (for example MP 3 s and CDs) and in order to be heard through speakers they must be converted into an analog signal n Video: Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. http: //en. wikipedia. org/wiki/Digital-to-analog_converter 37

References n n n Alciatore, “Introduction to Mechatronics and Measurement Systems, ” Mc. Graw-Hill, 2003 Horowitz and Hill, “The Art of Electronics, ” Cambridge University Press, 2 nd Ed. 1995 http: //products. analog. com/products/info. asp? product=AD 7224 http: //courses. washington. edu/jbcallis/lectures/C 464_Lec 5_Sp 02. pdf http: //www. eecg. toronto. edu/~kphang/ece 1371/chap 11_slides. pd f Previous students’ lectures on DAC 38

Questions? 39