2025 question paper

Signal Conditioning and Data Acquisition System

26 questions

  1. Q1(a). Data acquisition (DAQ) system is primarily used for: (i) Data storage (ii) Converting physical quantities into digital data (iii) Wireless communication (iv) Power amplification2025?m

    Module 1: Introduction

    Data acquisition (DAQ) system is primarily used for:
    (i) Data storage
    (ii) Converting physical quantities into digital data
    (iii) Wireless communication
    (iv) Power amplification

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    Worked Solution

    Answer

    Correct option: (ii) Converting physical quantities into digital data

    Explanation

    A Data Acquisition (DAQ) system collects real-world physical signals and converts them into a form that a computer or microcontroller can process.

    A typical DAQ sequence is:

    Physical quantity → Sensor → Signal Conditioning → ADC → Digital Data → Processing/Storage

    For example, a temperature sensor produces an electrical signal corresponding to temperature. The signal is conditioned if required and then converted into a digital value by an Analog-to-Digital Converter (ADC).

    Why the other options are incorrect

    • (i) Data storage: Storage may be included in a DAQ system, but it is not its primary purpose.
    • (iii) Wireless communication: Wireless communication may be used for transmitting acquired data, but it is not the fundamental purpose of DAQ.
    • (iv) Power amplification: Power amplification is not the primary function of a DAQ system.

    Therefore, the correct answer is (ii).

  2. Q1(b). Signal conditioning is required to: (i) Improve computer speed (ii) Modify the sensor signal for ADC (iii) Reduce sampling time (iv) Increase AC voltage2025?m

    Module 2: Signal Conditioning Systems

    Signal conditioning is required to:
    (i) Improve computer speed
    (ii) Modify the sensor signal for ADC
    (iii) Reduce sampling time
    (iv) Increase AC voltage

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    Worked Solution

    Answer

    Correct option: (ii) Modify the sensor signal for ADC

    Explanation

    Signal conditioning prepares a raw sensor signal so that it is suitable for accurate measurement and conversion by an ADC.

    Common signal-conditioning operations include:

    • Amplification – increases a weak sensor signal.
    • Filtering – removes unwanted noise and interference.
    • Isolation – protects circuits and reduces ground-loop problems.
    • Linearization – improves the relationship between sensor output and measured quantity.
    • Level shifting – adjusts the signal to the ADC input range.

    For example, if a sensor produces 0–100 mV while an ADC accepts 0–5 V, an amplifier can increase the sensor signal before conversion.

    Therefore, the correct answer is (ii).

  3. Q1(c). Filtering is mainly used to remove: (i) Useful signals (ii) High-frequency noise (iii) DC (iv) Mechanical vibrations2025?m

    Module 2: Signal Conditioning Systems

    Filtering is mainly used to remove:
    (i) Useful signals
    (ii) High-frequency noise
    (iii) DC
    (iv) Mechanical vibrations

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    Worked Solution

    Answer

    Correct option: (ii) High-frequency noise

    Explanation

    A filter is a signal-conditioning circuit that allows desired frequency components to pass while attenuating unwanted frequency components.

    In DAQ systems, filters are commonly used to remove high-frequency noise, electrical interference and other unwanted components before the signal reaches the ADC.

    For example, a low-pass filter allows low-frequency measurement signals to pass while reducing high-frequency noise.

    Importance in DAQ

    Filtering improves:

    1. Signal quality.
    2. Measurement accuracy.
    3. ADC performance.
    4. Resistance to unwanted interference.
    5. Protection against aliasing when used as an anti-aliasing filter before sampling.

    Therefore, the correct answer is (ii).

  4. Q1(d). A first-order filter consists of: (i) One resistor and one capacitor (ii) Two inductors (iii) Operational amplifier only (iv) A transformer2025?m

    Module 2: Signal Conditioning Systems

    A first-order filter consists of:
    (i) One resistor and one capacitor
    (ii) Two inductors
    (iii) Operational amplifier only
    (iv) A transformer

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    Worked Solution

    Answer

    Correct option: (i) One resistor and one capacitor

    Explanation

    A basic first-order RC filter is made using one resistor and one capacitor. It has one energy-storage element and therefore has a roll-off of approximately 20 dB/decade beyond its cutoff frequency.

    For a simple RC low-pass filter, the cutoff frequency is:

    fc=12πRCf_c = \frac{1}{2\pi RC}

    Below the cutoff frequency, the signal passes with relatively little attenuation. Above the cutoff frequency, higher-frequency components are increasingly attenuated.

    Therefore, the correct answer is (i).

  5. Q1(e). Which of the following is NOT part of a typical microcontroller? (i) CPU (ii) RAM (iii) I/O Ports (iv) Hard Disk2025?m

    Module 3: Embedded Microcontrollers – PIC18F / Others

    Which of the following is NOT part of a typical microcontroller?
    (i) CPU
    (ii) RAM
    (iii) I/O Ports
    (iv) Hard Disk

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    Worked Solution

    Answer

    Correct option: (iv) Hard Disk

    Explanation

    A typical microcontroller integrates essential computing and control resources on a single chip, such as:

    • CPU: Executes program instructions.
    • RAM: Temporarily stores variables and runtime data.
    • I/O ports: Interface with sensors, actuators and external devices.
    • Timers/counters: Generate timing functions and count events.
    • Peripherals: May include ADC, communication interfaces, PWM and other modules.

    A hard disk is a separate mass-storage device and is not normally an integrated component of a microcontroller.

    Therefore, the correct answer is (iv).

  6. Q1(f). A timer in a microcontroller counts: (i) External pulses only (ii) Internal clock pulses (iii) Code instructions (iv) Data bytes2025?m

    Module 3: Embedded Microcontrollers – PIC18F / Others

    A timer in a microcontroller counts:
    (i) External pulses only
    (ii) Internal clock pulses
    (iii) Code instructions
    (iv) Data bytes

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    Worked Solution

    Answer

    Correct option: (ii) Internal clock pulses

    Explanation

    A timer in a microcontroller is generally driven by the internal system clock or a clock derived from it. It increments its count at regular intervals and is used for generating delays, measuring time intervals, scheduling tasks and producing periodic events.

    A counter can instead be configured to count external events or pulses.

    Example

    If a timer receives a 1 MHz clock, one clock period is:

    T=11MHz=1μsT = \frac{1}{1\,MHz} = 1\,\mu s

    The timer can therefore measure time by counting these clock periods.

    Therefore, the correct answer is (ii).

  7. Q1(g). RISC microcontrollers are characterized by: (i) Many complex instructions (ii) Simple and fast instructions (iii) No registers (iv) Only analog operations2025?m

    Module 3: Embedded Microcontrollers – PIC18F / Others

    RISC microcontrollers are characterized by:
    (i) Many complex instructions
    (ii) Simple and fast instructions
    (iii) No registers
    (iv) Only analog operations

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    Worked Solution

    Answer

    Correct option: (ii) Simple and fast instructions

    Explanation

    RISC (Reduced Instruction Set Computer) microcontrollers use a relatively small and simple instruction set. Instructions are designed to execute efficiently, often in a small number of clock cycles.

    Main characteristics of RISC

    • Small and simple instruction set.
    • Fast instruction execution.
    • Large or efficient register usage.
    • Simple instruction formats.
    • Efficient pipelining in many architectures.
    • Suitable for embedded real-time applications.

    This approach makes the processor easier to implement and can provide high performance for a given clock frequency.

    Therefore, the correct answer is (ii).

  8. Q1(h). A microcontroller-based DAQ system mainly performs: (i) Data storage only (ii) Conversion of physical signals into digital form (iii) Power amplification (iv) Battery charging2025?m

    Module 4: DAQ Systems

    A microcontroller-based DAQ system mainly performs:
    (i) Data storage only
    (ii) Conversion of physical signals into digital form
    (iii) Power amplification
    (iv) Battery charging

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    Worked Solution

    Answer

    Correct option: (ii) Conversion of physical signals into digital form

    Explanation

    A microcontroller-based DAQ system acquires signals from sensors and converts them into digital values for processing.

    The typical sequence is:

    Sensor → Signal Conditioning → ADC → Microcontroller → Processing/Storage/Communication

    For example, an analog temperature sensor may produce 0–5 V. The ADC inside or connected to the microcontroller converts this voltage into a digital code, which the microcontroller can use to calculate temperature.

    Therefore, the correct answer is (ii).

  9. Q1(i). The main objective of data processing is to: (i) Reduce microcontroller load (ii) Extract meaningful insights (iii) Increase clock frequency (iv) Improve battery capacity2025?m

    Module 5: Data Processing

    The main objective of data processing is to:
    (i) Reduce microcontroller load
    (ii) Extract meaningful insights
    (iii) Increase clock frequency
    (iv) Improve battery capacity

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    Worked Solution

    Answer

    Correct option: (ii) Extract meaningful insights

    Explanation

    Data processing converts raw acquired data into useful information that can be interpreted or used for decision-making.

    Typical processing operations include:

    • Data cleaning and removal of invalid values.
    • Noise reduction and filtering.
    • Calibration and scaling.
    • Averaging and statistical calculations.
    • Feature extraction.
    • Conversion into engineering units.
    • Preparation of data for visualization or control.

    For example, raw vibration samples can be processed to calculate RMS vibration, peak amplitude or frequency components, helping identify a machine fault.

    Therefore, the correct answer is (ii).

  10. Q1(j). Which of the following is not a data storage device used in embedded systems? (i) EEPROM (ii) SRAM (iii) SD card (iv) Transformer2025?m

    Module 5: Data Processing

    Which of the following is not a data storage device used in embedded systems?
    (i) EEPROM
    (ii) SRAM
    (iii) SD card
    (iv) Transformer

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    Worked Solution

    Answer

    Correct option: (iv) Transformer

    Explanation

    Embedded systems commonly use different types of memory and storage devices, including:

    • EEPROM: Non-volatile memory used for storing configuration data and calibration values.
    • SRAM: Fast volatile memory used for variables and temporary runtime data.
    • SD card: Removable non-volatile storage suitable for large amounts of logged data.

    A transformer is an electrical power/isolating component. It is not a data-storage device.

    Therefore, the correct answer is (iv).

  11. Q2(a). Explain the architecture and working of a Data Acquisition System (DAQ).20257m

    Module 1: Introduction

    Explain the architecture and working of a Data Acquisition System (DAQ).

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    Worked Solution

    Solution: Architecture and Working of a Data Acquisition System (DAQ)

    Definition

    A Data Acquisition System (DAQ) is a system used to collect physical measurements from the real world, convert them into electrical and digital signals, process the acquired data, and finally display, store, or transmit the information.

    Examples include temperature measurement, vibration monitoring, motor-speed measurement and heart-rate monitoring.

    Basic Block Diagram

    Physical Quantity
           ↓
    Sensor / Transducer
           ↓
    Signal Conditioning
           ↓
    Multiplexer (for multiple channels)
           ↓
    Sample & Hold
           ↓
    ADC
           ↓
    Microcontroller / Computer
           ↓
    Processing → Storage → Display / Communication / Control
    

    Main Components

    1. Sensor / Transducer

    Converts a physical quantity such as temperature, pressure, displacement or heart rate into an electrical signal.

    2. Signal Conditioning

    Prepares the sensor output for digitization. It may involve:

    • Amplification
    • Filtering
    • Isolation
    • Linearization
    • Level shifting

    3. Multiplexer

    In a multichannel DAQ, a multiplexer selects one input channel at a time and sends it to the acquisition path.

    4. Sample-and-Hold

    Samples the analog signal and holds its value constant during ADC conversion when required by the ADC architecture.

    5. ADC

    The Analog-to-Digital Converter converts the conditioned analog voltage into a digital number. For an ideal nn-bit ADC with input range VFSV_{FS}, the approximate LSB size is:

    LSB=VFS2nLSB = \frac{V_{FS}}{2^n}

    6. Microcontroller / Computer

    Processes the digital samples, performs calculations and may execute control algorithms.

    7. Storage and Display

    Data can be stored in memory, SD cards or a computer and presented as numerical values, graphs or reports.

    Working

    1. The physical parameter is measured by a sensor.
    2. The sensor produces an electrical signal.
    3. Signal conditioning amplifies, filters and scales the signal.
    4. The multiplexer selects a channel when multiple sensors are present.
    5. The signal is sampled and converted into digital form by the ADC.
    6. The microcontroller or computer processes the digital samples.
    7. The resulting information is stored, displayed, transmitted or used for automatic control.

    Single-Channel and Multichannel DAQ

    Type Description
    Single-channel Acquires data from one sensor/input.
    Multichannel Acquires data from several sensors/inputs using multiplexing or multiple ADC channels.

    Applications

    • Temperature data logging
    • Motor-speed monitoring
    • Industrial process control
    • Vibration monitoring
    • Heart-rate monitoring
    • Environmental monitoring
    • Biomedical instrumentation

    Conclusion

    A DAQ system forms the complete measurement chain from physical quantity → sensor → signal conditioning → ADC → digital processing → storage/display/control. Its accuracy depends on sensor quality, conditioning, sampling rate, ADC resolution and proper noise reduction.

  12. Q2(b). Describe the signal conditioning process in a DAQ system and explain how it is used in real-time applications.20257m

    Module 2: Signal Conditioning Systems

    Describe the signal conditioning process in a DAQ system and explain how it is used in real-time applications.

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    Worked Solution

    Solution: Signal Conditioning Process and Real-Time Applications

    Definition

    Signal conditioning is the process of modifying a sensor's raw electrical output so that it becomes suitable for accurate measurement, analog-to-digital conversion, processing, and control.

    A typical chain is:

    Sensor → Amplification → Filtering → Isolation / Linearization → ADC → Processor
    

    Why Signal Conditioning is Required

    Sensor outputs are often:

    • Very small in amplitude.
    • Noisy.
    • Non-linear.
    • Outside the input range of the ADC.
    • Sensitive to electrical interference.
    • Referenced to a different ground potential.

    Signal conditioning solves these problems before digitization.

    Major Signal-Conditioning Operations

    1. Amplification

    A weak sensor signal is amplified to use the available ADC input range effectively.

    For an amplifier:

    Vout=GVinV_{out}=G V_{in}

    where GG is the voltage gain.

    2. Filtering

    Filters remove unwanted frequency components and noise.

    A low-pass filter is commonly placed before an ADC to remove high-frequency noise and prevent aliasing.

    For a first-order RC low-pass filter:

    fc=12πRCf_c=\frac{1}{2\pi RC}

    3. Isolation

    Isolation electrically separates the sensor side from the measurement electronics. It helps protect circuits and reduce ground-loop interference.

    Common techniques include transformers, opto-isolators and isolation amplifiers.

    4. Linearization

    Some sensors have non-linear output characteristics. Linearization converts the sensor response into a more useful relationship with the measured physical quantity.

    This may be performed using analog circuits or digitally in the microcontroller.

    5. Level Shifting and Scaling

    The signal is adjusted to match the ADC input range.

    For example, if a sensor produces 0–100 mV and the ADC accepts 0–5 V, an amplifier can scale the signal so that the ADC uses more of its resolution.

    6. Excitation

    Some sensors such as resistive bridges require an excitation voltage or current. The signal-conditioning system may provide this excitation and measure the resulting response.

    Real-Time DAQ Applications

    Temperature Monitoring

    Temperature Sensor → Amplifier/Filter → ADC → Microcontroller → Display/Alarm
    

    The microcontroller continuously samples the sensor and can activate an alarm if temperature exceeds a limit.

    Motor-Speed Monitoring

    A speed sensor produces pulses proportional to motor speed. Conditioning removes noise and shapes the pulses before the microcontroller counts them.

    Heart-Rate Monitoring

    A biomedical sensor produces a small physiological signal. Amplification and filtering remove unwanted noise and interference. The conditioned signal is digitized and processed to calculate heart rate.

    Importance in Real-Time Systems

    Proper signal conditioning provides:

    1. Better measurement accuracy.
    2. Improved signal-to-noise ratio.
    3. Protection of ADC and processing electronics.
    4. Better use of ADC resolution.
    5. Reliable real-time decision-making.
    6. Reduced aliasing and interference.

    Conclusion

    Signal conditioning is a critical stage between the sensor and ADC. By amplifying, filtering, isolating, scaling and linearizing the sensor signal, it ensures that the DAQ system receives a clean and measurable signal suitable for reliable real-time monitoring and control.

  13. Q3. Explain the different types of signal conditioning used in data acquisition systems.20257m

    Module 2: Signal Conditioning Systems

    Explain the different types of signal conditioning used in data acquisition systems.

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    Worked Solution

    Solution: Types of Signal Conditioning in DAQ Systems

    Signal conditioning prepares a sensor signal for accurate measurement and ADC conversion.

    1. Amplification

    Weak sensor outputs are increased to a suitable voltage range.

    Vout=GVinV_{out}=G V_{in}

    Operational amplifiers and instrumentation amplifiers are commonly used.

    2. Filtering

    Filters remove unwanted frequency components and noise.

    • Low-pass: removes high-frequency noise.
    • High-pass: removes unwanted low-frequency/DC components.
    • Band-pass: passes a selected frequency band.
    • Notch: rejects a narrow interfering frequency such as 50/60 Hz.

    3. Isolation

    Electrical isolation prevents unwanted current paths and protects the measurement system. Isolation amplifiers and opto-isolators are common methods.

    4. Linearization

    Some sensors have nonlinear input-output characteristics. Linearization converts the response into a more convenient relationship, either using analog circuits or software.

    5. Level Shifting and Scaling

    The signal is shifted or scaled to match the ADC input range. For example, a 0–100 mV sensor can be amplified to 0–5 V.

    6. Excitation

    Resistive and bridge-type sensors may require a stable excitation voltage or current before their output can be measured.

    7. Signal Conversion

    A conditioning stage may convert one signal form to another, such as current-to-voltage conversion for a 4–20 mA transmitter.

    8. Sample-and-Hold / Anti-Aliasing

    A sample-and-hold circuit maintains the signal during conversion, while an analog anti-aliasing filter limits frequencies above the useful measurement bandwidth.

    Conclusion

    The major conditioning functions are amplification, filtering, isolation, linearization, scaling, excitation and signal conversion. Proper conditioning improves signal-to-noise ratio, ADC utilization, accuracy and reliability.

  14. Q4(a). Describe the various noise sources and noise reduction techniques in signal measurement systems.20257m

    Module 2: Signal Conditioning Systems

    Describe the various noise sources and noise reduction techniques in signal measurement systems.

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    Worked Solution

    Solution: Noise Sources and Noise Reduction Techniques

    Noise

    Noise is an unwanted electrical signal that interferes with the desired measurement signal and reduces measurement accuracy.

    Major Noise Sources

    1. Thermal Noise

    Produced by random motion of charge carriers in resistive components. Its noise power increases with temperature and bandwidth.

    2. Shot Noise

    Caused by the random arrival of charge carriers, especially in semiconductor devices and junctions.

    3. Flicker Noise

    Also called 1/f noise. It becomes important at low frequencies and is associated with electronic devices and materials.

    4. Electromagnetic Interference (EMI)

    Motors, transformers, switching circuits, mobile/radio transmitters and power lines can induce unwanted signals.

    5. Ground Loops

    Different ground potentials can create unwanted circulating currents and 50/60 Hz interference.

    6. Crosstalk

    A signal from one channel can couple into another through electrical or electromagnetic coupling.

    7. Quantization Noise

    Introduced when an analog value is represented by a finite number of ADC levels.

    Noise Reduction Techniques

    1. Shielding

    Use shielded cables and conductive enclosures to reduce electromagnetic pickup.

    2. Proper Grounding

    Use a carefully designed grounding scheme and avoid unnecessary ground loops.

    3. Twisted-Pair Cables

    Twisting reduces pickup from external electromagnetic fields, especially for differential signals.

    4. Differential Measurement

    Measure the voltage difference between two signal terminals rather than relying on a common ground reference. This improves rejection of common-mode interference.

    5. Filtering

    Use low-pass, high-pass, band-pass or notch filters according to the measurement bandwidth.

    6. Isolation

    Isolation amplifiers, transformers or digital isolators can break unwanted electrical paths.

    7. Short and Proper Wiring

    Keep sensitive signal wires short, route them away from high-power cables and separate analog and noisy digital wiring.

    8. Averaging and Digital Filtering

    Repeated measurements can be averaged, and digital filters can reduce random noise after acquisition.

    Conclusion

    Noise reduction requires a combination of shielding, grounding, differential measurement, filtering, isolation and proper wiring. The best technique depends on the source and frequency of the interference.

  15. Q4(b). Explain the architecture of a microcontroller with neat block diagram. Describe the basics of assembly language and C-language programming used for microcontrollers.20257m

    Module 3: Embedded Microcontrollers – PIC18F / Others

    Explain the architecture of a microcontroller with neat block diagram. Describe the basics of assembly language and C-language programming used for microcontrollers.

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    Worked Solution

    Solution: Microcontroller Architecture, Assembly and C Programming

    Microcontroller Architecture

    A microcontroller is a compact integrated circuit containing a processor, memory, I/O and peripherals for embedded control applications.

                  ┌─────────────────────┐
                  │        CPU          │
                  │ ALU + Control Unit  │
                  │ Registers           │
                  └──────────┬──────────┘
                             │ System Bus
            ┌────────────────┼────────────────┐
            ↓                ↓                ↓
       Program Memory    Data Memory       I/O Ports
       Flash/ROM         RAM/EEPROM        GPIO
            │                │                │
            └────────────────┼────────────────┘
                             ↓
                  Timers / Counters
                  ADC / PWM / DAC
                  SPI / I²C / UART
    

    Major blocks

    • CPU: Executes instructions.
    • ALU: Performs arithmetic and logical operations.
    • Registers: High-speed temporary storage.
    • Program memory: Stores firmware.
    • RAM: Stores temporary variables and stack data.
    • EEPROM/Flash: Stores non-volatile data or program code.
    • GPIO: Interfaces with external sensors and actuators.
    • Timers/Counters: Generate delays and measure/count events.
    • ADC/DAC/PWM: Interface between digital electronics and analog systems.
    • Communication peripherals: SPI, I²C, UART/USART and others.

    Assembly Language Programming

    Assembly language uses processor-specific mnemonics representing machine instructions.

    Example:

    MOVLW 05H
    MOVWF COUNT
    INCF  COUNT, F
    

    The exact instructions depend on the microcontroller architecture.

    Advantages

    • Precise hardware control.
    • Efficient execution.
    • Small and predictable code.

    Limitations

    • Difficult to write and maintain for large applications.
    • Processor-specific.

    C Language Programming

    C provides structured, readable programming while still allowing direct hardware control through registers, pointers and bit operations.

    Example:

    #include <stdint.h>
    
    int main(void)
    {
        uint8_t count = 0;
        while (1)
        {
            count++;
        }
    }
    

    In practical firmware, initialization functions configure clocks, GPIO, ADC, timers and communication peripherals before the main loop executes.

    Assembly vs C

    Feature Assembly C
    Readability Low High
    Hardware control Very direct Direct through registers/APIs
    Portability Low Higher
    Development time Longer Shorter
    Optimization Can be highly optimized Compiler-dependent

    Conclusion

    A microcontroller combines processing, memory and peripherals in one device. Assembly provides low-level control, while C provides a practical balance of performance, readability and portability for embedded DAQ applications.

  16. Q5(a). Describe the working of ADC and DAC in a microcontroller system with examples.20257m

    Module 3: Embedded Microcontrollers – PIC18F / Others

    Describe the working of ADC and DAC in a microcontroller system with examples.

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    Worked Solution

    Solution: ADC and DAC in a Microcontroller System

    ADC: Analog-to-Digital Converter

    An ADC converts an analog voltage into a digital code that a microcontroller can process.

    Working

    Analog Sensor → Signal Conditioning → ADC → Digital Code → CPU
    
    1. The analog signal is applied to the ADC input.
    2. The ADC samples the signal.
    3. The input range is divided into discrete levels.
    4. The nearest digital code is generated.
    5. The microcontroller reads the code and converts it into engineering units.

    For an ideal nn-bit ADC with input range VFSV_{FS}:

    LSB=VFS2nLSB = \frac{V_{FS}}{2^n}

    Approximately, the ADC code is:

    CodeVinVFS(2n1)Code \approx \frac{V_{in}}{V_{FS}}(2^n-1)

    Example

    For a 10-bit ADC with 0–5 V input:

    LSB51024=4.883 mVLSB \approx \frac{5}{1024}=4.883\text{ mV}

    DAC: Digital-to-Analog Converter

    A DAC converts a digital number generated by the microcontroller into an analog voltage or current.

    CPU → Digital Code → DAC → Analog Voltage → Actuator
    

    For an ideal nn-bit voltage DAC with reference VrefV_{ref}:

    VoutCode2n1VrefV_{out}\approx\frac{Code}{2^n-1}V_{ref}

    The exact transfer equation depends on the DAC architecture and datasheet conventions.

    Applications

    • ADC: temperature, pressure, light and biomedical sensors.
    • DAC: waveform generation, motor control references, audio and analog actuator control.

    ADC vs DAC

    Feature ADC DAC
    Conversion Analog → Digital Digital → Analog
    Input Voltage/current Digital code
    Output Digital code Analog voltage/current
    Use Measurement Control/output generation

    Conclusion

    ADC enables the microcontroller to measure the physical world, while DAC enables it to generate controlled analog outputs.

  17. Q5(b). Explain the architecture and working of a microcontroller-based Data Acquisition (DAQ) system.20257m

    Module 4: DAQ Systems

    Explain the architecture and working of a microcontroller-based Data Acquisition (DAQ) system.

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    Worked Solution

    Solution: Microcontroller-Based DAQ System

    Definition

    A microcontroller-based DAQ system uses a microcontroller to acquire, digitize, process, store and/or transmit sensor data.

    Architecture

    Sensor
      ↓
    Signal Conditioning
      ↓
    ADC ───────────────┐
      ↓                │
    Microcontroller ← Timers / Interrupts
      ↓
    Data Processing
      ├──→ Display
      ├──→ Memory / SD Card
      └──→ UART / SPI / I²C / USB → Computer/Network
    

    Working

    1. A sensor measures the physical quantity.
    2. Signal conditioning amplifies and filters the sensor output.
    3. The ADC converts the analog signal to digital data.
    4. The microcontroller samples the data at a programmed rate.
    5. Firmware performs scaling, calibration, filtering or feature extraction.
    6. The processed data is displayed, stored or transmitted.
    7. The controller can also generate control outputs based on measured data.

    Important Components

    • Sensors/transducers
    • Signal-conditioning circuits
    • ADC
    • Microcontroller
    • Timers and interrupts
    • Memory/storage
    • Communication interfaces
    • Display or actuator interface

    Advantages

    • Compact and low cost.
    • Programmable and flexible.
    • Easy data logging.
    • Real-time processing.
    • Multiple communication options.
    • Suitable for portable biomedical and industrial instruments.

    Example: Temperature Logger

    Temperature Sensor
           ↓
    Amplifier + Low-pass Filter
           ↓
    ADC
           ↓
    Microcontroller
           ↓
    Convert Code → Temperature
           ↓
    SD Card / LCD / USB
    

    The microcontroller periodically samples the temperature, converts the ADC code into temperature units, adds a timestamp and stores the result.

    Conclusion

    A microcontroller-based DAQ integrates measurement, conversion, processing, communication and storage into a compact embedded system.

  18. Q5(c). Describe hardware communication interface programming used to connect data loggers in microcontroller-based DAQ systems.20257m

    Module 4: DAQ Systems

    Describe hardware communication interface programming used to connect data loggers in microcontroller-based DAQ systems.

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    Worked Solution

    Solution: Hardware Communication Interface Programming for Data Loggers

    A data logger needs communication interfaces to transfer acquired data between the microcontroller, sensors, memory devices and computers.

    1. SPI

    SPI (Serial Peripheral Interface) is a synchronous, high-speed interface using signals such as SCLK, MOSI, MISO and CS.

    MCU SCLK ───────── Device
    MCU MOSI ───────── Device
    MCU MISO ───────── Device
    MCU CS   ───────── Device
    

    It is commonly used with SD cards, external ADCs and DACs.

    Programming sequence

    1. Configure SPI clock and mode.
    2. Configure GPIO pins.
    3. Select the slave using CS.
    4. Transmit command/address/data bytes.
    5. Read returned data when required.
    6. Release CS.

    2. I²C

    I²C uses two lines:

    • SDA: data
    • SCL: clock

    It supports multiple addressed devices on the same bus.

    Typical sequence:

    START → Address + R/W → ACK → Data → ACK → STOP

    It is useful for EEPROMs, sensors and low-speed peripherals.

    3. UART/USART

    UART is an asynchronous serial interface using TX and RX. A typical frame contains a start bit, data bits, optional parity and stop bit(s).

    Typical configuration includes:

    • Baud rate
    • Data bits
    • Parity
    • Stop bits

    UART is commonly used to transfer logged data to a PC or another controller.

    4. USB

    USB provides higher-speed communication between the embedded data logger and a host computer. Firmware must configure the appropriate USB device class and endpoints according to the application.

    Basic Data Logger Flow

    Sensor → ADC → MCU RAM/Buffer → Communication Interface → Storage/PC
    

    The firmware normally uses a buffer so that data acquisition can continue while blocks of data are written to storage.

    Interface Selection

    Interface Main advantage Typical use
    SPI High speed, simple SD card, ADC/DAC
    I²C Addressed multi-device bus Sensors, EEPROM
    UART Simple point-to-point PC/debug/modem
    USB High-speed host connection PC data transfer

    Conclusion

    Communication interface programming involves configuring the peripheral, transferring data according to its protocol, handling errors/timeouts and buffering acquired samples so that continuous logging is reliable.

  19. Q6(a). Explain the complete data processing cycle in a microcontroller-based system.20257m

    Module 5: Data Processing

    Explain the complete data processing cycle in a microcontroller-based system.

    View this question on its own page →
    Worked Solution

    Solution: Complete Data Processing Cycle

    Definition

    Data processing converts raw acquired samples into meaningful information that can be stored, displayed, transmitted or used for control.

    Processing Cycle

    Data Acquisition
          ↓
    Data Validation
          ↓
    Pre-processing / Filtering
          ↓
    Calibration & Scaling
          ↓
    Feature Extraction / Computation
          ↓
    Analysis
          ↓
    Storage / Display / Communication / Control
    

    1. Data Acquisition

    Sensors and ADCs generate digital samples at a selected sampling rate.

    2. Data Validation

    The system checks for missing, out-of-range or corrupted values.

    3. Pre-processing

    Noise may be reduced using averaging or digital filters. Signals can also be normalized or resampled when appropriate.

    4. Calibration and Scaling

    ADC codes are converted into engineering units such as °C, V, Pa or rpm.

    5. Feature Extraction

    Useful quantities are calculated from raw samples, such as peak, RMS, mean, frequency or heart rate.

    For a set of NN samples xix_i, the mean is:

    xˉ=1Ni=1Nxi\bar{x}=\frac{1}{N}\sum_{i=1}^{N}x_i

    6. Analysis

    Statistical, frequency-domain or trend analysis can be applied depending on the application.

    7. Storage and Output

    Processed or raw data can be saved to flash, EEPROM, SD card or a computer and displayed or transmitted.

    Real-Time Considerations

    The processing time must be sufficiently small compared with the sampling interval. Buffering and interrupts/DMA can help prevent sample loss.

    Conclusion

    A complete data-processing cycle transforms raw sensor samples into reliable, useful information through validation, filtering, calibration, computation and analysis.

  20. Q6(b). Describe various data storage options available in microcontroller systems and explain how data can be logged or stored using programming techniques.20257m

    Module 5: Data Processing

    Describe various data storage options available in microcontroller systems and explain how data can be logged or stored using programming techniques.

    View this question on its own page →
    Worked Solution

    Solution: Data Storage Options and Data Logging

    Data Storage Options

    Storage Nature Typical use
    SRAM Volatile, fast Temporary buffers
    EEPROM Non-volatile Calibration/configuration data
    Internal Flash Non-volatile Firmware and small datasets
    External Flash Non-volatile Larger embedded storage
    SD card Removable, high capacity Continuous data logging
    USB/Computer External Long-term transfer/storage

    Data Logging Process

    Sensor → ADC → MCU → RAM Buffer → Storage Interface → File/Memory
    

    Steps

    1. Initialize the sensor and ADC.
    2. Configure the sampling timer.
    3. Acquire a sample at every sampling instant.
    4. Convert the ADC code into the required format.
    5. Add a timestamp or channel identifier when necessary.
    6. Store samples in a RAM buffer.
    7. When the buffer is sufficiently full, write a block to non-volatile storage.
    8. Repeat until logging ends.

    Why Buffering is Important

    Storage devices such as SD cards may have variable write latency. A RAM buffer allows acquisition to continue while data is being written in blocks.

    Example Pseudocode

    while (logging)
    {
        sample = read_adc();
        buffer[index++] = sample;
    
        if (index == BUFFER_SIZE)
        {
            storage_write(buffer, BUFFER_SIZE);
            index = 0;
        }
    }
    

    A real implementation should also handle write failures, buffer overflow, timestamps, file-system errors and safe shutdown.

    Storage Selection

    • Use EEPROM for small calibration/configuration data.
    • Use Flash for firmware and moderate non-volatile data.
    • Use SD cards for large continuous logs.
    • Use computer/USB/network storage when very large datasets must be transferred or archived.

    Conclusion

    Efficient data logging depends on selecting suitable storage, using buffering and ensuring that the sustained storage throughput is greater than the incoming data rate.

  21. Q7(a). Explain the various data retrieving and plotting techniques used in microcontroller-based and computer-based data acquisition systems.20257m

    Module 6: Analysis

    Explain the various data retrieving and plotting techniques used in microcontroller-based and computer-based data acquisition systems.

    View this question on its own page →
    Worked Solution

    Solution: Data Retrieval and Plotting Techniques

    Data Retrieval

    Data retrieval means reading stored or acquired data from a microcontroller, data logger or computer for further processing and visualization.

    Common methods

    1. UART/Serial: Simple method for transferring measurements to a PC terminal or application.
    2. USB: High-speed transfer between embedded hardware and a computer.
    3. SPI/SD card: Data is retrieved from removable storage.
    4. I²C: Used to read data from sensors and EEPROMs.
    5. Network/Wireless: Data can be transferred remotely using appropriate communication hardware.

    Typical Retrieval Flow

    Sensor Data → Storage/Data Logger → Communication Interface → Computer → Analysis Software
    

    Plotting Techniques

    1. Time-Domain Plot

    Plots signal amplitude against time.

    Useful for temperature, heart rate, vibration and other time-varying signals.

    2. XY Plot

    Plots one measured variable against another, such as pressure versus temperature.

    3. Frequency Spectrum

    Uses techniques such as the Fast Fourier Transform (FFT) to show signal magnitude versus frequency.

    Useful for vibration and periodic-signal analysis.

    4. Trend Plot

    Shows long-term changes such as temperature over several hours or days.

    Typical Software Workflow

    1. Connect to the data logger.
    2. Retrieve raw samples.
    3. Parse the data format.
    4. Add timestamps/channel information.
    5. Apply calibration and units.
    6. Remove invalid values if required.
    7. Plot the data.
    8. Save the graph or processed dataset.

    Example

    For vibration data, the time-domain graph can show transient events, while an FFT plot can identify dominant vibration frequencies.

    Conclusion

    Data retrieval transfers stored measurements into an analysis environment, while plotting converts numerical data into visual information that makes trends, abnormalities and frequency components easier to identify.

  22. Q7(b). Discuss various data analysis techniques used in embedded and data acquisition systems.20257m

    Module 6: Analysis

    Discuss various data analysis techniques used in embedded and data acquisition systems.

    View this question on its own page →
    Worked Solution

    Solution: Data Analysis Techniques in Embedded and DAQ Systems

    1. Statistical Analysis

    Basic statistics summarize acquired data.

    Mean

    xˉ=1Ni=1Nxi\bar{x}=\frac{1}{N}\sum_{i=1}^{N}x_i

    Variance

    σ2=1Ni=1N(xixˉ)2\sigma^2=\frac{1}{N}\sum_{i=1}^{N}(x_i-\bar{x})^2

    Other useful measures include minimum, maximum, range and standard deviation.

    2. Filtering

    Digital low-pass, high-pass, band-pass and notch filters can remove unwanted frequency components.

    3. Time-Domain Analysis

    Examines how the signal changes with time. Peak value, RMS value, rise time, pulse width and zero crossings may be measured.

    For samples xix_i, RMS is:

    xRMS=1Ni=1Nxi2x_{RMS}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}x_i^2}

    4. Frequency-Domain Analysis

    The FFT (Fast Fourier Transform) converts sampled time-domain data into frequency-domain information. It is widely used for vibration, audio and periodic-signal analysis.

    5. Trend Analysis

    Long-term trends are examined to detect gradual changes, drift or degradation.

    6. Threshold and Event Detection

    The system can compare a measurement against predefined limits and generate an alarm or control action.

    7. Correlation Analysis

    Correlation measures the relationship between two signals or variables and can help identify related system behavior.

    8. Feature Extraction

    Important features such as mean, RMS, peak, frequency and pulse rate are extracted from raw data for classification or monitoring.

    9. Calibration and Error Analysis

    Measured values are compared with known references to determine offset, gain error, sensitivity and other measurement errors.

    Embedded Implementation

    To perform analysis on a microcontroller, efficient algorithms, fixed-point arithmetic where appropriate, buffering and interrupt/DMA-based acquisition may be used.

    Conclusion

    DAQ analysis combines statistical, time-domain, frequency-domain, filtering, trend, threshold, correlation and calibration techniques to convert raw measurements into useful engineering information.

  23. Q8(a). A microcontroller system needs to store real-time vibration data at 10 kSamples/s, each sample being 16 bits. (i) Calculate the minimum memory size required for storing 5 minutes of data. (ii) Suggest a suitable data storage interface (SPI/I2C/Parallel) and justify with bandwidth calculations.20257m

    Module 5: Data Processing

    A microcontroller system needs to store real-time vibration data at 10 kSamples/s, each sample being 16 bits.
    (i) Calculate the minimum memory size required for storing 5 minutes of data.
    (ii) Suggest a suitable data storage interface (SPI/I2C/Parallel) and justify with bandwidth calculations.

    View this question on its own page →
    Worked Solution

    Solution: Vibration Data Storage Calculation

    Given:

    • Sampling rate = 10 kSamples/s = 10,00010,000 samples/s
    • Sample size = 16 bits = 2 bytes/sample
    • Duration = 5 minutes = 300 s

    (i) Minimum Memory Required

    Data rate:

    10,000×16=160,000 bits/s10,000\times16=160,000\text{ bits/s}

    Convert to bytes/s:

    160,0008=20,000 bytes/s\frac{160,000}{8}=20,000\text{ bytes/s}

    For 300 seconds:

    20,000×300=6,000,000 bytes20,000\times300=6,000,000\text{ bytes}

    Therefore:

    6,000,000 bytes6 MB\boxed{6,000,000\text{ bytes}\approx6\text{ MB}}

    Using binary units, this is approximately:

    6,000,0001,048,5765.72 MiB\frac{6,000,000}{1,048,576}\approx5.72\text{ MiB}

    So at least 6 MB decimal storage is required, excluding filesystem overhead and metadata.

    (ii) Suitable Interface

    The raw required throughput is:

    20,000 bytes/s=20 kB/s20,000\text{ bytes/s}=20\text{ kB/s}

    or:

    160 kbps=0.16 Mbps160\text{ kbps}=0.16\text{ Mbps}

    SPI

    SPI is the best choice among the given options for a typical embedded data logger because it provides high throughput with simple hardware and is widely supported by SD cards and external memory.

    Even a modest SPI clock of 1 MHz can theoretically transfer:

    1 Mbit/s=125 kB/s1\text{ Mbit/s}=125\text{ kB/s}

    which is well above the required 20 kB/s, leaving margin for protocol and storage overhead.

    I²C

    I²C is convenient for sensors and EEPROMs, but its lower typical speed makes it less attractive for continuous high-rate storage.

    Parallel

    Parallel interfaces can provide high throughput but require more pins and hardware complexity.

    Final Answer

    • Minimum data storage: 6,000,0006,000,000 bytes ≈ 6 MB
    • Raw data rate: 0.16 Mbps = 20 kB/s
    • Recommended interface: SPI, because it easily provides sufficient bandwidth with low pin count and is well suited to SD-card/external-memory logging.
  24. Q8(b). A system uses an SPI-based 8-bit DAC to generate an analog output signal between 0–5 V. (i) Explain the SPI timing requirements and derive the formula for DAC output voltage. (ii) If the SPI clock is 4 MHz, calculate the maximum update rate achievable.20257m

    Module 4: DAQ Systems

    A system uses an SPI-based 8-bit DAC to generate an analog output signal between 0–5 V.
    (i) Explain the SPI timing requirements and derive the formula for DAC output voltage.
    (ii) If the SPI clock is 4 MHz, calculate the maximum update rate achievable.

    View this question on its own page →
    Worked Solution

    Solution: SPI 8-bit DAC

    Given:

    • DAC resolution = 8 bits
    • Output range = 0–5 V
    • SPI clock = 4 MHz

    (i) SPI Timing and DAC Output

    SPI is a synchronous serial protocol. The master provides the clock on SCLK, sends data on MOSI, and selects the DAC using chip select (CS).

    Typical sequence:

    CS ↓ → Send command/data bits on MOSI → Clock pulses → CS ↑ → DAC updates output
    

    The exact sampling clock edge and timing depend on the DAC's SPI mode specified in its datasheet.

    For an ideal 8-bit DAC, the input code ranges from:

    0 to 281=2550\text{ to }2^8-1=255

    For a 0–5 V output using the common ideal endpoint convention:

    Vout=D255×5V_{out}=\frac{D}{255}\times5

    where DD is the decimal DAC code.

    Thus:

    • D=0Vout=0D=0 \Rightarrow V_{out}=0 V
    • D=255Vout=5D=255 \Rightarrow V_{out}=5 V

    The approximate voltage step is:

    5256=19.53 mV\frac{5}{256}=19.53\text{ mV}

    The exact transfer function should follow the DAC datasheet if it uses a different reference/output convention.

    (ii) Maximum Update Rate

    An 8-bit DAC requires at least 8 clock cycles per update if the SPI frame contains only the 8 data bits.

    SPI clock:

    fSPI=4 MHzf_{SPI}=4\text{ MHz}

    Therefore:

    fupdate,max=4×1068f_{update,max}=\frac{4\times10^6}{8}

    fupdate,max=500,000 updates/s\boxed{f_{update,max}=500,000\text{ updates/s}}

    or:

    500 kUpdates/s\boxed{500\text{ kUpdates/s}}

    Important practical note

    If the DAC requires more than 8 bits per SPI frame—for example, command bits, address bits or control bits—the actual maximum update rate will be lower:

    fupdate,max=fSPINbits/framef_{update,max}=\frac{f_{SPI}}{N_{bits/frame}}

    Final Answer

    • DAC output: Vout=D255×5V_{out}=\frac{D}{255}\times5 V under the stated endpoint convention.
    • Approximate LSB step: 19.53 mV.
    • Maximum theoretical update rate for an 8-bit frame: 500 kUpdates/s.
  25. Q9(a). A DAQ system samples 4 channels simultaneously at 25 kS/s per channel. Each sample is 12 bits. The microcontroller writes data to an SD card via SPI at 12 Mbps. The SD card uses 512-byte sectors and write operations must be in whole sectors. The MCU packs samples channel-wise into frames and writes continuously. (i) Compute the raw data rate in Mbps and the required sustained write throughput in MB/s (account for packing). (ii) Design a framing strategy: pack samples into 512-byte sectors with minimal wasted space—compute how many samples per sector and how many sectors per second must be written.20257m

    Module 5: Data Processing

    A DAQ system samples 4 channels simultaneously at 25 kS/s per channel. Each sample is 12 bits. The microcontroller writes data to an SD card via SPI at 12 Mbps. The SD card uses 512-byte sectors and write operations must be in whole sectors. The MCU packs samples channel-wise into frames and writes continuously.
    (i) Compute the raw data rate in Mbps and the required sustained write throughput in MB/s (account for packing).
    (ii) Design a framing strategy: pack samples into 512-byte sectors with minimal wasted space—compute how many samples per sector and how many sectors per second must be written.

    View this question on its own page →
    Worked Solution

    Solution: Multichannel DAQ Data Rate and SD-Card Framing

    Given:

    • Number of channels = 4
    • Sampling rate per channel = 25 kS/s
    • ADC resolution = 12 bits/sample
    • SPI rate to SD card = 12 Mbps
    • Sector size = 512 bytes

    (i) Raw Data Rate

    Total samples per second across all channels:

    4×25,000=100,000 samples/s4\times25,000=100,000\text{ samples/s}

    Each sample contains 12 bits, so:

    Rraw=100,000×12=1,200,000 bits/sR_{raw}=100,000\times12=1,200,000\text{ bits/s}

    Therefore:

    Rraw=1.2 Mbps\boxed{R_{raw}=1.2\text{ Mbps}}

    In bytes/s:

    1,200,0008=150,000 bytes/s\frac{1,200,000}{8}=150,000\text{ bytes/s}

    So:

    Rraw=0.15 MB/s\boxed{R_{raw}=0.15\text{ MB/s}}

    Account for packing

    Because SD-card writes are byte-addressable, 12-bit samples cannot simply occupy 12 bits independently unless the firmware packs them.

    A convenient packing scheme stores two 12-bit samples in 3 bytes:

    2×12=24 bits=3 bytes2\times12=24\text{ bits}=3\text{ bytes}

    Thus efficient packing produces exactly the theoretical raw rate of 0.15 MB/s, excluding filesystem and protocol overhead.

    The available SPI bandwidth is:

    12 Mbps=1.5 MB/s12\text{ Mbps}=1.5\text{ MB/s}

    Therefore the nominal raw data rate is only:

    0.151.5=10%\frac{0.15}{1.5}=10\%

    of the stated SPI link capacity, leaving substantial bandwidth margin.

    (ii) 512-Byte Sector Framing

    A 512-byte sector contains:

    512×8=4096 bits512\times8=4096\text{ bits}

    With 12-bit samples, the maximum number of complete samples is:

    409612=341 samples\left\lfloor\frac{4096}{12}\right\rfloor=341\text{ samples}

    341 samples use:

    341×12=4092 bits=511.5 bytes341\times12=4092\text{ bits}=511.5\text{ bytes}

    So one sector can contain 341 complete 12-bit samples if the packing is bit-level, leaving:

    40964092=4 bits4096-4092=4\text{ bits}

    unused.

    However, a cleaner byte-aligned scheme is to pack 340 samples:

    340×12=4080 bits=510 bytes340\times12=4080\text{ bits}=510\text{ bytes}

    leaving exactly 2 bytes for metadata, a timestamp, frame counter, CRC, or padding.

    Recommended framing

    Use 340 samples per 512-byte sector and reserve 2 bytes for metadata, or use a 341-sample bit-packed payload with 4 unused bits plus a defined header/trailer.

    At 100,000 samples/s:

    100,000340=294.12 sectors/s\frac{100,000}{340}=294.12\text{ sectors/s}

    Thus the system needs approximately:

    295 sectors/s\boxed{295\text{ sectors/s}}

    with 340 samples/sector, ignoring additional metadata.

    For maximum packing efficiency using 341 samples/sector:

    100,000341=293.26 sectors/s\frac{100,000}{341}=293.26\text{ sectors/s}

    so approximately 294 sectors/s are required.

    Final Answer

    • Raw data rate: 1.2 Mbps = 0.15 MB/s
    • SPI capacity: 12 Mbps = 1.5 MB/s
    • Maximum complete 12-bit samples in 512 bytes: 341 samples
    • Efficient practical framing: 340 samples + 2 bytes metadata/padding
    • Sectors/s: approximately 295 sectors/s for 340-sample frames, or 294 sectors/s with 341-sample bit packing.

    The stated SPI bandwidth is comfortably sufficient for the raw acquisition rate.

  26. Q9(b). A 14-bit ADC (counts 0...16383) is used with an input range of 0...2.500 V to read a temperature sensor whose output is linearly 0–2.5 V (for 0–200°C). During calibration you measure that a known 100°C reference gives an ADC code of 6550. (i) Compute the ideal LSB (in volts) and the ideal code corresponding to 100°C. (ii) From the calibration reading (6550), find the offset error in volts and in °C.20257m

    Module 2: Signal Conditioning Systems

    A 14-bit ADC (counts 0...16383) is used with an input range of 0...2.500 V to read a temperature sensor whose output is linearly 0–2.5 V (for 0–200°C). During calibration you measure that a known 100°C reference gives an ADC code of 6550.
    (i) Compute the ideal LSB (in volts) and the ideal code corresponding to 100°C.
    (ii) From the calibration reading (6550), find the offset error in volts and in °C.

    View this question on its own page →
    Worked Solution

    Solution: ADC Resolution and Calibration Error

    Given:

    • ADC resolution = 14 bits
    • ADC counts = 00 to 1638316383
    • Input range = 0–2.500 V
    • Temperature range = 0–200°C
    • Sensor output = 0–2.5 V linearly
    • Measured code at 100°C = 6550

    (i) Ideal LSB and Ideal Code at 100°C

    Step 1: Calculate ideal LSB

    A 14-bit ADC has:

    214=163842^{14}=16384

    quantization intervals.

    Therefore:

    LSB=2.50016384LSB=\frac{2.500}{16384}

    LSB=0.0001525879 VLSB=0.0001525879\text{ V}

    Hence:

    LSB152.59μV\boxed{LSB\approx152.59\,\mu V}

    Step 2: Ideal voltage at 100°C

    The sensor is linear from 0 V at 0°C to 2.5 V at 200°C.

    At 100°C, which is half of the temperature range:

    V100=2.5×100200=1.25 VV_{100}=2.5\times\frac{100}{200}=1.25\text{ V}

    Step 3: Ideal ADC code

    Using the ideal ADC transfer convention:

    Codeideal=V100VFS(2141)Code_{ideal}=\frac{V_{100}}{V_{FS}}(2^{14}-1)

    =1.252.5×16383=\frac{1.25}{2.5}\times16383

    =8191.5=8191.5

    So the ideal code is approximately:

    8192\boxed{8192}

    (ii) Offset Error

    Measured code:

    Codemeasured=6550Code_{measured}=6550

    Ideal code:

    Codeideal8192Code_{ideal}\approx8192

    Code error:

    ΔCode=65508192=1642\Delta Code=6550-8192=-1642

    Convert this code error into voltage using the LSB:

    ΔV=ΔCode×LSB\Delta V=\Delta Code\times LSB

    =1642×0.0001525879=-1642\times0.0001525879

    ΔV0.25055 V\boxed{\Delta V\approx-0.25055\text{ V}}

    So the measured result is approximately 0.251 V below the ideal value.

    Equivalent temperature error

    The sensor has a range of:

    2.5 V200°C2.5\text{ V}\leftrightarrow200°C

    Therefore its sensitivity is:

    2002.5=80°C/V\frac{200}{2.5}=80°C/V

    Hence:

    ΔT=ΔV×80\Delta T=\Delta V\times80

    =0.25055×80=-0.25055\times80

    ΔT20.04°C\boxed{\Delta T\approx-20.04°C}

    Therefore, at the 100°C reference point, the calibrated reading corresponds to an error of approximately −20°C relative to the ideal transfer.

    Cross-check Using Measured Code

    Measured voltage corresponding to code 6550:

    Vmeasured6550×2.516384V_{measured}\approx6550\times\frac{2.5}{16384}

    0.99945 V\approx0.99945\text{ V}

    This corresponds to:

    Tmeasured0.999452.5×200T_{measured}\approx\frac{0.99945}{2.5}\times200

    79.96°C\approx79.96°C

    So a true 100°C input is being reported at approximately 79.96°C, giving an error of approximately:

    79.9610020.04°C79.96-100\approx-20.04°C

    Final Answer

    Quantity Result
    ADC resolution 14 bit
    Ideal LSB 152.59 μV
    Ideal code at 100°C ≈ 8192
    Measured code 6550
    Code error −1642 counts
    Offset error ≈ −0.2506 V
    Equivalent temperature error ≈ −20.04°C
    Measured temperature equivalent ≈ 79.96°C

    Note: Strictly, a single calibration point reveals a combined offset/gain error unless the gain is independently known. Under the exam's stated linear-sensor assumption, the difference at the 100°C reference is treated as the offset error.