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EET 252 Unit 6 Analog-to-Digital Conversion Read Floyd, Section 12-1 and Study Unit 6 e-Lesson. Do Lab #6. Homework #6 and Lab #6 due next week. Quiz next week.

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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. Analog Quantities

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To use a computer to process analog information, we must first use an analog-to- digital 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. Interfacing to the Analog World

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A Typical Application Transducer Physical variable ADCDAC Actuator Computer Control physical variable Analog input (voltage or current) Digital inputs Digital outputs Analog output (voltage or current)

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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.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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. Sampling Rate 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.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed The Nyquist Sampling Theorem states that: The Nyquist Sampling Theorem where f sample = sampling frequency f a(max) = highest harmonic in the analog signal Stated as an equation, f sample > 2f a(max) In order to recover a signal, the sampling rate must be greater than twice the highest frequency in the 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.

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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.oscilloscope’s manual

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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.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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 kHz.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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-and- hold circuit produces the staircase representation shown in red. 0 V 10 V

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Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey All rights reserved. Digital Fundamentals, Tenth Edition Thomas L. Floyd 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.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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. Analog-to-Digital Conversion (Quantization)

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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). Number of Bits and Accuracy

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Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey All rights reserved. Digital Fundamentals, Tenth Edition Thomas L. Floyd 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.

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Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey All rights reserved. Digital Fundamentals, Tenth Edition Thomas L. Floyd Figure 12.8 Light gray = original waveform. Blue = Reconstructed waveform using four quantization levels (2 bits).

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Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey All rights reserved. Digital Fundamentals, Tenth Edition Thomas L. Floyd 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.

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Copyright ©2009 by Pearson Higher Education, Inc. Upper Saddle River, New Jersey All rights reserved. Digital Fundamentals, Tenth Edition Thomas L. Floyd Figure Light gray = original waveform. Blue = Reconstructed waveform using sixteen quantization levels (4 bits).

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Several common ways of specifying an ADC’s resolution: Number of bits, n Number of output codes, = 2 n, or number of steps in the output, = 2 n − 1 Percentage resolution, = 1 / (2 n − 1), expressed as a percentage Step size, = V ref / 2 n Resolution

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Resolution: Examples Formula4-bit ADC10-bit ADC Number of bits n 4 Number of output codes 2n2n 16 Number of steps in the output 2 n −1 15 Percentage resolution 1 / (2 n −1) 6.67% Step size (assuming 5 V reference voltage) V ref / 2 n mV

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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 How to Build an ADC

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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…. Operational Amplifiers

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Op amps are often used as comparators, in which case there is no feedback between the op amp’s output and either input: Op Amp with No Feedback V out is HIGH when V in2 > V in1. V out is LOW when V in2 < V in1.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed Flash ADC The flash ADC: The flash ADC uses a series of high- speed comparators that compare the input with reference voltages. Flash ADCs are fast but require 2 n – 1 comparators to convert an analog input to an n-bit binary number. How many comparators are needed by a 10-bit flash ADC? 1023

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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). 2. After each test, the DAC produces an output voltage that represents the bit. 3. The comparator compares this voltage with the input signal. If the input is larger, the bit is retained; otherwise it is reset (0). SAR DAC V out Parallel binary output CLK D0D0 D1D1 D2D2 D3D3 Serial binary output Input signal Comparator (MSB)(LSB) The method is fast and has a fixed conversion time for all inputs.

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© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed© 2009 Pearson Education, Upper Saddle River, NJ All Rights ReservedFloyd, Digital Fundamentals, 10 th ed 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 s). The completion is signaled by the INTR line going LOW.

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ADC0804 (Datasheet on course website)ADC0804 Note separate analog and digital grounds, series RC network to control timing, and “handshaking lines” that a microprocessor uses to communicate with the ADC. A Popular ADC Chip

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