Digital to Analog Converter - gatech.edu

1 1 Digital to Analog ConverterJungchul LeeKamran JeelaniJonathan BeckwithTopics of Discussion What is a DAC? Types of DAC Circuits Resistor-string DAC N-Bit Binary weighted DAC R-2R Ladder DAC Specifications of DAC Applications2 What is a DAC? Digital -to- Analog Converter : An electronic device, oftenan integrated circuit, that converts a Digital number into a corresponding Analog voltage or current. Relation between Analog signal and Digital equivalentnareiifi1V2bV == AD conversion Va-> bi(encoder) ex) Transducer interface DA conversion bi-> Va(decoder) ex) motor, heater controlDAC configurations Assume the Analog signal is a voltageN-bit Digital wordAnalog voltage , , D0 VRefVOutVOut=Vref*D/2N3 Types of DAC Circuits1. Resistor-string 2. N-Bit Binary Weighted Resistor3. R-2R LadderA Resistor-string DACN1i0 Refi1i0bVV2 +== Example of 3 bit resistor-string DACR equired component- a resistor string- a set of switches select output to use- opamp buffer RR10 RRV RefRRRR101010101010B2B1B0Vo4 Resistor String DAC Example How many resistors and switches would be required to implement an 8 bit resistor-string DAC?

2 Ans)# of resistors = 2N=28=256# of switches = Impracticalfor converters with more than a few bits of resolutionN1i8i0221255 == = N-Bit Binary Weighted ResistorR/2 LSB+-V out21453122R12RV Ref128R12 MSB4R2^(N-1) ()Ni0Ri1i1bIV2R == 0f0V = -RI5N-bit binary weighted Example Find output voltage, current, and resolution for a binary weighted resistor DAC of 4 bits- given conditionR = 10 k , Rf= 5 k , VR= -10 VApplied binary word is 10012 RRf=R/2R0 Bit213+-Vout214533 Bit213 RVR4R1 Bit2138R2 Bit213 Example Solutions1 0 0 1 binary input-10 V? 5 k 10 k 6 Example Solutions (Cont.)00414243430f0 Refn410 V1001I210210210210 AV R I(5 10) ( ) = LSB= =+++ = = = ===Ans)Example Solutions (Cont.) Binary Word input = 10012= 910 # of input combination : 24=16 Vout= Vref* D/2N = 10*9/16 = , , D0 VRefVOutVOut=Vref*D/2N7 Limitations of the Binary Weighted DAC 1.

3 If R = 10 k , 8 bits DAC, and VRef= 10 VR8= 28-1*(10 k ) = 1280 k I8= VRef/R8=10V/1280 k = AOp-amps that can handle those currents are rare and If R = 10 and VRef= 10 VR1= 21-1*(10 ) = 10 I1= VRef/R1= 10V/10 = 1 AThis current is more than a typical op-amp can Resistor Ladder DAC2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2R Simplest type of DAC Requires only two precision resistance value (R and 2R)8R-2R Resistor Ladder DACEach Bit controls a switch between ground and the inverting input of the op ampThe switch is connected to ground if the corresponding bit = 02 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2R4 Bit ConverterV3V2V1V0R-2R DAC ExampleEx. Convert 0001 to analog2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2 ROOO1 Digital Value:Switch for bit 0 is connected to op amp input. All other switches connected to groundV32R2RV2V1V09R-2R DAC Example (cont.)

4 2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2 RNon-inverting input is connected to ground. Therefore, inverting input is at virtual groundV3V2V1V0 Find Equivalent ResistanceR-2R DAC Example (cont.)Bit 02R2RV0 Req = 2R // 2R = R2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2RV2V1V0V3 Apply voltage division:V0= V1x ReqV0= V1(Req+R)10R-2R DAC Example (cont.)2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2RV2V1V0V3We have shown that V0= V1 Similarly, It can be proven that :V1= V2V2= V3 ANDT herefore:V0= 1/8 V3= 1/8 VsR-2R DAC Example (cont.)2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2RV3V2V1V0V0is the input to the inverting amplifier circuit, which has a gain of:Av = -R/2R = -1/2 Therefore, the Analog output voltage corresponding to the binary input 0001 is:Vout0= Av (V0) = (-1/2)(1/8*Vs)Vout0= -1/16 Vs11R-2R DAC Example (cont.)We have shown that the Analog output voltage for the Digital input 0001 is:Vout0= -1/16 VsSimilarly, it can be show that:Vout1= -1/8 VsFor input = 0010:For input = 0100:Vout2= -1/4 VsFor input = 1000:Vout3= -1/2 VsThe output for any combination of bits comprising the input binary number can now be found using the principle of superposition:Vout= b3 Vout3+ b2 Vout2+ b1 Vout1+ b0 Vout0 General DAC CharacteristicsThere are six key parameters you should consider when choosing a DAC.

5 Reference Voltage Resolution Linearity Speed Settling Time Error12 Reference VoltageTo a large extent, the characteristics of a DAC are defined by its reference voltage. Non-multiplier DAC: Vrefis fixed (specified by the manufacturer) Multiplier DAC: Vrefis provided via an external source Full Scale VoltageDefined as the output when the Digital input word is all 1 s. =NNreffsVV21213 ResolutionResolution is a measure of precision, not accuracy. It is defined as the voltage change corresponding to changing the LSB. Many options in the 8-16 bit range, with 12 bits being a typical cost / resolution trade off. More bits More steps Greater ResolutionResolution = VLSB= VRef/ 2N *where N is the number of bitsLinearity Ideally, a DAC will produce a linear relationship between a binary word and Analog output01234567 Digital Input Signal (3-bit)Voltage output00000111001001110010111114 SpeedUsually specified as conversion or sampling rate.

6 High speed DACs are typically defined as >1MS/s (1 Mhz) Some current 12-16 bit DACs can reach the 1 GHz range Conversion of input signal is limited by Clock speed of the input signal Settling time of the DACS ettling Time Ideally, an instantaneous change in Analog voltage would occurwhen a new binary word enters into a DAC. Settling time is the time taken by the DAC to reach of the LSBof its new voltage. Components include delay, slew time, and ring time. Fast converters reduce slew time, but usually result in longer ringtimes. Delay time is normally a small term. 15 Settling Time (cont.)R-2R Resistor Ladder DAC2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2 RCause of Delay Time, Settling Time, and Ring TimeDelay time is caused by the time it takes to change these switches based on input time and Ring time is determined by the op-amp s slew rate16 Possible ErrorBecause we do not live in an ideal world, considerations forpossible error should be made.

7 Non-Linearity Integral Differential Non Monotonicity Offset Error Gain ErrorIntegral Non-linearity 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 Non-Linearity The difference between an actual step height and the ideal value of 1 LSB. Should be less than or equal to one to insure InputAnalog OutputNon-Monotonicity A monotonic DAC yields an increase in output as input increases. If a differential non-linearity of greater than 1 LSB occurs, increasing the Digital input may actually result in a decreased Error Defined as the difference between the ideal max output voltage and the actual max output voltage (after subtracting offset error).)

8 Changes the slope of the output, thereby creating the same percentage error for each step. Expressed in mV as a percentage of the maximum Error The offset error equals the Analog output when the Digital signal is zero. Typically defined in absolute millivolts with (10mV being acceptable).19R-2R Resistor Ladder DAC2 RBit 3 VoutBit 02 RVs2 RBit 22 RBit 1R+-RRR2 RCause of Non-Linearity, Gain error, and Offset errorNon-linearity is caused bythe resistors. Resistors in D/A converters need to be matched but manufacturing exact resistors is Error and Offset Error is caused by op-amp and or op-amp s feedback resistorDAC Applications DAC s can be found in any device that interfaces Digital and Analog circuitry Analog Displays Digital Control Systems Digital Audio Communications Countless other applications20 References Digital - Analog Converters Are a "Bit" Analog Maxim Semiconductors( ) Component and Measurement Advances Ensure 16-Bit DAC Settling Time Jim Williams, Linear Technology July 1998 Introduction to Mechatronics and Measurement systems David G.

9 Alciatore and Michael B. Histand, McGrawHill Mechatronics-Electronic control systems in mechanical and electrical engineering-W. Bolton, Longman Introduction to Electronic Circuit Design-Richard R. Spencer and Mohammed S. Ghausi, PrenticeHallQuestions ??