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EET 252 Unit 6 Analog-to-Digital Conversion Read Floyd, Section 12-1 and 12-2. Study Unit 6 e-Lesson. Do Lab #6. Homework #6 and Lab #6 due next week. Quiz next week. Analog Quantities •Most physical quantities (temperature, pressure, light intensity, etc.) are analog quantities. •Transducers are devices that convert one of these physical quantities to an analog voltage or current. •Example, a temperature sensor might produce a voltage in mV that is proportional to the temperature in degrees Fahrenheit. Interfacing to the Analog World •To use a computer to process analog information, we must first use an analog-todigital converter (ADC) to transform the analog values into digital binary values. •Conversely, we use a digital-to-analog converter (DAC) to transform digital values from the computer into analog values that can be used to control analog devices. A Typical Application Digital outputs Digital inputs Analog input (voltage or current) Physical variable Transducer Analog output (voltage or current) ADC . . . Computer . . . DAC Actuator Control physical variable ADC: A Three-Step Process •On the previous slide, the box labeled ADC actually represents three steps: 1. Anti-aliasing Filter 2. Sample and Hold 3. Analog-to-Digital Conversion (Quantization) • The circuits that perform these steps may be on separate chips or may be combined onto a single ADC chip. Sampling Rate Most input signals to an electronic system start out as analog signals. One step in converting the input to a digital signal is sampling the input repeatedly. If we want to get an accurate representation of the original signal, we must sample at a high enough rate that we capture the signal’s variations. Floyd, Digital Fundamentals, 10th ed Analog input signal Sampling circuit Sampling pulses Sampled version of input signal © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved The Nyquist Sampling Theorem The Nyquist Sampling Theorem states that: In order to recover a signal, the sampling rate must be greater than twice the highest frequency in the signal. Stated as an equation, fsample > 2fa(max) where fsample = sampling frequency fa(max) = highest harmonic in the analog signal If the signal is sampled less frequently than this, the recovery process will produce frequencies that are entirely different than in the original signal. These “masquerading” signals are called aliases. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Aliasing on the Digital Oscilloscope •To see an example of aliasing, use the oscilloscope to display a 10 kHz sine wave. •For this frequency, what is a reasonable value for the SEC/DIV setting? •Try setting the SEC/DIV to a much higher value, and you’ll see an alias of the original sine wave. •Se discussion on page 20 of oscilloscope’s manual. Anti-Aliasing Filters •The job of an anti-aliasing filter is to remove frequencies from the input signal that are higher than our sampling circuit can handle. •This prevents the system from being fooled into thinking that the input signal contains frequencies that it doesn’t really contain. Anti-aliasing Filter An example of a reasonable sampling rate is in a digital audio CD. For audio CDs, sampling is done at 44.1 kHz because audio frequencies above 20 kHz are not detectable by the ear. What cutoff frequency should an anti-aliasing filter have for a digital audio CD? Less than 22.05 kHz. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Sample and Hold After the anti-aliasing filter, the next step in converting a signal to digital form is the sample-and-hold circuit. This circuit samples the input signal at a rate determined by a clock signal and holds the level on a capacitor until the next clock pulse. A positive half-wave from 0-10 V is shown in blue. The sample-andhold circuit produces the staircase representation shown in red. Floyd, Digital Fundamentals, 10th ed 10 V 0V © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Figure 12.5 Illustration of a sample-and-hold operation. Note: I’ve modified this figure by making the first sample much closer to 0 than is shown in the original figure. Digital Fundamentals, Tenth Edition Thomas L. Floyd Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Analog-to-Digital Conversion (Quantization) The final step is to quantize these staircase levels to binary coded form using an analog-to-digital converter (ADC). The digital values can then be processed by a computer. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Number of Bits and Accuracy •During the quantization process, the ADC converts each sampled value of the analog signal into a binary code. •The more bits that are used in this code, the more accurate is the representation of the original signal. •The following slides show an example of how using 2 bits (Figures 12.7 and 12.8) results in much less accuracy than using 4 bits (Figures 12.9 and 12.10). Figure 12.7 Light gray = original waveform. Blue = Sample-and-hold output waveform. Pink = Four quantization levels if we use 2 bits to quantize. Next figure shows the result of this 2-bit quantization. Digital Fundamentals, Tenth Edition Thomas L. Floyd Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Figure 12.8 Light gray = original waveform. Blue = Reconstructed waveform using four quantization levels (2 bits). Digital Fundamentals, Tenth Edition Thomas L. Floyd Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Figure 12.9 Light gray = original waveform. Blue = Sample-and-hold output waveform. Pink = Sixteen quantization levels if we use 4 bits to quantize. Next figure shows the result of this 4-bit quantization. Digital Fundamentals, Tenth Edition Thomas L. Floyd Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Figure 12.10 Light gray = original waveform. Blue = Reconstructed waveform using sixteen quantization levels (4 bits). Digital Fundamentals, Tenth Edition Thomas L. Floyd Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Resolution •Several common ways of specifying an ADC’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 Number of bits Number of output codes Number of steps in the output Percentage resolution Step size (assuming 5 V reference voltage) Formula 4-bit ADC n 2n 4 16 2n−1 15 1 / (2n−1) 6.67% n Vref / 2 312.5 mV 10-bit ADC How to Build an ADC •There are several standard designs: 1. Digital-Ramp ADC 2. Successive Approximation ADC* 3. Flash ADC* 4. Dual-Slope ADC* 5. Sigma-Delta ADC* 6. Up/Down Digital-Ramp ADC 7. Voltage-to-Frequency ADC *Discussed in the textbook Operational Amplifiers •Many ADCs and DACs contain one or more operational amplifiers (op amps). •Op amps are extremely versatile devices that you’ll study in EET 207. •We just need to know a little bit about op amps…. Op Amp with No Feedback •Op amps are often used as comparators, in which case there is no feedback between the op amp’s output and either input: •Vout is HIGH when Vin2 > Vin1. •Vout is LOW when Vin2 < Vin1. Flash ADC +VREF Op-amp comparators R Input from sampleand-hold The flash ADC: The flash ADC uses a series of highspeed comparators that compare the input with reference voltages. Flash ADCs are fast but require 2n – 1 comparators to convert an analog input to an n-bit binary number. + – R + – R + – R R R R Priority encoder 7 6 5 + – 4 + – 1 0 1 2 4 3 2 D0 Parallel D1 binary output D2 EN + – + – Enable pulses R How many comparators are needed by a 10-bit flash ADC? 1023 Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Successive Approximation ADC The successive approximation ADC: 1. Starting with the MSB, each bit in the successive approximation register (SAR) is activated and tested by the digital-to-analog converter (DAC). Vout DAC 2. After each test, the DAC produces an output voltage that D0 represents the bit. D1 3. The comparator compares this voltage with the input Input signal. If the input is larger, signal the bit is retained; otherwise it is reset (0). Comparator D2 – + Parallel binary output D3 (MSB) D CLK (LSB) SAR C Serial binary output The method is fast and has a fixed conversion time for all inputs. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved ADC0804 Chip An integrated circuit successive approximation ADC is the ADC804. This popular ADC is an 8-bit converter that completes a conversion in 64 clock periods (100 ms). VCC (20) (1) (2) (3) (4) (6) (7) (9) ADC0804 ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ CS RD WR CLK IN Vin+ Analog input Vin– REF/2 (8) (5) INTR (19) (18) CLK R (out) D0 (17) D1 (16) D2 (15) Digital D3 (14) data D4 output (13) D5 (12) D6 (11) D7 The completion is signaled by the INTR line going LOW. (10) ANLG DGTL GND GND Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved A Popular ADC Chip •ADC0804 (Datasheet on course website) •Note separate analog and digital grounds, series RC network to control timing, and “handshaking lines” that a microprocessor uses to communicate with the ADC.