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EET 252 Unit 7 Digital-to-Analog Conversion Read Floyd, Sections 12-3 to 12-5 (through page 707). Study Unit 7 e-Lesson. Do Lab #7. Homework #7 and Lab #7 due next week. Quiz next week. The Big Picture •An analog-to-digital converter (ADC) takes an analog voltage or current as its input and produces a digital code as its output. This digital code is proportional to the analog input. •A digital-to-analog converter (DAC) takes a digital code as its input and produces an analog voltage or current as its output. This analog output is proportional to the digital input. Review Digital outputs Digital inputs Analog input (voltage or current) Physical variable Transducer Analog output (voltage or current) ADC . . . Computer . . . DAC Actuator Control physical variable Review: Resolution •Just as with ADCs, there are several common ways of specifying a DAC’s resolution: •Number of bits, n n •Number of output codes, = 2 , or number of n steps in the output, = 2 − 1 n •Percentage resolution, = 1 / (2 − 1), expressed as a percentage •Step size, = Vref / 2 n Resolution: Examples Formula Number of bits Number of output codes Number of steps in the output Percentage resolution Step size (assuming 5 V reference voltage) n 2n 2n−1 1 / (2n−1) Vref / 2n 4-bit DAC 10-bit DAC An 8-Bit DAC in Multisim •Note 8 digital inputs, 1 analog output, and input reference voltage. Calculating the Output Voltage •For an 8-bit multiplying DAC like the one in previous slide, the output voltage is given by the following equation, where Din is the number (between 0 and 255) present on the digital inputs: V Vout Din ref 256 •This gives the ideal value. In practice, various factors can cause the actual value to deviate from this predicted value. Voltage or Current? •Some DACs are designed to produce an output current (rather than an output voltage) that is proportional to the digital input. •For such a DAC, we’d simply change our equation to I out Din I ref 256 •The DAC chip that we’ll use in this week’s lab is a current chip. How to Build a DAC •Two standard ways of building a digital-toanalog converter: 1. Binary-weighted input 2. R/2R Ladder •Both methods use operational amplifiers with negative feedback. Op Amp with Negative Feedback •In many applications, the op amp’s output is connected back to its inverting input directly or through a component (resistor or capacitor). This configuration is called negative feedback. For example: “Golden Rules” of Op Amps with Negative Feedback •In The Art of Electronics, Horowitz and Hill give two “golden rules” for analyzing circuits that contain op amps with negative feedback: 1. The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. 2. The inputs draw no current. • Warning: These two rules apply only if the op amp has negative feedback. Binary-weighted-input DAC In a binary-weighted-input DAC, the input current in each resistor is proportional to the column weight in the binary numbering system. It requires very accurate resistors and identical HIGH level voltages. The MSB is represented by the largest current, so it has the smallest resistor. To simplify analysis, assume all current goes through Rf and none into the op-amp. Floyd, Digital Fundamentals, 10th ed LSB D0 8R 4R I0 Rf + If D1 2R I1 D2 D3 MSB – I=0 R I2 – + Vout Analog output I3 © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Binary-weighted-input DAC A certain binary-weighted-input DAC has a binary input of 1101. If a HIGH = +3.0 V and a LOW = 0 V, what is Vout? 120 kW Rf +3.0 V 60 kW 0V 30 kW +3.0 V 10 kW – Vout + 15 kW +3.0 V I out ( I 0 I1 I 2 I 3 ) 3.0 V 3.0 V 3.0 V 0 V 0.325 mA 120 k W 30 k W 15 k W Vout = Iout Rf = (−0.325 mA)(10 kW) = −3.25 V Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved R/R2 Ladder DAC The R-2R ladder DAC requires only two values of resistors. By calculating a Thevenin equivalent circuit for each input, you can show that the output is proportional to the binary weight of inputs that are HIGH. Each input that is HIGH contributes to the output: where VS = input HIGH level voltage n = number of bits Inputs i = bit number D0 D1 D2 For accuracy, the resistors R1 R3 R5 must be precise ratios, 2R 2R 2R R2 R4 R6 R8 which is easily done in integrated circuits. 2R R R R Floyd, Digital Fundamentals, 10th ed D3 R7 2R Rf = 2R – + Vout © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved R/R2 Ladder DAC An R-2R ladder DAC has a binary input of 1011. If a HIGH = +5.0 V and a LOW = 0 V, what is Vout? D0 +5.0 V R2 50 kW D1 +5.0 V R1 50 kW R4 D2 0V D3 +5.0 V R3 50 kW R6 R5 50 kW R8 25 kW 25 kW 25 kW R7 50 kW Rf = 50 kW – Vout + Apply to all HIGH inputs, then sum the results. Applying superposition, Vout = −6.875 V Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Using a Reference Voltage •In the previous circuits, the output voltage depended on the precise voltage present on the digital inputs. This is undesirable, since a digital HIGH on one of these pins could be anywhere from about 2.4 V to about 5 V. •We’d rather have the output voltage depend only on whether the inputs are HIGH or LOW, regardless of the precise voltage. •So most DAC chips use additional circuitry and a reference voltage that sets the full-scale output, independent of the precise voltages present on the digital inputs. Binary-Weighted DAC, Using a Reference Voltage A Popular DAC Chip •MC1408 8-bit DAC (Datasheet on course website.) •It’s also known as a DAC0808. •This chip requires a ground connection and positive (VCC) & negative (VEE) supply voltages. •Its output current is given by Io = Iref x Din / 256 where Iref is the current into pin 14 (typically 2 mA). Digital Signal Processing A digital signal processor (DSP) is optimized for speed and working in real time (as events happen). It is basically a specialized microprocessor with a reduced instruction set. After filtering and converting the analog signal to digital, the DSP takes over. It may enhance the signal in some predetermined way (reducing noise or echoes, improving images, encrypting the signal, etc.). The signal can then be converted back to analog form if desired. Analog signal Anti-aliasing filter Floyd, Digital Fundamentals, 10th ed Sample-andhold circuit 10110 01101 00011 11100 ADC 10110 01101 00011 11100 DSP DAC Reconstruction filter Enhanced analog signal © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved