Digital to Analog Converter

Transcription

1 Digital to Analog Converter Jungchul Lee Kamran Jeelani Jonathan Beckwith Topics of Discussion What is a DAC? Types of DAC Circuits esistorstring DAC NBit Binary weighted DAC Ladder DAC Specifications of DAC Applications

2 What is a DAC? DigitaltoAnalog Converter: An electronic device, often an integrated circuit, that converts a digital number into a corresponding analog voltage or current. elation between analog signal and digital equivalent a n i = bi i= V 2 AD conversion V a > b i (encoder) ex) Transducer interface DA conversion b i > V a (decoder) ex) motor, heater control V ref DAC configurations Assume the analog signal is a voltage D N, D N2 D, D Nbit digital word Analog voltage signal V ef V Out DAC =V ref *D/2 N V Out

3 Types of DAC Circuits. esistorstring 2. NBit Binary Weighted esistor 3. Ladder V ef A esistorstring DAC Example of 3 bit resistorstring DAC equired component a resistor string a set of switches select output to use opamp buffer V o V b N i = Vef i i= 2 B 2 B B

4 esistor String DAC Example How many resistors and switches would be required to implement an 8 bit resistorstring DAC? Ans) # of resistors = 2 N =2 8 =256 N i 8 # of switches = 2 = 2 = 255 i= Impractical for converters with more than a few bits of resolution NBit Binary Weighted esistor /2 MSB I i 4 V out 2 ( i ) 5 3 I N b = V i= LSB 2 2^(N) V = I f V ef

5 Nbit binary weighted Example Find output voltage, current, and resolution for a binary weighted resistor DAC of 4 bits given condition = kω, f = 5 kω, V = V Applied binary word is Example Solutions f=/2 5 kω Vout? 8 4 kω Bit 3 2 Bit 2 Bit 3 Bit binary input V V

6 Example Solutions (Cont.) Ans) I V = Ω =.25 A V = fi = (5 Ω ) (.25A) = 5.625V Vef V esolution = LSB= = =.625V n Example Solutions (Cont.) D N, D N2 D, D V ef VOut DAC =V ref *D/2 N V Out Binary Word input = 2 = 9 # of input combination : 2 4 =6 V out = V ref * D/2 N = *9/6 =5.625 V

7 Limitations of the Binary Weighted DAC. If = kω, 8 bits DAC, and V ef = V 8 = 2 8 *( kω) = 28 kω I 8 = V ef / 8 =V/28 kω = 7.8 µa Opamps that can handle those currents are rare and expensive. 2. If = Ω and V ef = V = 2 *( Ω) = Ω I = V ef / = V/ Ω = A This current is more than a typical opamp can handle. esistor Ladder DAC Vs Bit 3 Bit 2 Bit Bit Vout Simplest type of DAC equires only two precision resistance value ( and )

8 esistor Ladder DAC Vs V3 V2 V V Bit 3 Bit 2 Bit Bit 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 = Vout 4 Bit Converter DAC Example Ex. Convert to analog Vs V3 V2 V V Switch for bit is connected to op amp input. All other switches connected to ground Bit 3 Bit 2 Bit Bit Digital Value: O O O Vout

9 DAC Example (cont.) Vs V3 V2 V V Find Equivalent esistance Bit 3 Bit 2 Bit Bit Noninverting input is connected to ground. Therefore, inverting input is at virtual ground Vout DAC Example (cont.) Vs V3 V2 V V V Bit 3 Bit 2 Bit Bit Bit Vout eq = // = Apply voltage division: V = V x eq V = ½ V (eq)

10 DAC Example (cont.) Vs V3 V2 V V We have shown that V = ½ V Bit 3 Bit 2 Bit Bit Similarly, It can be proven that : Vout V = ½ V 2 AND V 2 = ½ V 3 Therefore: V = /8 V 3 = /8 V s DAC Example (cont.) Vs V3 V2 V V Bit 3 Bit 2 Bit Bit Vout V is the input to the inverting amplifier circuit, which has a gain of: Av = / = /2 Therefore, the analog output voltage corresponding to the binary input is: Vout = Av (V ) = (/2)(/8*Vs) Vout = /6 Vs

11 DAC Example (cont.) We have shown that the analog output voltage for the digital input is: Similarly, it can be show that: V out = /6 Vs For input = : For input = : For input = : V out = /8 Vs V out2 = /4 Vs V out3 = /2 Vs The output for any combination of bits comprising the input binary number can now be found using the principle of superposition: V out = b 3 V out3 b 2 V out2 b V out b V out General DAC Characteristics There are six key parameters you should consider when choosing a DAC. eference Voltage esolution Linearity Speed Settling Time Error

12 eference Voltage To a large extent, the characteristics of a DAC are defined by its reference voltage. Nonmultiplier DAC: V ref is fixed (specified by the manufacturer) Multiplier DAC: V ref is provided via an external source Full Scale Voltage Defined as the output when the digital input word is all s. N 2 V fs = V ref N 2

13 esolution esolution is a measure of precision, not accuracy. It is defined as the voltage change corresponding to changing the LSB. Many options in the 86 bit range, with 2 bits being a typical cost / resolution trade off. More bits More steps Greater esolution esolution = V LSB = V ef / 2 N *where N is the number of bits Linearity Ideally, a DAC will produce a linear relationship between a binary word and analog output Voltage output Digital Input Signal (3bit)

14 Speed Usually specified as conversion or sampling rate. High speed DACs are typically defined as >MS/s (Mhz) Some current 26 bit DACs can reach the GHz range Conversion of input signal is limited by Clock speed of the input signal Settling time of the DAC Settling Time Ideally, an instantaneous change in analog voltage would occur when a new binary word enters into a DAC. Settling time is the time taken by the DAC to reach ½ of the LSB of its new voltage. Components include delay, slew time, and ring time. Fast converters reduce slew time, but usually result in longer ring times. Delay time is normally a small term.

15 Settling Time (cont.) Cause of Delay Time, Settling Time, and ing Time esistor Ladder DAC Vs Bit 3 Bit 2 Bit Bit Delay time is caused by the time it takes to change these switches based on input bits. Settling time and ing time is determined by the opamp s slew rate Vout

16 Possible Error Because we do not live in an ideal world, considerations for possible error should be made. NonLinearity Integral Differential Non Monotonicity Offset Error Gain Error Integral Nonlinearity Defined as the deviation of a DAC's transfer function from a straight line. The straight line can be a best approximation to the actual transfer function, or a line drawn between the transfer function's end points (after subtracting the gain and offset errors

17 Differential NonLinearity The difference between an actual step height and the ideal value of LSB. Should be less than or equal to one to insure monotonicity. NonMonotonicity A monotonic DAC yields an increase in output as input increases. If a differential nonlinearity of greater than LSB occurs, increasing the digital input may actually result in a decreased output Analog Output LSB.75LSB Digital Input

18 Gain Error Defined as the difference between the ideal max output voltage and the actual max output voltage (after subtracting offset error). Changes the slope of the output, thereby creating the same percentage error for each step. Expressed in mv as a percentage of the maximum output. Offset Error The offset error equals the analog output when the digital signal is zero. Typically defined in absolute millivolts with (mv being acceptable).

19 Cause of NonLinearity, Gain error, and Offset error esistor Ladder DAC Vs Nonlinearity is caused by the resistors. esistors in D/A converters need to be matched but manufacturing exact resistors is difficult. Bit 3 Bit 2 Bit Bit Vout Gain Error and Offset Error is caused by opamp and or opamp s feedback resistor DAC Applications DAC s can be found in any device that interfac es digital and analog circuitry Analog Displays Digital Control Systems Digital Audio Communications Countless other applications

20 eferences DigitalAnalog Converters Are a "Bit" Analog Maxim Semiconductors ( Component and Measurement Advances Ensure 6Bit DAC Settling Time Jim Williams, Linear Technology July 998 Introduction to Mechatronics and Measurement systems David G. Alciatore and Michael B. Histand, McGrawHill MechatronicsElectronic control systems in mechanical and electrical engineeringw. Bolton, Longman Introduction to Electronic Circuit Designichard. Spencer and Mohammed S. Ghausi, PrenticeHall Questions??