AECD_CO5_SLM_10 SESSIONS Analog to Digital Converters PDF

CO-5 TOPICS Analog to digital converters, Digital to analog converters, S/H circuits and multiplexers Session 1 Introduction to data converters Session 2 Analog to digital converter-Successive approximation ADC Session 3 Integrating ADC and Flash ADC Session 4 Pipelined ADC Session 5 Sigma delta ADC Session 6 Digital to analog converter Session 7 Weighted resistor DAC Session 8 R-2R ladder DAC Session 9 S/H circuits Session10 Multiplexers KONERU LAKSHMAIAH EDUCATION FOUNDATION (Deemed to be University estd, u/s, 3 of the UGC Act, 1956) (NAAC Accredited “A++” Grade University) Green Fields, Guntur District, A.P., India – 522502 Department of Electronics and Communication Engineering (DST - FIST Sponsored Department) B.Tech.II ECE PROGRAM A.Y.2023-24ODD, Semester-III 22EC22104 Analog Electronic Circuit Design CO2 1. Course Description (Description about the subject) This course provides the student with the fundamental skills to apply the basics ofsemiconductor and devices like Bipolar junction transistor, FET, MOSFET and operational amplifier.It would build mathematical and numerical background for design of electronics circuit. Studentsequipped with the knowledge and skilling provided in the course would enable them to design, developelectronic circuits for real time applications. 2.Aim The aim of this course is to make the students to apply the basics of semiconductor physics, outline the input and output characteristics of bipolar and unipolar transistors such as JFET and MOSFET, interpret its behavior under different biasing condition, discuss the characteristics of Op-amp, analyze its variouslinear, nonlinear applications, and characterize the design of an OP- amp filters, Oscillators, and itsapplications. 3. Instructional Objectives (Course Objectives)  To impart knowledge on working of a bipolar transistor, its configuration, and its applications.  To impart knowledge on the need of biasing, types of biasing and interpret its performance.  To impart knowledge on working of a JFET and MOSFET and interpret its characteristics and parameters.  To impart knowledge on operational amplifiers and analyse the characteristics of Op- Amp circuitsto perform various linear and nonlinear applications.  To impart knowledge on Operational amplifiers to perform as Active filters and Oscillators and analyze its applications.  To familiarize with theoretical and mathematical aspects related to electronic circuits, such that student will be able to design electronic systems for real time applications. 4.Learning Outcomes (Course Outcome) CO.No. Course Outcome (CO) PO/PSO BTL CO 1 Apply the knowledge of Semiconductor physics PO1, PSO1 3 and discuss BJT configurations and its applications CO 2 Apply the limitations of BJT and discuss the PO1, PSO1 3 characteristics and applications of Field Effect Transistors CO 3 Apply the linear and nonlinear circuits approaches PO1, PO2, PSO1 4 and realize the characteristics of operational Amplifiers CO 4 Apply the concept of feedback system and realize PO1, PO2, PSO1 4 the working principles of Oscillators and multivibrators CO 5 Design and analyze analog circuits for real time PO2, PO3, PSO1 4 applications using Passive and Active Components. CO 6 Simulate and analyze Electronic Circuit using PO2, PO3, PSO1 4 Cadence Virtuoso full suite/Multisim 5. Module Description (CO-5 Description) This module provides the application and analysis of various analog to digital and digital to analog interfaces. 6. Session Outcomes  Describe the operation of data converters.  Demonstrate the applications of A/D and D/A interfaces. SESSION-1 Introduction to data converters Session Introduction Data converters are electronic devices that facilitate the conversion of analog signals to digital representations and vice versa. They play a crucial role in modern communication systems and digital processing applications. Analog-to-Digital Converters (ADCs) transform continuous analog signals into discrete digital codes, enabling digital processing and storage. Conversely, Digital-to-Analog Converters (DACs) convert digital information back into continuous analog signals for output to external devices. Data converters are employed in various domains, including telecommunications, audio systems, measurement equipment, and sensor interfaces. Their performance metrics, such as resolution, sampling rate, linearity, and accuracy, are critical in ensuring reliable and high-quality signal conversion. The continuous advancements in data converter technology have driven the development of numerous innovative applications and digital systems. Session description Data converters, or specifically analog-to-digital converters (ADCs) and digital-to-analog converters (DACs), play an important role in the design of data acquisition units in communication and microprocessor-based instrumentation systems. They include analog and digital building blocks and form the main interface component in mixed-signal processing systems. Data Converter Specifications for Some Applications Applications Resolution (bits) Sampling Frequency Audio device 14–24 < 200 kHz Digital oscilloscope 8 150 MHz Magnetic read channel equalizer 6–8 (50–200) MHz Wireless local area network 6–10 (1–50) MHz Digital video camera 8–12 20 MHz TV baseband processor 8–10 20 MHz Modem 8–10 (10–20) MHz The process of converting an analog signal into a digital sequence, as illustrated in Figure, involves three operations: sampling, quantization, and coding. After the filtering operation, a sample-and-hold circuit first picks up the signal representative, which is maintained constant for the duration required by the converter to provide a digital word. Continuous-time signal with the maximum frequency, fm, can adequately be represented by its samples acquired at the rate fs ≥ fN = 2fm, where fN is termed the Nyquist rate or frequency. To maintain the frequency content of the input signal within the Nyquist bandwidth, an analog lowpass filter, also known as an anti-aliasing filter, is placed before the sample-and-hold circuit. Ideally, this filter should attenuate signal components with a frequency above fs/2. The sampled signal is then transformed into one of a finite set of prescribed values by a quantizer, the levels of which can be uniformly or nonuniformly spaced. The transfer characteristic and error, e, of a uniform quantizer, whose implementation is the simplest of both, is shown in Figure. The error caused by the quantization is defined as the difference between the discrete output level and theactual analog input, eQ = ˆx − x. It is in the range ±∆/2 as long as the quantizer does not saturate. The transfer characteristic of Figure 2.2 belongs to a quantizer of the mid-tread type because it follows the input axis about zero. As a result, the output is insensitive to small input variation in the absence of signal in contrast to the mid-riser characteristic, which is supported by the output axis about zero. The coding then consists of assigning a unique binary number to each quantization level. Assuming that the number of bits, N , is 3, the 2N quantization levels can be coded in an N -bit number representation. The step size of the converter, ∆, represents the least significant bit (LSB) of the digital number and is given by ∆ = F SR/2N , where F SR is the quantizer range or full-scale range (FSR). By using the two’s complement code, the sign of the input sample is determined by the most significant bit (MSB). A real number, X, which can be represented as Corresponds to the value Where b1 is the MSB. Other codes can also be used depending on signal characteristics and the desired application; however, the two’s complement representation is a convenient way of representing signed numbers and the most suitable for addition and subtraction operations A digital-to-analog conversion stage, as shown in Figure 2.3, generally con tains a DAC, a sample-and-hold (S/H) circuit, and a low pass filter (LPF). The DAC is used to transform a finite number of digital codes into the corresponding analog discrete-time signal. Its transfer characteristic is shown in Figure 2.4 for a bipolar input code. In contrast to the ADC, which exhibits a quantization error due to the fact that any voltage within a given step size is mapped to the same output code, the DAC uniquely assigns each input code to an output level without an inherent error. Therefore, DACs do not directly realize the inverse function of ADCs. In general, the DAC output signal, X0, can ideally be put in the form where G is the gain, XREF is the reference signal, D is the decimal equivalent of the binary input code, and K1 and K2 are the gain and offset constants, respectively. In the case of unipolar conversion, K1 = 1 and K2 = 0, and the output range is from 0 to G · XREF. For bipolar DACs based on the offset binary input coding, the constants are chosen as K1 = 2 and K2 = −1 to produce an output swing between −G · XREF and G · XREF. Note that the two’s complement representation is converted into offset binary code only by inverting the MSB. The digital-to-analog conversion process should be realized with the highest fidelity and minimal lag in time. The S/H introduces a delay in the output of the DAC to allow the current sample at the DAC output to reach the steady state. An LPF, often referred to as a smoothing (or reconstruction) filter, is used to remove the frequency components above fs/2 from the converter output. It also smooths the signal provided by the S/H by removing all sharp discontinuities. Various architectures are known for the implementation of data converters. They can be divided into two main groups: Nyquist and oversampling converters. Nyquist converters operate at a sampling rate close to the Nyquist frequency or slightly higher than twice the bandwidth of the input signal; therefore their output data rate can be very high. On the other hand, the op eration of oversampling converters, which can achieve a higher resolution even with low- precision components, requires a sampling rate that is several times higher than the Nyquist frequency. By relying on the averaging of multiple samples performed by a digital filter for each conversion, oversampling converters feature a longer acquisition time than the one of Nyquist converters, which processes each input sample independently. Data Converters in Applications Data converters are used in a wide variety of applications, including:  Telecommunications: Data converters are used in telecommunications systems to convert analog signals, such as voice and video, into digital signals that can be transmitted over long distances.  Medical imaging: Data converters are used in medical imaging systems to convert analog signals, such as X-rays and MRI scans, into digital signals that can be stored and processed.  Audio and video processing: Data converters are used in audio and video processing systems to convert analog signals, such as music and movies, into digital signals that can be edited and stored.  Instrumentation: Data converters are used in instrumentation systems to convert analog signals, such as temperature and pressure, into digital signals that can be monitored and controlled.  Control systems: Data converters are used in control systems to convert analog signals, such as sensor readings, into digital signals that can be used to control motors and other devices. Performance of Data Converters The performance of a data converter is measured by a number of factors, including:  Resolution: The resolution of a data converter is the number of bits used to represent each sample. The higher the resolution, the more accurate the digital representation of the analog signal.  Accuracy: The accuracy of a data converter is the degree to which the digital signal represents the analog signal. Accuracy is typically expressed as a percentage of full scale.  Speed: The speed of a data converter is the rate at which samples can be taken or converted. Speed is typically expressed in samples per second.  Power consumption: The power consumption of a data converter is the amount of power required to operate the data converter. Activities/ Case studies/related to the session 1. Find the applications of ADCs in differten applications along with performance requirements Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. https://www.e3sconferences.org/articles/e3sconf/abs/2020/44/ e3sconf_icmed2020_01025/e3sconf_icmed2020_01025.html 2. https://www.sciencedirect.com/topics/engineering/analog-to-digital-converter 3. https://www.arrow.com/en/research-and-events/articles/engineering-resource- basics-of-analog-to-digital-converters SAQ's-Self Assessment Questions 1. What is the purpose of an analog-to-digital converter (ADC)? 2. What is the purpose of a digital-to-analog converter (DAC)? 3. What is the basic principle behind an ADC? 4. What is the basic principle behind a DAC? 5. What are the common types of ADCs? 6. What are the common types of DACs? 7. How does a successive approximation ADC work? 8. What is the resolution of an ADC? 9. How is the resolution of an ADC determined? 10. What is quantization error in ADCs? 11. What is the Nyquist-Shannon sampling theorem? 12. What is aliasing in the context of ADCs? 13. What is the purpose of a sample-and-hold circuit in an ADC? 14. How does a weighted resistor DAC work? 15. What is the purpose of a reconstruction filter in a DAC? 16. What is the difference between an ideal ADC and a practical ADC? 17. How does an integrating ADC work? 18. What is the purpose of oversampling in ADCs? 19. What are the advantages and disadvantages of delta-sigma ADCs? 20. How does a digital potentiometer work in the context of DACs? Summary Data converters, including analog-to-digital converters (ADCs) and digital-to-analog converters (DACs), play a vital role in modern electronics. ADCs convert continuous analog signals into discrete digital representations, enabling the processing and storage of real-world data in digital systems. They capture the amplitude and frequency characteristics of signals and digitize them through sampling and quantization. On the other hand, DACs convert digital data back into continuous analog signals, allowing digital systems to interact with the physical world. These converters are used in various applications, such as telecommunications, audio processing, sensor systems, and measurement equipment, where the conversion between the analog and digital domains is crucial for accurate and reliable information transfer. Terminal Questions 1. Identify the applications of analog to digital converters 2. Discuss about analog to digital converters with block diagram Case Studies (Co Wise) NA Answer Key 1. Data converters, such as analog-to-digital converters (ADCs) and digital-to-analog converters (DACs), have numerous applications across various industries. Some of the common applications of data converters include: Communications: Data converters are used in telecommunications systems for encoding and decoding voice and data signals. They enable the conversion of analog signals into digital form for transmission, and vice versa for reception. Audio Processing: ADCs and DACs are extensively used in audio systems, such as audio interfaces, sound cards, and music production equipment. ADCs convert analog audio signals from microphones or instruments into digital format for recording and processing, while DACs convert digital audio data back into analog signals for playback through speakers or headphones. Industrial Control Systems: Data converters are employed in industrial automation and control systems to interface with sensors and actuators. ADCs convert analog sensor measurements (such as temperature, pressure, or position) into digital signals for processing and control, while DACs generate analog control signals to drive actuators or control devices. Medical Instrumentation: In medical applications, data converters are used for capturing and processing physiological signals from sensors, such as electrocardiograms (ECGs), electroencephalograms (EEGs), and blood pressure monitors. ADCs convert these analog signals into digital form for analysis and diagnosis, while DACs are used in therapeutic devices that require precise control over analog outputs. Test and Measurement Equipment: Data converters play a crucial role in test and measurement instruments, such as oscilloscopes, spectrum analyzers, and data loggers. ADCs capture analog signals for analysis and display, while DACs generate analog test signals or stimulus for testing and calibration purposes. Automotive Systems: Data converters are utilized in various automotive applications, including engine control units (ECUs), infotainment systems, and advanced driver-assistance systems (ADAS). They facilitate the conversion of analog signals from sensors, such as temperature, pressure, and position sensors, into digital form for processing, control, and decision-making. Aerospace and Defense: Data converters are widely employed in aerospace and defense systems, including radar systems, satellite communication systems, avionics, and electronic warfare systems. They are crucial for capturing and processing analog signals, as well as generating accurate control signals for mission-critical operations. 2. The process of converting an analog signal into a digital sequence, as illustrated in Figure, involves three operations: sampling, quantization, and coding. After the filtering operation, a sample-and-hold circuit first picks up the signal representative, which is maintained constant for the duration required by the converter to provide a digital word. Continuous-time signal with the maximum frequency, fm, can adequately be represented by its samples acquired at the rate fs ≥ fN = 2fm, where fN is termed the Nyquist rate or frequency. To maintain the frequency content of the input signal within the Nyquist bandwidth, an analog lowpass filter, also known as an anti- aliasing filter, is placed before the sample-and-hold circuit. Ideally, this filter should attenuate signal components with a frequency above fs/2. The sampled signal is then transformed into one of a finite set of prescribed values by a quantizer, the levels of which can be uniformly or nonuniformly spaced. The transfer characteristic and error, e, of a uniform quantizer, whose implementation is the simplest of both, is shown in Figure. Glossary Analog-to-Digital Converter (ADC): A device that converts continuous analog signals into discrete digital representations by sampling and quantizing the input signal. Digital-to-Analog Converter (DAC): A device that converts digital data into corresponding continuous analog signals. Resolution: The number of distinct digital values that an ADC or DAC can represent. It is often expressed in bits and determines the level of detail in the conversion process. Sampling: The process of measuring and capturing the amplitude of an analog signal at regular intervals of time. Quantization: The process of assigning digital values to the continuous amplitude levels of an analog signal during conversion. Quantization Error: The difference between the actual analog signal value and the nearest representable digital value due to quantization. Nyquist-Shannon Sampling Theorem: A principle stating that in order to accurately reconstruct an analog signal from its digital samples, the sampling rate must be at least twice the maximum frequency present in the signal. Aliasing: The phenomenon where high-frequency components of an analog signal are erroneously represented as lower-frequency components due to inadequate sampling rates. Successive Approximation ADC: An ADC architecture that iteratively approximates the input signal's value by comparing it with a series of binary-weighted voltage levels. Delta-Sigma ADC: An ADC that oversamples the input signal and uses a delta-sigma modulation technique to achieve high resolution and low noise performance. Integrating ADC: An ADC that integrates the input voltage over a fixed period of time to generate a digital output proportional to the average value of the input signal. Sample-and-Hold Circuit: A circuit that samples the input analog signal and holds the sampled value constant during the conversion process. Weighted Resistor DAC: A DAC architecture that uses a combination of resistors with different weights to generate analog output voltages corresponding to digital input codes. Reconstruction Filter: A low-pass filter used in a DAC to smooth out the staircase-like output waveform and remove unwanted high-frequency components. Oversampling: The process of sampling an analog signal at a rate higher than the Nyquist rate to improve the effective resolution and reduce quantization noise in ADCs. Digital Potentiometer: A digital circuit that emulates the functionality of a traditional potentiometer and is used in DACs to control the output voltage level digitally. Linearity: The degree to which the output of a data converter faithfully represents the input signal without introducing distortions or nonlinearities. Signal-to-Noise Ratio (SNR): A measure of the quality of a data converter, indicating the ratio of the desired signal level to the background noise level in the converted signal. Spurious-Free Dynamic Range (SFDR): A measure of the dynamic range of a data converter, representing the difference between the desired signal level and the highest spurious signal level. Latency: The delay between the application of an input signal to a data converter and the availability of the converted output signal. References of books, sites, links 1. https://easyelectronics.co.in/data-converters/ 2. https://www.electronics-tutorial.net/analog-integrated-circuits/data-converters/ 3. https://hasler.ece.gatech.edu/Courses/ECE3400/Proj4/ Data_Converter_Overview.pdf Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Analog-to-Digital Converter (ADC), Digital-to-Analog Converter (DAC), Resolution, Sampling Quantization, Quantization Error, Nyquist-Shannon Sampling Theorem, Aliasing, Successive Approximation ADC, Delta-Sigma ADC, Integrating ADC, Sample-and-Hold Circuit, Weighted Resistor DAC, Reconstruction Filter, Oversampling, Digital Potentiometer, Linearity, Signal-to- Noise Ratio (SNR), Spurious-Free Dynamic Range (SFDR), Latency SESSION-2 Analog to digital converter-Successive approximation ADC Session Introduction A successive approximation analog-to-digital converter (ADC) is a type of ADC that uses a binary search algorithm to convert an analog input signal into a digital representation. It operates by iteratively comparing the input voltage to a series of voltage thresholds and progressively narrowing down the range of possible values. The converter starts with the most significant bit (MSB) and makes a tentative decision based on the comparison result. It then moves on to the next bit, adjusting the tentative decision based on the updated voltage range. This iterative process continues until the least significant bit (LSB) is reached, resulting in a digital output that closely approximates the original analog input. The successive approximation ADC offers high- speed conversion with good accuracy and is commonly used in various applications, including data acquisition systems and sensor interfacing. Session description An Analog to Digital Converter (ADC) is a type of device which helps us to process the chaotic real-world data in a digital standpoint. To understand real-world data like temperature, humidity, pressure, position, we need transducers, all of those measure certain parameters and give us an electrical signal back in the form of voltage and current. Since the majority of our devices nowadays are digital, it becomes necessary to convert those signals into digital signals. That is where the ADC comes in, though there are many different types of ADCs out there but in this article, we are going to talk about one of the most used ADC types which are known as the successive approximation ADC. The Successive Approximation ADC is the ADC of choice for low-cost medium to high-resolution applications, the resolution for SAR ADCs ranges from 8 - 18 bits, with sample speeds up to 5 mega-samples per second (Msps). Also, it can be constructed in a small form factor with low power consumption, which is why this type of ADC is used for portable battery-powered instruments. As the name implies, this ADC applies a binary search algorithm to convert the values, which is why the internal circuitry may be running at several MHZ but the actual sample rate is much less due to the Successive Approximation algorithm. Working of Successive Approximation ADC The cover image shows the basic successive approximation ADC circuit. But to understand the working principle a little better, we are going to use a 4-bit version of it. The image below shows exactly that. As you can see, this ADC consists of a comparator, a digital to analog converter, and a successive approximation register along with the control circuit. Now, whenever a new conversation starts, the sample and hold circuit samples the input signal. And that signal is compared with the specific output signal of the DAC. Now let's say, the sampled input signal is 5.8V. The reference of the ADC is 10V. When the conversion starts, the successive approximation register sets the most significant bit to 1 and all other bits to zero. This means the value becomes 1, 0, 0, 0, which means, for a 10V reference voltage, the DAC will produce a value of 5V which is half of the reference voltage. Now this voltage will be compared to the input voltage and based on the comparator output, the output of the successive approximation register will be changed. The image below will clarify it more. Further, you can look at a generic reference table for more details on DAC. Previously we have made many projects on ADCs and DACs, you can check those out for more information. This means if Vin is greater than the output of the DAC, the most significant bit will stay as it is, and the next bit will be set for a new comparison. Otherwise, if the input voltage is less than the DAC value, the most significant bit will be set to zero, and the next bit will be set to 1 for a new comparison. Now if you see the below image, the DAC voltage is 5V and as it is less than the input voltage, the next bit before the most significant bit will set to one, and other bits will set to zero, this process will continue until the value closest to the input voltage reaches. This is how the successive approximation ADC changes 1 bit at a time to determine the input voltage and produce the output value. And whatever the value might be in four iterations, we will get the output digital code from the input value. Finally, a list of all possible combinations for a four-bit successive approximation ADC is shown below. Conversion Time, Speed, and Resolution of Successive Approximation ADC Conversion Time: In general, we can say that for an N bit ADC, it will take N clock cycles, which means the conversion time of this ADC will become- Tc = N x Tclk *Tc is short for Conversion Time. And unlike other ADCs, the conversion time of this ADC is independent of the input voltage. As we are using a 4-bit ADC, to avoid aliasing effects, we need to take a sample after 4 consecutive clock pulses. Conversion Speed: The typical conversion speed of this type of ADC is around 2 - 5 Mega Samples Per Seconds (MSPS), but there are few which can reach up to 10 (MSPS). Resolution: The resolution of this type of ADC can be around 8 - 16 bits, but some types can go up to 20- bits. Advantages and Disadvantages of Successive Approximation ADC This type of ADCs has many advantages over others. It has high accuracy and low power consumption, whereas it's easy to use and has a low latency time. The latency time is the time of the beginning of the signal acquisition and the time when the data is available to fetch from the ADC, typically this latency time is defined in seconds. But also some datasheets refer to this parameter as conversion cycles, in a particular ADC if the data is available to fetch within one conversion cycle, we can say it has a one conversation cycle latency. And if the data is available after N cycles, we can say it has a one conversion cycle latency. A major disadvantage of SAR ADC is its design complexity and cost of production. Applications of SAR ADC As this is a most commonly used ADC, it's used for many applications like uses in biomedical devices that can be implanted in the patient, these types of ADCs are used because it consumes very less power. Also, many smart watches and sensors used this type of ADC. Activities/ Case studies/related to the session 1. Identify the matching application where SAR ADC is the preferable choice Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. https://link.springer.com/article/10.1007/s10470-020-01742-6 2. https://onlinelibrary.wiley.com/doi/full/10.1002/tee.22290 3. https://indjst.org/articles/12-bit-clock-gated-sar-adc-for-bio-medical- applications SAQ's-Self Assessment Questions 1. What does SAR stand for in SAR ADC? 2. How does a SAR ADC convert an analog signal into a digital representation? 3. What is the main advantage of SAR ADCs over other types of ADCs? 4. What is the typical resolution range of SAR ADCs? 5. How does the number of comparators in a SAR ADC affect its performance? 6. What is the purpose of the sample and hold circuit in a SAR ADC? 7. What is the role of the digital-to-analog converter (DAC) in a SAR ADC? 8. What is the concept of "successive approximation" in a SAR ADC? 9. What is the significance of the acquisition time in SAR ADCs? 10. How does the conversion speed of a SAR ADC compare to other ADC architectures? 11. What are the typical power requirements for SAR ADCs? 12. What are some common applications of SAR ADCs? 13. What is the impact of input capacitance on the performance of a SAR ADC? 14. What is the effect of noise on the accuracy of SAR ADCs? 15. How does the resolution of a SAR ADC affect its conversion time? 16. What are the advantages of using a SAR ADC in battery-powered applications? 17. How does the input voltage range affect the design considerations of a SAR ADC? 18. What are the key factors to consider when selecting a SAR ADC for a specific application? 19. What is the role of the control logic in a SAR ADC? 20. How does the accuracy of a SAR ADC relate to the number of bits in its digital output? Summary A Successive Approximation Register (SAR) ADC is a type of analog-to-digital converter that uses a binary search algorithm to convert analog signals into digital values. It operates by comparing the input voltage with a series of thresholds, starting from the most significant bit (MSB) and iteratively narrowing down the possible values. A sample and hold circuit captures and maintains the input voltage during the conversion process. The ADC's control logic guides the successive approximation by adjusting the tentative decision based on the comparison results. SAR ADCs offer a balance between speed and accuracy, making them suitable for various applications, including data acquisition, sensor interfacing, and battery-powered devices. Terminal Questions 1. Explain the working of SAR ADC 2. Identify the advantages and disadvantages of SAR ADC? Case Studies (Co Wise) 1. Compare SAR ADC with other ADC’S Answer Key 1. The cover image shows the basic successive approximation ADC circuit. But to understand the working principle a little better, we are going to use a 4-bit version of it. The image below shows exactly that. As you can see, this ADC consists of a comparator, a digital to analog converter, and a successive approximation register along with the control circuit. Now, whenever a new conversation starts, the sample and hold circuit samples the input signal. And that signal is compared with the specific output signal of the DAC. Now let's say, the sampled input signal is 5.8V. The reference of the ADC is 10V. When the conversion starts, the successive approximation register sets the most significant bit to 1 and all other bits to zero. This means the value becomes 1, 0, 0, 0, which means, for a 10V reference voltage, the DAC will produce a value of 5V which is half of the reference voltage. Now this voltage will be compared to the input voltage and based on the comparator output, the output of the successive approximation register will be changed. The image below will clarify it more. Further, you can look at a generic reference table for more details on DAC. Previously we have made many projects on ADCs and DACs, you can check those out for more information. 2. Advantages and Disadvantages of Successive Approximation ADC This type of ADCs has many advantages over others. It has high accuracy and low power consumption, whereas it's easy to use and has a low latency time. The latency time is the time of the beginning of the signal acquisition and the time when the data is available to fetch from the ADC, typically this latency time is defined in seconds. But also some datasheets refer to this parameter as conversion cycles, in a particular ADC if the data is available to fetch within one conversion cycle, we can say it has a one conversation cycle latency. And if the data is available after N cycles, we can say it has a one conversion cycle latency. A major disadvantage of SAR ADC is its design complexity and cost of production. Glossary SAR ADC: Successive Approximation Register Analog-to-Digital Converter. Analog-to-Digital Converter: A device that converts analog signals into digital values. Binary Search Algorithm: An algorithm used by SAR ADCs to iteratively narrow down the range of possible digital values. Digital-to-Analog Converter (DAC): A circuit that converts digital signals into analog voltages. Most Significant Bit (MSB): The highest-weighted bit in a binary number representation. Sample and Hold Circuit: A circuit that captures and maintains the analog input voltage during the conversion process. Control Logic: The circuitry that guides the successive approximation process in a SAR ADC. Threshold: A reference voltage against which the input voltage is compared during the conversion. Tentative Decision: An initial estimation of the digital value based on the comparison of the input voltage with the thresholds. Least Significant Bit (LSB): The lowest-weighted bit in a binary number representation. Resolution: The number of bits used to represent the digital output of the ADC. Acquisition Time: The time taken to sample and hold the analog input voltage before the conversion process. Conversion Speed: The time required for the SAR ADC to complete the conversion process. References of books, sites, links 1. https://circuitdigest.com/article/how-does-successive-approximation-sar-adc-work- and-where-is-it-best-used 2. https://www.electronics-tutorial.net/analog-integrated-circuits/data-converters/ successive-approximation-type-adc/ 3. https://ecstudiosystems.com/discover/textbooks/basic-electronics/ad-and-da- converters/successive-approximation-adc/ Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Analog-to-Digital Converter, Binary Search Algorithm, Digital-to-Analog Converter, Most Significant Bit (MSB), Sample and Hold Circuit, Control Logic, Threshold, Tentative Decision, Least Significant Bit (LSB), Resolution, Acquisition Time, Conversion Speed, Input Capacitance, Noise, Power Requirements SESSION-3 Integrating ADC and Flash ADC Session Introduction Integrating ADC and Flash ADC are two distinct types of analog-to-digital converters (ADCs) commonly used in various applications. An Integrating ADC, also known as a ramp ADC, utilizes the principle of integrating the input voltage over time and converting it into a digital representation. It employs a sample and hold circuit, an integrator, and a counter to measure the time required to reach a specific voltage level. On the other hand, a Flash ADC employs a parallel array of comparators to instantaneously compare the input voltage against multiple reference voltages. It provides very high-speed conversions but is limited in resolution due to the large number of comparators required. Both ADC architectures offer unique trade-offs in terms of resolution, speed, and complexity, making them suitable for different application requirements. Session description Dual slope ADC The dual-slope ADC architecture was a breakthrough in ADCs for high-resolution applications such as digital voltmeters (DVMs). The dual-slope ADC has the following advantages:  Noise present on the input voltage is reduced by averaging  The values of the capacitor and conversion clock do not affect conversion accuracy since they act equivalently on the up-slope and down-slope  Linearity is very good and extremely high-resolution measurements can be obtained Its main disadvantage is a slow conversion rate, often in the range of 10 samples/second. In applications where this is not a problem, such as in measuring temperature transducers, a dual- slope ADC is a good choice. In a dual-slope ADC as shown in Figure 1, the input signal is applied to an integrator. At the same time, a counter begins counting clock pulses. After a predetermined amount of time (T), a reference voltage with opposite polarity is applied to the integrator. At that instant, the accumulated charge on the integrating capacitor is proportional to the average value of the input over the interval T as shown in Figure 2. The integral of the reference is an opposing ramp with a slope of VREF/RC. Simultaneously, the counter is again counting from zero. When the integrator output reaches zero, the counter stops, and the analog circuitry is reset. Since the charge gained is proportional to VIN × T, and the equal amount of charge lost is proportional to V REF × tx, then the number of counts relative to the full-scale count is proportional to tx/T, or VIN/VREF. If the output of the counter is a binary number, it will therefore be a binary representation of the input voltage. Overview of Flash ADC An “N-bit flash” or “parallel-architecture” ADC employs an array of 2n–1 comparators, as shown in Figure. The analog signal is applied simultaneously to each comparator, and each comparator has a different reference voltage on its other input with the voltages ascending in voltage increments equivalent to 1 LSB. A resistive voltage divider generates the reference voltages, so they’re as precise as the precision of the resistors. Flash ADCs are very fast because they generate an output in one ADC for every clock cycle. Unfortunately, requiring 2n-1 comparators can be a disadvantage of flash ADCs because they often lead to large power dissipation and a larger area. Due to these power and area constraints, flash ADCs usually have a resolution of no more than 10 bits. Activities/ Case studies/related to the session 1. Identify the applications of FLASH converter Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. https://www.sciencedirect.com/topics/engineering/dual-slope 2. https://digitalcommons.lsu.edu/cgi/viewcontent.cgi? article=6062&context=gradschool_theses 3. https://ieeexplore.ieee.org/document/4315423 SAQ's-Self Assessment Questions Dual Slope ADC: 1. What is a Dual Slope ADC and how does it work? 2. What are the advantages of using a Dual Slope ADC? 3. What is the principle behind integrating a Dual Slope ADC? 4. What are the applications of Dual Slope ADCs? 5. How does a Dual Slope ADC achieve higher resolution compared to other ADC architectures? 6. What are the limitations of Dual Slope ADCs? 7. Can a Dual Slope ADC be used for high-speed applications? Why or why not? 8. What is the significance of the reference voltage in a Dual Slope ADC? 9. What is the difference between single-slope and dual-slope ADCs? 10. How is noise performance affected in a Dual Slope ADC? Flash ADC: 1. What is a Flash ADC and how does it work? 2. What are the advantages of using a Flash ADC? 3. What is the resolution of a Flash ADC? 4. How does the number of comparators affect the performance of a Flash ADC? 5. How does the speed of a Flash ADC compare to other ADC architectures? 6. What is the power consumption of a Flash ADC? 7. How does a Flash ADC handle non-linearities in the input signal? 8. Can a Flash ADC provide high resolution? Why or why not? 9. What is the relationship between the number of comparators and the resolution of a Flash ADC? 10. What are the limitations of a Flash ADC? Summary Dual Slope ADC: A Dual Slope ADC, also known as a Dual Integration ADC, is a type of analog-to-digital converter that achieves high resolution by integrating the input signal over two different time periods. It works by comparing the integrated voltage of the input signal during the first period (integration phase) with the integrated voltage of a known reference voltage during the second period (reference phase). The ratio of these integrated voltages determines the digital representation of the input signal. Dual Slope ADCs are known for their high accuracy, low noise, and good linearity. They are commonly used in applications that require high-resolution conversions but are not time-critical, such as digital multimeters and data acquisition systems. Flash ADC: A Flash ADC, also known as a Parallel ADC, is a type of high-speed analog-to- digital converter that provides fast conversion times but typically has limited resolution. It works by using a set of comparators, with each comparator comparing the input signal to a different reference voltage level. The outputs of the comparators are encoded into a digital code, representing the input signal's amplitude. Flash ADCs are known for their fast conversion times and high sampling rates, making them suitable for applications that require high-speed data acquisition, such as high-speed communications and video processing. However, Flash ADCs suffer from limitations in resolution, power consumption, and complexity due to the large number of comparators required for higher resolutions. In summary, Dual Slope ADCs offer high resolution and accuracy but are relatively slow compared to Flash ADCs. They are suitable for applications that prioritize accuracy over speed. On the other hand, Flash ADCs provide fast conversion times but have limited resolution and higher power consumption. They are commonly used in applications that require high-speed data acquisition but can tolerate lower resolutions. The choice between Dual Slope ADC and Flash ADC depends on the specific requirements of the application, such as resolution, speed, accuracy, and power consumption. Terminal Questions 1. Explain about working of dual slope ADC with neat diagram 2. Discuss the operation of flash converter Case Studies (Co Wise) NA Answer Key 1. In a dual-slope ADC as shown in Figure 1, the input signal is applied to an integrator. At the same time, a counter begins counting clock pulses. After a predetermined amount of time (T), a reference voltage with opposite polarity is applied to the integrator. At that instant, the accumulated charge on the integrating capacitor is proportional to the average value of the input over the interval T as shown in Figure 2. The integral of the reference is an opposing ramp with a slope of VREF/RC. Simultaneously, the counter is again counting from zero. When the integrator output reaches zero, the counter stops, and the analog circuitry is reset. Since the charge gained is proportional to VIN × T, and the equal amount of charge lost is proportional to V REF × tx, then the number of counts relative to the full-scale count is proportional to tx/T, or VIN/VREF. If the output of the counter is a binary number, it will therefore be a binary representation of the input voltage. 2. An “N-bit flash” or “parallel-architecture” ADC employs an array of 2n–1 comparators, as shown in Figure. The analog signal is applied simultaneously to each comparator, and each comparator has a different reference voltage on its other input with the voltages ascending in voltage increments equivalent to 1 LSB. A resistive voltage divider generates the reference voltages, so they’re as precise as the precision of the resistors Glossary Flash ADC: Also known as Parallel ADC, it is a high-speed analog-to-digital converter that provides fast conversion times by using a set of comparators. Comparator: A circuit element that compares two voltages and outputs a digital signal indicating which voltage is higher. Reference Voltage: A set of voltage levels against which the input signal is compared by the comparators in a Flash ADC. Conversion Time: The time taken by the ADC to convert an analog input into a digital output. Sampling Rate: The rate at which the ADC samples the input signal to capture its digital representation. Power Consumption: The amount of electrical power consumed by the ADC during its operation. Non-Linearity: The deviation from a linear relationship between the input signal and the digital output code. Resolution: The number of distinct digital output codes that the ADC can produce, typically determined by the number of comparators used in the Flash ADC. References of books, sites, links 1. https://www.electronicshub.org/types-of-adc-circuit/ 2. https://www.asdlib.org/onlineArticles/elabware/Scheeline_ADC/ ADC_ADC_Dual_Slope.html 3. https://www.rfwireless-world.com/Terminology/Difference-between-ADC-types.html Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Dual Slope ADC, Dual Integration ADC, Integration Phase, Reference Phase, Resolution, Accuracy, Linearity, Noise, Analog-to-Digital Converter, Digital Multimeter, Data Acquisition System, Flash ADC, Parallel ADC, Comparator, Reference Voltage, Conversion Time, Sampling Rate, Power Consumption, Non-Linearity, Analog-to-Digital Converter, High-Speed Data, Acquisition, Communications, Video Processing SESSION-4 Pipelined ADC Session Introduction A pipelined ADC, also known as a multi-stage ADC, is a type of analog-to-digital converter that utilizes a pipeline architecture to achieve high-speed and high-resolution conversions. It is a widely used ADC architecture in many applications, including digital signal processing, telecommunications, and image sensors. Pipelined ADCs offer several advantages, including high-speed operation, good resolution, and low power consumption. However, they also come with some limitations, such as complexity, higher cost, and potential non-linearity due to the inter-stage errors. An algorithmic ADC, also known as a successive approximation ADC, is a type of analog-to-digital converter that employs a binary search algorithm to approximate and convert an analog input into a digital representation. It is commonly used in various applications, such as portable devices, sensors, and instrumentation. Algorithmic ADCs offer several advantages, including simplicity, moderate speed, and good resolution. They are also known for their relatively low power consumption compared to other high-speed ADC architectures. However, they may exhibit non-linearity due to the approximation process and may be sensitive to noise and variations in the analog input. Session description General Pipelined System Each stage performs an operation on the signal, provides the output for the following sampler, and, once the sampler has acquired the data, begins the same operation on the next signal.  Different stages process different samplers concurrently.  Throughput rate depends on only the speed of each stage (and the acquisition time of the next sampler). Example: Two-Step Pipelined ADC: General Pipelined ADC Pipelined architectures are especially efficient if several of these operations can be combined. Old wisdom has it that their area and power dissipation grow almost linearly with the number of bits: Need gain between stages to avoid corrupting the data. Actual implementations vary from cascaded flash stages to one-bit-per-stage sopologies. The pipelined analog-to-digital converter (ADC) has become the most popular ADC architecture for sampling rates from a few megasamples per second (Msps) up to 100Msps+. Resolutions range from eight bits at the faster sample rates up to 16 bits at the lower rates. These resolutions and sampling rates cover a wide range of applications, including CCD imaging, ultrasonic medical imaging, digital receivers, base stations, digital video (for example, HDTV), xDSL, cable modems, and fast Ethernet. Applications with lower sampling rates are still the domain of the successive approximation register (SAR) and integrating architectures, and more recently, oversampling/sigma-delta ADCs. The highest sampling rates (a few hundred Msps or higher) are still obtained using flash ADCs. Nonetheless, pipelined ADCs of various forms have improved greatly in speed, resolution, dynamic performance, and low power in recent years. Pipelined ADC Architecture In this schematic, the analog input, VIN, is first sampled and held steady by a sample-and-hold (S&H), while the flash ADC in stage one quantizes it to three bits. The 3-bit output is then fed to a 3-bit DAC (accurate to about 12 bits), and the analog output is subtracted from the input. This "residue" is then gained up by a factor of four and fed to the next stage (Stage 2). This gained-up residue continues through the pipeline, providing three bits per stage until it reaches the 4-bit flash ADC, which resolves the last 4LSB bits. Because the bits from each stage are determined at different points in time, all the bits corresponding to the same sample are time-aligned with shift registers before being fed to the digitalerror-correction logic. Note when a stage finishes processing a sample, determining the bits, and passing the residue to the next stage, it can then start processing the next sample received from the sampleand-hold embedded within each stage. This pipelining action is the reason for the high throughput. Data Latency Because each sample must propagate through the entire pipeline before all its associated bits are available for combining in the digital-error-correction logic, data latency is associated with pipelined ADCs. In the example in Figure, this latency is about three cycles. Activities/ Case studies/related to the session NA Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. https://www.design-reuse.com/articles/20284/pipeline-sigma-delta-adc.html 2. https://ieeexplore.ieee.org/document/8509051 3. https://www.sciencedirect.com/science/article/abs/pii/S1434841117321854 SAQ's-Self Assessment Questions 1. What is a pipeline ADC, and how does it differ from other ADC architectures? 2. Explain the concept of a pipeline in the context of a pipeline ADC. 3. What are the key components of a pipeline ADC? 4. How does a pipeline ADC achieve high-speed conversion? 5. What is the role of sample-and-hold circuits in a pipeline ADC? 6. How does the digital error correction mechanism work in a pipeline ADC? 7. What are the advantages of using a pipeline ADC? 8. What are the limitations or challenges associated with pipeline ADCs? 9. How does the resolution of a pipeline ADC depend on the number of pipeline stages? 10. Can a pipeline ADC provide high accuracy and linearity? 11. What is the impact of inter-stage errors on the performance of a pipeline ADC? 12. How does the power consumption of a pipeline ADC compare to other ADC architectures? 13. What are the typical applications of pipeline ADCs? 14. How does the speed of a pipeline ADC relate to the sampling rate? 15. How does the settling time of a sample-and-hold circuit affect the overall performance of a pipeline ADC? 16. What is the role of the digital-to-analog converter (DAC) in a pipeline ADC? 17. Can a pipeline ADC operate with different voltage references for each stage? 18. How does the input bandwidth of a pipeline ADC affect its performance? 19. What techniques are used to mitigate the effects of inter-stage errors in a pipeline ADC? 20. How does the pipeline ADC architecture impact the complexity and cost of the overall system? Summary A pipeline ADC is an analog-to-digital converter that achieves high-speed and high-resolution conversions by breaking down the conversion process into multiple stages. Each stage operates concurrently, processing different portions of the input signal. The stages consist of sample-and- hold circuits, comparators, and digital-to-analog converters (DACs). The input signal is compared to a reference voltage ladder generated by the DACs, and the digital output is determined through a binary search algorithm. The pipeline architecture allows for parallel processing, enabling fast conversion times. However, inter-stage errors and complexity can pose challenges. Pipeline ADCs find applications in digital signal processing, telecommunications, and image sensors, offering a balance of speed, resolution, and power consumption. Terminal Questions 1. Write a short notes on pipelining system 2. Explain the operation of pipeline ADC architecture Case Studies (Co Wise) NA Answer Key 1. General Pipelined System Each stage performs an operation on the signal, provides the output for the following sampler, and, once the sampler has acquired the data, begins the same operation on the next signal.  Different stages process different samplers concurrently.  Throughput rate depends on only the speed of each stage (and the acquisition time of the next sampler). Example: Two-Step Pipelined ADC: General Pipelined ADC 2. Pipelined ADC Architecture In this schematic, the analog input, VIN, is first sampled and held steady by a sample-and-hold (S&H), while the flash ADC in stage one quantizes it to three bits. The 3-bit output is then fed to a 3-bit DAC (accurate to about 12 bits), and the analog output is subtracted from the input. This "residue" is then gained up by a factor of four and fed to the next stage (Stage 2). This gained-up residue continues through the pipeline, providing three bits per stage until it reaches the 4-bit flash ADC, which resolves the last 4LSB bits. Because the bits from each stage are determined at different points in time, all the bits corresponding to the same sample are time-aligned with shift registers before being fed to the digitalerror-correction logic. Note when a stage finishes processing a sample, determining the bits, and passing the residue to the next stage, it can then start processing the next sample received from the sampleand-hold embedded within each stage. This pipelining action is the reason for the high throughput. Glossary Pipeline ADC: A type of analog-to-digital converter that breaks down the conversion process into multiple stages to achieve high-speed and high-resolution conversions. Stage: Each individual block in a pipeline ADC responsible for processing a portion of the input signal. Sample-and-Hold Circuit: A circuit that captures and holds the analog input voltage for a specific period to enable accurate conversion. Comparator: A circuit element that compares two voltages and outputs a digital signal indicating which voltage is higher. Digital-to-Analog Converter (DAC): A circuit that converts digital signals into corresponding analog voltages. Binary Search Algorithm: An algorithm used in pipeline ADCs to iteratively determine the digital representation of the analog input by comparing it to a reference voltage ladder. Resolution: The smallest distinguishable change in the input signal that can be detected and represented by the ADC. Accuracy: The closeness of the measured value to the true value. Linearity: The ability of the ADC to provide a linear relationship between the input signal and the digital output code. Inter-Stage Errors: Errors introduced between different stages of the pipeline ADC, which can affect overall accuracy and linearity. Digital Error Correction: A mechanism used in pipeline ADCs to correct errors introduced by previous stages, improving the overall linearity and accuracy. Power Consumption: The amount of electrical power consumed by the ADC during its operation. Sampling Rate: The rate at which the ADC samples the input signal to capture its digital representation. Settling Time: The time required for the sample-and-hold circuit to settle to a stable voltage level after capturing the input signal. References of books, sites, links 1. https://www.analog.com/en/technical-articles/understanding-pipelined-adcs.html 2. https://inst.eecs.berkeley.edu/~ee247/fa10/files07/lectures/L22_2_f10.pdf 3.https://www.eecis.udel.edu/~vsaxena/courses/ece614/Handouts/Pipelined%20ADC %20Slides%20v1_1.pdf Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Pipeline ADC, Analog-to-Digital Converter, Conversion Stages, Sample-and-Hold Circuit, Comparator, Digital-to-Analog Converter (DAC), Binary Search Algorithm, Resolution, Accuracy, Linearity, Inter-Stage Errors, Digital Error Correction, Power Consumption, Sampling Rate, Settling Time, Input Bandwidth, Complexity, Applications, Pipeline Delay, Voltage Reference SESSION-5 Sigma delta ADC Session Introduction A Sigma-Delta ADC (Analog-to-Digital Converter) is a type of converter that achieves high- resolution conversions by oversampling the analog input signal. It operates on the principle of noise shaping, where the input signal is oversampled at a very high sampling rate. The oversampled signal is then converted to a lower bit rate through a process of decimation. By using a feedback loop and integrating the quantization noise, Sigma-Delta ADCs push the noise energy away from the frequency band of interest, resulting in improved resolution. Sigma-Delta ADCs are commonly used in audio applications, sensors, and other systems where high- resolution and accuracy are required, at the expense of lower conversion speed. Session description One of the more advanced ADC technologies is the so-called delta-sigma, or ΔΣ (using the proper Greek letter notation). In mathematics and physics, the capital Greek letter delta (Δ) represents difference or change, while the capital letter sigma (Σ) represents summation: the adding of multiple terms together. Sometimes this converter is referred to by the same Greek letters in reverse order: sigma-delta, or ΣΔ.In a ΔΣ converter, the analog input voltage signal is connected to the input of an integrator, producing a voltage rate-of-change, or slope, at the output corresponding to input magnitude. This ramping voltage is then compared against ground potential (0 volts) by a comparator.The comparator acts as a sort of 1-bit ADC, producing 1 bit of output (“high” or “low”) depending on whether the integrator output is positive or negative. The comparator’s output is then latched through a D-type flip-flop clocked at a high frequency, and fed back to another input channel on the integrator, to drive the integrator in the direction of a 0 volt output. The basic circuit looks like this: The leftmost op-amp is the (summing) integrator. The next op-amp the integrator feeds into is the comparator, or 1-bit ADC. Next comes the D-type flip-flop, which latches the comparator’s output at every clock pulse, sending either a “high” or “low” signal to the next comparator at the top of the circuit. This final comparator is necessary to convert the single- polarity 0V / 5V logic level output voltage of the flip-flop into a +V / -V voltage signal to be fed back to the integrator. If the integrator output is positive, the first comparator will output a “high” signal to the D input of the flip-flop. At the next clock pulse, this “high” signal will be output from the Q line into the noninverting input of the last comparator. This last comparator, seeing an input voltage greater than the threshold voltage of 1/2 +V, saturates in a positive direction, sending a full +V signal to the other input of the integrator. This +V feedback signal tends to drive the integrator output in a negative direction. If that output voltage ever becomes negative, the feedback loop will send a corrective signal (-V) back around to the top input of the integrator to drive it in a positive direction. This is the delta-sigma concept in action: the first comparator senses a difference (Δ) between the integrator output and zero volts. The integrator sums (Σ) the comparator’s output with the analog input signal. Functionally, this results in a serial stream of bits output by the flip-flop. If the analog input is zero volts, the integrator will have no tendency to ramp either positive or negative, except in response to the feedback voltage. In this scenario, the flip-flop output will continually oscillate between “high” and “low,” as the feedback system “hunts” back and forth, trying to maintain the integrator output at zero volts: Output Waveforms If, however, we apply a negative analog input voltage, the integrator will have a tendency to ramp its output in a positive direction. Feedback can only add to the integrator’s ramping by a fixed voltage over a fixed time, and so the bit stream output by the flip-flop will not be quite the same: By applying a larger (negative) analog input signal to the integrator, we force its output to ramp more steeply in a positive direction. Thus, the feedback system has to output more 1’s than before to bring the integrator output back to zero volts: As the analog input signal increases in magnitude, so does the occurrence of 1’s in the digital output of the flip-flop: A parallel binary number output is obtained from this circuit by averaging the serial stream of bits together. For example, a counter circuit could be designed to collect the total number of 1’s output by the flip-flop in a given number of clock pulses. This count would then be indicative of the analog input voltage. Variations on this theme exist, employing multiple integrator stages and/or comparator circuits outputting more than 1 bit, but one concept common to all ΔΣ converters is that of oversampling. Oversampling is when multiple samples of an analog signal are taken by an ADC (in this case, a 1-bit ADC), and those digitized samples are averaged. The end result is an effective increase in the number of bits resolved from the signal. In other words, an oversampled 1-bit ADC can do the same job as an 8-bit ADC with one-time sampling, albeit at a slower rate. Activities/ Case studies/related to the session 1. Analog-to-digital converters (ADCs). For example, in high-quality audio DACs, Sigma-Delta Modulators are used to convert the digital audio signal into an analog form with high resolution and low distortion. The oversampling technique and noise shaping characteristics of Sigma-Delta Modulators help achieve excellent signal-to-noise ratio (SNR) and dynamic range in audio systems, resulting in high-fidelity sound reproduction. 2. Sensor Interface: Sigma-Delta Modulators find applications in sensor interface circuits, where they are used to convert analog sensor signals into digital form for processing. One example is in pressure sensors, where Sigma-Delta Modulators are employed to digitize the sensor's analog output. The modulator's high resolution and ability to handle small signal variations make it suitable for accurate measurement and monitoring of pressure levels. Sigma-Delta Modulators also provide built-in noise rejection capabilities, making them robust against external noise sources and interference. Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. https://www.analog.com/en/technical-articles/behind-the-sigma-delta-adc- topology.html 2. https://www.mdpi.com/1424-8220/20/18/5309 3. https://ieeexplore.ieee.org/document/8227915 SAQ's-Self Assessment Questions 1. What is a Sigma-Delta ADC, and how does it differ from other ADC architectures? 2. How does oversampling contribute to the performance of a Sigma-Delta ADC? 3. What is the purpose of the modulator in a Sigma-Delta ADC? 4. Explain the concept of noise shaping in a Sigma-Delta ADC. 5. How does a Sigma-Delta ADC achieve high resolution? 6. What are the advantages of using a Sigma-Delta ADC? 7. What is the role of decimation in a Sigma-Delta ADC? 8. Can a Sigma-Delta ADC be used for both analog-to-digital and digital-to-analog conversion? 9. How does the order of a Sigma-Delta modulator affect its performance? 10. What is the impact of the oversampling ratio on the performance of a Sigma-Delta ADC? 11. How does a Sigma-Delta ADC handle quantization noise? 12. Can a Sigma-Delta ADC provide linear and accurate conversion? 13. What are the typical applications of Sigma-Delta ADCs? 14. How does the power consumption of a Sigma-Delta ADC compare to other ADC architectures? 15. What is the trade-off between conversion speed and resolution in a Sigma-Delta ADC? 16. What are the potential sources of non-linearity in a Sigma-Delta ADC? 17. How does the input bandwidth of a Sigma-Delta ADC affect its performance? 18. What are the challenges in designing a Sigma-Delta ADC for high-frequency applications? 19. How does the digital filter design impact the performance of a Sigma-Delta ADC? 20. Can a Sigma-Delta ADC handle multiple input channels simultaneously? Summary A Sigma-Delta ADC (Analog-to-Digital Converter) is a type of converter that achieves high- resolution digital conversions by oversampling the input signal. It utilizes a modulator to continuously convert the analog signal into a high-frequency stream of 1-bit digital data. This data is then filtered and decimated to obtain the desired digital output. The oversampling and noise shaping techniques employed by Sigma-Delta ADCs allow for improved resolution and high signal-to-noise ratio, making them suitable for applications requiring precise measurements and high fidelity, such as audio systems and sensor interfaces. Sigma-Delta ADCs offer advantages in terms of simplicity, low cost, and suitability for low-frequency or moderate-speed applications. Terminal Questions 1. With neat sketch explain the operation of sigma delta ADC 2. List the major components of sigma delta modulator Case Studies (Co Wise) NA Answer Key 1. One of the more advanced ADC technologies is the so-called delta-sigma, or ΔΣ (using the proper Greek letter notation). In mathematics and physics, the capital Greek letter delta (Δ) represents difference or change, while the capital letter sigma (Σ) represents summation: the adding of multiple terms together. Sometimes this converter is referred to by the same Greek letters in reverse order: sigma-delta, or ΣΔ.In a ΔΣ converter, the analog input voltage signal is connected to the input of an integrator, producing a voltage rate-of-change, or slope, at the output corresponding to input magnitude. This ramping voltage is then compared against ground potential (0 volts) by a comparator.The comparator acts as a sort of 1-bit ADC, producing 1 bit of output (“high” or “low”) depending on whether the integrator output is positive or negative. The comparator’s output is then latched through a D-type flip-flop clocked at a high frequency, and fed back to another input channel on the integrator, to drive the integrator in the direction of a 0 volt output. The basic circuit looks like this: 2. A Sigma-Delta ADC (Analog-to-Digital Converter) consists of several key components that work together to achieve high-resolution conversions. The major components of a Sigma-Delta ADC include: Modulator: The modulator is a crucial component of the Sigma-Delta ADC. It takes the analog input signal and converts it into a stream of 1-bit digital data. The modulator utilizes oversampling and noise shaping techniques to push the quantization noise out of the frequency band of interest. Integrator: The integrator is responsible for integrating the analog input signal over a specific period of time. It helps in removing high-frequency noise and enhances the overall resolution of the ADC. Feedback Loop: The feedback loop connects the output of the modulator to the input of the integrator. It enables the Sigma-Delta ADC to continuously adjust the integrator's output based on the difference between the actual signal and the feedback signal. This feedback mechanism helps in achieving high linearity and accuracy. Digital Filter: After the modulator, the 1-bit digital data undergoes digital filtering. The digital filter removes the quantization noise and shapes the noise spectrum to further improve the ADC's resolution and signal-to-noise ratio. Decimator: The decimator is responsible for reducing the sample rate of the digital data stream. It discards redundant data and performs downsampling, resulting in a lower output data rate with the desired resolution. Digital-to-Analog Converter (DAC): In some cases, a DAC may be included in the Sigma-Delta ADC to convert the digital output into an analog signal for further processing or usage. Glossary Sigma-Delta Modulator: A key component of a Sigma-Delta ADC, responsible for converting analog signals into a stream of 1-bit digital data. Oversampling: The process of sampling the analog input signal at a much higher rate than the Nyquist rate, allowing for improved resolution and noise performance. Noise Shaping: A technique employed by Sigma-Delta Modulators to push the quantization noise out of the frequency band of interest, resulting in enhanced dynamic range and signal-to- noise ratio. Quantization Noise: The error introduced when an analog signal is converted into a digital representation with limited bit-depth, typically in the form of random variations. Feedback Loop: The connection between the output of the modulator and its input, allowing the modulator to continuously adjust its operation based on the difference between the actual signal and the feedback signal. Integrator: A component that performs the integration of the analog input signal, smoothing out high-frequency noise and enhancing the resolution of the ADC. Order: The number of integrators in a Sigma-Delta Modulator, indicating the complexity and performance of the modulator. Digital Filter: A component in the Sigma-Delta Modulator that processes the 1-bit digital data stream, shaping the noise spectrum and removing unwanted high-frequency components. Decimation: The process of reducing the sample rate of the digital data stream, discarding redundant data to achieve the desired output data rate. References of books, sites, links 1. https://www.analog.com/en/technical-articles/behind-the-sigma-delta-adc- topology.html 2. https://www.stg-maximintegrated.com/en/design/technical-documents/tutorials/ 1/1870.html 3. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1795&context=etd Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Sigma-Delta ADC, Oversampling, Noise Shaping, Quantization Noise, Feedback Loop, Modulator, Integrator, Order, Digital Filter, Decimation, Digital-to-Analog Converter (DAC) Dynamic Range, Signal-to-Noise Ratio (SNR), Resolution, Linearity, Nyquist Rate, Sampling Rate, Bit stream, Aliasing, Anti-aliasing Filter. SESSION-6 Digital to analog converter Session Introduction A Digital-to-Analog Converter (DAC) is a device that converts digital signals into analog voltage or current outputs. It plays a crucial role in digital systems where digital data needs to be transformed into continuous analog signals for various applications. The DAC receives a binary digital input and generates a corresponding analog output that represents the magnitude of the input value. This conversion is achieved through various techniques such as resistor networks, current steering, or sigma-delta modulation. DACs are commonly used in audio systems, telecommunications, instrumentation, and control systems, enabling digital devices to interface with the analog world and accurately reproduce continuous signals for smooth and precise operation. Session description Digital to analog converter is an electronic circuit that converts any digital signal (such as binary signal) into an analog signal (voltage or current). The digital signal such as the binary signal exist in the form of bits & it is the combination of 1’s & 0’s (or High & low voltage levels). The DAC converts these bits into an analog voltage or current. Working of DAC The digital binary data exists in the form of bits. Each bit is either 1 or 0 & they represent its weight corresponding to its position. The weight is 2n where the n is the position of the bit from right hand side & it start from 0. Bit Weight = 2n Bit weight of 4th bit from left= 2n = 23 = 8 The bit weight is multiplied by the bit value. Since the bit could be either 0 or 1, it means; Bit value of 1 x bit weight = 1 x 2n = 2n Bit value of 0 x bit weight = 0 x 2(n-1) = 0 Now adding the weights of all the bits with its value in a binary number 10011; 1 00112 = (1 x 24) + (0 x 23) + (0 x 22) + (1 x 21) + (1 x 20) 100112 = 16 + 0 + 0 + 2 + 1 100112 = 19 This is how the digital to analog converter DAC works by adding the weights of all corresponding bits with its value to generate the analog value at its output. Types of DAC The DAC can be designed using one of the following types of circuits. Weighted Resistor Method The weighted resistor method utilizes the summing operational amplifier circuit. The summing amplifier adds the input signals with different gains corresponding to their resistors R-2R Ladder Circuit This method is more precise, accurate & easy to design then the weighted resistor method. R- 2R ladder circuit is made by adding combination R & 2R resistor in cascaded form as shown in the following figure. PWM Based Conversion It is another method used in digital to analog converter & microcontrollers such as Arduino can be easily programmed to utilize its PWM function to generate an analog output. Pulse Width Modulation or PWM is a method of varying the average power of a signal by varying its duty cycle. He duty is the % turn on time of the signal, the % amount of time for which the signal remains high. Like 40% duty cycle signal means it stays high for 40% of time & stays low for 60%. We can use a binary number to generate such type signal whose duty cycle depends on the binary digit. The PWM wave is the filtered using a low pass filter to remove the fluctuations & provide a smooth analog voltage. The low pass filter used can be a first order. 2nd order low pass filter would be a great choice for a PWM base digital to analog converter. Activities/ Case studies/related to the session NA Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. Digital-to-Analog Converter - an overview | ScienceDirect Topics 2. The evolution of digital to analog converter | IEEE Conference Publication | IEEE Xplore 3. What is a Digital to Analog Converter? How Does a DAC work? | Arrow.com | Arrow.com SAQ's-Self Assessment Questions 1. What is a digital-to-analog converter (DAC)? 2. What is the purpose of a DAC in electronic systems? 3. What are the two common types of DAC architectures? 4. How does a binary-weighted DAC work? 5. How does an R-2R ladder DAC function? 6. What is the difference between a current output DAC and a voltage output DAC? 7. What are the key parameters to consider when selecting a DAC? 8. What is the resolution of a DAC, and how is it determined? 9. What is the settling time of a DAC? 10. How does the linearity of a DAC affect its performance? 11. What is the concept of integral non-linearity (INL) in a DAC? 12. What is differential non-linearity (DNL) in a DAC? 13. What are the main applications of DACs in real-world systems? 14. What is the significance of the DAC's reference voltage? 15. How does the choice of sampling rate impact DAC performance? 16. What is the concept of oversampling in DACs? 17. What is the difference between a single-ended DAC and a differential DAC? 18. How does a sigma-delta DAC work? 19. What are the advantages and disadvantages of a flash DAC? 20. What are some common sources of errors in DACs, and how can they be minimized? Summary A digital-to-analog converter (DAC) is an essential component in electronic systems that converts digital signals into continuous analog signals. It enables the translation of discrete digital data into a smooth, varying voltage or current output. DACs come in different architectures, such as binary-weighted and R-2R ladder, each with its advantages and trade-offs. Key considerations when selecting a DAC include resolution, settling time, linearity, and reference voltage. DACs find applications in audio equipment, telecommunications, control systems, and more. They play a crucial role in transforming digital information into analog form for accurate representation, enabling seamless communication and interaction between digital devices and the analog world. Terminal Questions 1. Explain the working of digital to analog converters 2. List the types of D/A converters and explain Case Studies (Co Wise) NA Answer Key 1. The digital binary data exists in the form of bits. Each bit is either 1 or 0 & they represent its weight corresponding to its position. The weight is 2n where the n is the position of the bit from right hand side & it start from 0. Bit Weight = 2n Bit weight of 4th bit from left= 2n = 23 = 8 The bit weight is multiplied by the bit value. Since the bit could be either 0 or 1, it means; Bit value of 1 x bit weight = 1 x 2n = 2n Bit value of 0 x bit weight = 0 x 2(n-1) = 0 Now adding the weights of all the bits with its value in a binary number 10011; 1 00112 = (1 x 24) + (0 x 23) + (0 x 22) + (1 x 21) + (1 x 20) 100112 = 16 + 0 + 0 + 2 + 1 100112 = 19 This is how the digital to analog converter DAC works by adding the weights of all corresponding bits with its value to generate the analog value at its output. 2. The DAC can be designed using one of the following types of circuits. Weighted Resistor Method The weighted resistor method utilizes the summing operational amplifier circuit. The summing amplifier adds the input signals with different gains corresponding to their resistors R-2R Ladder Circuit This method is more precise, accurate & easy to design then the weighted resistor method. R- 2R ladder circuit is made by adding combination R & 2R resistor in cascaded form as shown in the following figure. PWM Based Conversion It is another method used in digital to analog converter & microcontrollers such as Arduino can be easily programmed to utilize its PWM function to generate an analog output. Pulse Width Modulation or PWM is a method of varying the average power of a signal by varying its duty cycle. He duty is the % turn on time of the signal, the % amount of time for which the signal remains high. Like 40% duty cycle signal means it stays high for 40% of time & stays low for 60%. Glossary Digital-to-analog converter (DAC): A device that converts digital signals into analog signals. Analog output: The continuous, varying voltage or current output produced by a DAC. Binary-weighted DAC: A type of DAC architecture where the input digital bits are weighted based on their binary value. R-2R ladder DAC: A type of DAC architecture that utilizes a ladder network of resistors to convert digital inputs into analog outputs. Current output DAC: A DAC that produces an analog output in the form of a current signal. Voltage output DAC: A DAC that generates an analog output as a varying voltage level. Resolution: The number of distinct output levels that a DAC can produce, typically specified in bits. Settling time: The time required for the output of a DAC to stabilize within a specified tolerance after a change in the digital input. Linearity: The degree to which the output of a DAC accurately follows the ideal linear relationship with the input. Integral non-linearity (INL): The measure of deviation from the ideal transfer function of a DAC, usually expressed in LSB (Least Significant Bit). Differential non-linearity (DNL): The measure of the difference between the ideal step size and the actual step size of a DAC. Reference voltage: The voltage against which the digital input is converted into an analog output in a DAC. Sampling rate: The rate at which the digital input is sampled and converted into analog values in a DAC. Oversampling: A technique where the sampling rate of a DAC is higher than the Nyquist rate to improve the signal quality. Single-ended DAC: A DAC that has a single output channel. Differential DAC: A DAC that has two output channels that produce the differential analog output. Sigma-delta DAC: A type of DAC that uses a sigma-delta modulation technique to achieve high resolution and low noise performance. Flash DAC: A type of DAC architecture that uses a combination of comparators and a resistor ladder to directly convert the digital input to an analog output. Error sources: Various factors, such as noise, non-ideal components, and imperfections in the DAC circuitry, that can introduce errors in the analog output of a DAC. Calibration: The process of adjusting the DAC's output to compensate for errors and improve its accuracy and performance. References of books, sites, links 1. DIgital to Analog Converter (DAC) Architecture and its Applications (elprocus.com) 2. https://easyelectronics.co.in/digital-to-analog-converter/ 3. Digital to Analog Converter | What is DAC, its Types, specification and Application - Easy Electronics Text Books: 1. Robert L. Boylestad and Louis Nashelsky - “Electronic Devices and Circuit Theory”, 7th Edition, Prentice Hall Publication (1998). 2.Ramakanth A. Gaykwad – “Op-Amps and Linear IC Applications”, 4 th Edition, Pearson Education (2015) 3. Thomas L. Floyd – “Electronic Devices – Electron Flow Version”, 4th Edition, Pearson Education (2001) 4. A.S. Sedra&K.C.Smith, Microelectronics Circuits, 7th Edition, Oxford University Press (2014) Reference Books: 1. Jacob Millman - “Electronic Devices and Circuits”, 4th Edition, McGraw Hill Education (2015) 2. D Roy Choudhury and Shail B. Jain – “Linear Integrated Circuits”, 4 th Edition, New Age International Pvt.Ltd. (2017) 3. David A. Bell - “Electronic Devices and Circuits”, 5th Edition, Oxford University Press (2008) 4. Behzad Razavi – “Design of Analog CMOS Integrated Circuit”,2 nd Edition, McGraw Hill Education (2017) 5. M. S. Tyagi “Introduction to Semiconductor Materials and Devices”, 2 nd Edition, John Wiley & Sons Inc (2008) 17. Keywords Digital-to-analog converter, DAC, Analog output, Binary-weighted DAC, R-2R ladder DAC Current output DAC, Voltage output DAC, Resolution, Settling time, Linearity, Integral non- linearity (INL), Differential non-linearity (DNL), Reference voltage, Sampling rate, Oversampling, Single-ended DAC, Differential DAC, Sigma-delta DAC, Flash DAC, Error sources SESSION-7 Binary weighted resistor DAC Session Introduction The binary-weighted resistor DAC is a popular architecture used in digital-to-analog converters (DACs) to convert digital signals into analog voltages. It employs a network of resistors, with each resistor's value determined by a binary weighting scheme. The input digital bits control switches connected to the resistors, selectively allowing current to flow through them. The output voltage is generated by the weighted sum of the currents through the activated resistors. Binary weighted resistor DACs offer high-speed operation, good linearity, and relatively simple circuitry. They find applications in audio processing, waveform generation, and communication systems, where accurate and fast conversion of digital data to analog voltages is essential. Session description Binary-Weighted Resistor DAC The binary-weighted-resistor DAC employs the characteristics of the inverting summer Op Amp circuit. In this type of DAC, the output voltage is the inverted sum of all the input voltages. If the input resistor values are set to multiples of two: 1R, 2R and 4R, the output voltage would be equal to the sum of V1, V2/2 and V3/4. V1 corresponds to the most significant bit (MSB) while V3 corresponds to the least significant bit (LSB). The circuit for a 4-bit DAC using binary weighted resistor network is shown below: The binary inputs, ai (where i = 1, 2, 3 and 4) have values of either 0 or 1. The value, 0, represents an open switch while 1 represents a closed switch. The operational amplifier is used as a summing amplifier, which gives a weighted sum of the binary input based on the voltage, Vref. For a 4-bit DAC, the relationship between Vout and the binary input is as follows: The negative sign associated with the analog output is due to the connection to a summing amplifier, which is a polarity-inverting amplifier. When a signal is applied to the latter type of amplifier, the polarity of the signal is reversed (i.e. a + input becomes -, or vice versa). For a n-bit DAC, the relationship between Vout and the binary input is as follows: The LSB, which is also the incremental step, has a value of - 0.625 V while the MSB or the full scale has a value of - 9.375 V. Practical Limitations: The most significant problem is the large difference in resistor values required between the LSB and MSB, especially in the case of high resolution DACs (i.e. those that has large number of bits). For example, in the case of a 12-bit DAC, if the MSB is 1 k Ω, then the LSB is a staggering 2 MΩ. The maintenance of accurate resistances over a large range of values is problematic. With the current IC fabrication technology, it is difficult to manufacture resistors over a wide resistance range that maintains an accurate ratio especially with variations in temperature. Activities/ Case studies/related to the session Case study Waveform Generation in Function Generators A function generator employed a binary weighted resistor DAC to generate precise analog waveforms. The DAC received digital input data representing the desired waveform shape and amplitude. The binary weighting scheme in the DAC was tailored to achieve accurate voltage levels corresponding to different digital input codes. By selectively activating the appropriate resistors, the DAC accurately reconstructed the desired waveform with high fidelity. The binary weighted resistor DAC enabled the function generator to produce a wide range of waveforms, including sine, square, triangle, and arbitrary waveforms, meeting the requirements of various test and measurement applications. Examples & contemporary extracts of articles/ practices to convey the idea of the session 1. Microsoft Word - str_0501-0509 (radioeng.cz) 2. igntu.ac.in/eContent/BScPhysics-4Sem-MrrajeshKumar.pdf 3. Design of binary weighted DAC for asynchronous ADC with improved slew rate and with calibrated size of capacitors - Extrica SAQ's-Self Assessment Questions 1. What is a binary weighted resistor DAC? 2. How does a binary weighted resistor DAC convert digital signals into analog voltages? 3. What is the purpose of using a binary weighting scheme in a DAC? 4. How does the value of each resistor in a binary weighted resistor DAC relate to the binary weight of its corresponding bit? 5. What advantages does a binary weighted resistor DAC offer in terms of linearity and accuracy? 6. How does the activation of specific resistors in a binary weighted resistor DAC affect the generated analog voltage? 7. What are the limitations of binary weighted resistor DACs? 8. How is the resolution of a binary weighted resistor DAC determined? 9. What considerations are important when selecting the resistor values for a binary weighted resistor DAC? 10. What are the typical applications of binary weighted resistor DACs? 11. How does the number of bits in the digital input affect the performance of a binary weighted resistor DAC? 12. What challenges are involved in manufacturing a high-resolution binary weighted resistor DAC? 13. How does the settling time of a binary weighted resistor DAC impact its performance? 14. Can a binary weighted resistor DAC provide a continuous range of analog voltages? 15. What measures can be taken to improve the linearity of a binary weighted resistor DAC? 16. How does temperature affect the performance of a binary weighted resistor DAC? 17. What role does the voltage reference play in a binary weighted resistor DAC? 18. What are the trade-offs between speed and accuracy in a binary weighted resistor DAC? 19. How does noise impact the performance of a binary weighted resistor DAC? 20. Are there alternative DAC architectures that can overcome the limitations of binary weighted resistor DACs? Summary A binary weighted resistor DAC is a type of digital-to-analog converter that converts digital signals into analog voltages using a network of resistors with binary weighting. Each resistor's value corresponds to a specific binary weight. By selectively activating the resistors based on the digital input bits, the DAC generates an analog voltage proportional to the weighted sum of the activated resistors. Binary weighted resistor DACs offer advantages such as good linearity, simplicity, and high-speed operation. They find applications in audio processing, waveform generation, instrumentation systems, and more. With their ability to accurately convert digital data into analog voltages, binary weighted resistor DACs play a crucial role in various electronic systems requiring precise analog outputs. Terminal Questions 1. Explain the working of Weighted resister DAC 2. Compare binary weighted DAC with R-2R DAC Case Studies (Co Wise) NA Answer Key 1. The binary-weighted-resistor DAC employs the characteristics of the inverting summer Op Amp circuit. In this type of DAC, the output voltage is the inverted sum of all the input voltages. If the input resistor values are set to multiples of two: 1R, 2R and 4R, the output voltage would be equal to the sum of V1, V2/2 and V3/4. V1 corresponds to the most significant bit (MSB) while V3 corresponds to the least significant bit (LSB). The circuit for a 4-bit DAC using binary weighted resistor network is shown below: The binary inputs, ai (where i = 1, 2, 3 and 4) have values of either 0 or 1. The value, 0, represents an open switch while 1 represents a closed switch. The operational amplifier is used as a summing amplifier, which gives a weighted sum of the binary input based on the voltage, Vref. For a 4-bit DAC, the relationship between Vout and the binary input is as follows:

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