Chapter 12_Digital Analog Conversion

1 Lecture: DIGITAL SYSTEMS Chapter 12: Digital-Analog Conversion University of Technical Education Faculty of Electrical & Electronic Engineering Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.1 Introduction 12.2 The R/2 n R DAC 12.3 The R/2R DAC 12.4 Digital ramp ADC 12.5 Successive approximation ADC 12.6 Tracking ADC 12.7 Slope (integrating) ADC 2 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 3 12.1 Introduction An ADC has an analog electrical signal input, such as voltage or current and its outputs are the binary digits as shown in Fig. 12.1. Nguyen Thanh Hai, PhD Fig. 12.1: Block diagram of the ADC University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 4 • A DAC, on the other hand, has inputs with the binary digits and its output is an analog voltage or current signal as shown in Fig. 12. 2. Nguyen Thanh Hai, PhD Fig. 12.2: Block diagram of the DAC 12.1 Introduction University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 5 Both the ADC and DAC are often used in digital systems to provide a complete interface between analog sensors and output devices for control systems as shown in Fig. 12.3. Nguyen Thanh Hai, PhD Fig. 12.3: Block diagram of the digital control system University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 6 In particular - Transducer: to vary voltage - Computer is to calculate and to process data - Actuator: to control devices with analog signals ADC DAC Digital system (e.g., computer) Transducer Actuator . . . . . . Physical variable Electrical Analog input Digital inputs Digital outputs Analog output To control physical variable Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 7 -Four-bit DAC with voltage output D/A converter (DAC) Digital inputs Digital outputs D C B A MSB LSB D C B A V out 0 0 0 0 0 0 0 0 1 1 0 0 1 0 2 0 0 1 1 3 0 1 0 0 4 0 1 0 1 5 0 1 1 0 6 0 1 1 1 7 1 0 0 0 8 1 0 0 1 9 1 0 1 0 10 1 0 1 1 11 1 1 0 0 12 1 1 0 1 13 1 1 1 0 14 1 1 1 1 15 Volts Volts Analog output = K x digital input V out = (1 V) x digital input * A digital input of 1100 2 = 12 10 : V out = 1 V x 12 = 12 V Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 8 Example 12.1: A five-bit DAC has a current output. For a digital input of 10100, an output current of 10 mA is produced. What will I out be for a digital input of 11101 Solution: 10100 2 = 20 10. Since I out = 10 mA, so the proportionality: k=10/20 = 0.5 mA If a digital input is 11101 2 =29 10 I out = (0.5 mA) x 29 = 14.5 mA Note: K can vary from one DAC to another and depends on the reference voltage/curent. Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 9 Example 12.2: What is the largest value of an output voltage from an eight-bit DAC that produces 1.0 V for a digital input of 00110010? Solution: 00110010 2 = 50 10 1.0 V = K x 50 Therefore, K = 20 mV The largest output will occur for an input of 11111111 2 = 255 10 . V out (max) = 20 mV x 255 = 5.10 V Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 10 Example 12.3: A five-bit D/A converter produces V out = 0.2 V for a digital input of 00001. Find the value of V out for an input of 11111 Solution: 0.2 V is the weight of the LSB. K= V out /digital input=0.2/1=0.2; 00001=1 Thus the weight of the other bits must be 0.4 V, 0.8 V, 1.6 V and 3.2 V. Therefore, for a digital input of 11111, the value of V out will be 3.2 V + 1.6 V + 0.8 V + 0.4 V + 0.2 V = 6.2 V. Resolution -A fs : the analog full-scale output -n: the number of bits 2.031/2.6 1)-(2 A K resolution n fs ==== Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 11 Example 12.4: For DAC of Example 10-2, determine V out for a digital input of 10001. Solution: The step size is 0.2 V, which is the proportionality factor K. The digital input is 10001 = 17 10 . Thus, we have . V out (max) = (0.2 V) x 17 = 3.4 V Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12 It is much easier to convert a digital signal into an analog signal than it is to do the reverse. Therefore, we will begin with DAC circuitry and then move to ADC circuitry. Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 13 12.2 The R/2 n R DAC • For a simple inverting summer circuit, all resistors must be of equal value. • If any of the input resistors were different, the input voltages would have different degrees of effect on the output, and the output voltage would not be a true sum. • Let's consider, however, intentionally setting the input resistors at different values. Suppose we were to set the input resistor values at multiple powers of two: R, 2R, and 4R, instead of all the same value R Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 14 Nguyen Thanh Hai, PhD Example 12.5: the same input resistors Introduction of some conversion circuits with the R/2 n R DAC. University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 15 Nguyen Thanh Hai, PhD Example 12.6: the different input resistors University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 16 [ ] REF 1n F 012n1no V R 2 R bb bbV − −− ×−= Nguyen Thanh Hai, PhD Example 12.7: the different input resistors University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 17 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 18 • We can adjust resistors values in this circuit to obtain output voltages directly corresponding to the binary input. For example, by making the feedback resistor 800 Ω instead of 1 kΩ, the DAC will output -1 volt for the binary input 001, - 4 volts for the binary input 100, -7 volts for the binary input 111, and so on. Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 19 12.2 The R/2 n R DAC Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 20 12.2 The R/2 n R DAC • If we wish to expand the resolution of this DAC (add more bits to the input), all we need to do is add more input resistors, holding to the same power-of-two sequence of values: Nguyen Thanh Hai, PhD [...]... of Electrical & Electronic Engineering Digital Analog Conversion 12.3 The R/2R DAC 21 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.3 The R/2R DAC 22 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.3 The R/2R DAC 23 Nguyen Thanh Hai,... R/2R DAC 23 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.3 The R/2R DAC 24 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Flash ADC • Also called the parallel A/D converter, this circuit is the simplest to understand • It is formed... active inputs 26 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Flash ADC 27 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Flash ADC • And, of course, the encoder circuit itself can be made from a matrix of diodes, demonstrating just... University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Flash ADC • When operated, the flash ADC produces an output that looks something like this: 29 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Digital ramp ADC • Also known as the stairstep-ramp, or simply counter... to the input of a DAC, then compare the analog output of the DAC with the analog input signal to be digitized and use the comparator's output to tell the counter when to stop counting and reset The following schematic shows the basic idea: 30 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Digital ramp ADC 31 Nguyen... ramp ADC 31 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Digital ramp ADC 32 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.4 Digital ramp ADC • Note how the time between updates (new digital output values) changes depending on how... Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.5 Successive approximation ADC • Without showing the inner workings of the successiveapproximation register (SAR), the circuit looks like this: 34 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.5 Successive approximation ADC 35 Nguyen Thanh... circuit: 38 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.6 Tracking ADC 39 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.7 Slope (integrating) ADC • So far, we've only been able to escape the sheer volume of components in the flash... & Electronic Engineering Digital Analog Conversion 12.7 Slope (integrating) ADC • This ADC circuit behaves very much like the digital ramp ADC, except that the comparator reference voltage is a smooth sawtooth waveform rather than a "stairstep:" 45 Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion -Take a look Examples from... goes into the "count up" mode • When the DAC output exceeds the analog input, the counter switches into the "count down" mode Either way, the DAC output always counts in the proper 36 Nguyen Thanh Hai, PhD direction to track the input signal University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 12.6 Tracking ADC 37 Nguyen Thanh Hai, PhD University . Electronic Engineering Digital Analog Conversion 12. 1 Introduction 12. 2 The R/2 n R DAC 12. 3 The R/2R DAC 12. 4 Digital ramp ADC 12. 5 Successive approximation ADC 12. 6 Tracking ADC 12. 7 Slope (integrating). Engineering Digital Analog Conversion 31 12. 4 Digital ramp ADC Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 32 12. 4. Engineering Digital Analog Conversion 19 12. 2 The R/2 n R DAC Nguyen Thanh Hai, PhD University of Technical Education Faculty of Electrical & Electronic Engineering Digital Analog Conversion 20 12. 2