Analog To Digital Converters MCQ Quiz - Objective Question with Answer for Analog To Digital Converters - Download Free PDF

Explanation:

Successive Approximation ADC (Analog-to-Digital Converter):

Definition: A successive approximation ADC is a type of analog-to-digital converter that uses a binary search algorithm to convert an analog signal into its corresponding digital representation. It achieves this by comparing the input signal to a series of reference voltages generated by a DAC (Digital-to-Analog Converter) in conjunction with a comparator and a control circuit.

Working Principle:

The successive approximation ADC works by iteratively refining the digital output to approximate the analog input signal. The process involves:

• Using an internal DAC to generate reference voltages based on the current digital approximation.
• Comparing the input analog signal with the reference voltage using a comparator.
• Adjusting the digital output bit-by-bit to minimize the difference between the reference voltage and the input signal, eventually converging on the closest digital representation.

Correct Option Analysis:

The correct option is:

Option 2: N clock pulses for conversion, a binary counter, and a comparator.

This option correctly describes the operation of a successive approximation ADC. Here’s why:

• N Clock Pulses: The successive approximation ADC requires precisely N clock pulses for conversion, where N is the number of bits in the digital output. During each clock pulse, one bit of the digital output is determined.
• Binary Counter: A binary counter is used to control the successive approximation process. It iteratively refines the digital output by setting or clearing individual bits, starting with the most significant bit (MSB) and moving to the least significant bit (LSB).
• Comparator: The comparator compares the input analog signal with the reference voltage generated by the DAC. Based on this comparison, the binary counter adjusts the digital output to improve accuracy.

Hence, option 2 correctly outlines the essential components and process required for the operation of a successive approximation ADC.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 2N clock pulses for conversion, an up-down counter, and a DAC.

This option is incorrect because:

• The successive approximation ADC does not require 2N clock pulses for conversion. Instead, it requires only N clock pulses, as each bit is determined sequentially in N steps.
• An up-down counter is not used in a successive approximation ADC. Instead, a binary counter is employed to refine the digital output systematically.

Option 3: 2N clock pulses for conversion and a binary counter only.

This option is partially correct but ultimately flawed:

• While the binary counter is an essential component of the successive approximation ADC, 2N clock pulses are not required. The conversion process is completed in N clock pulses.
• The absence of a comparator in this option makes it invalid, as the comparator is a critical component for comparing the input signal with the reference voltage.

Option 4: N clock pulses for conversion, an up-down counter, and a DAC.

This option is incorrect because:

• While the N clock pulses are correct, the use of an up-down counter is not appropriate for a successive approximation ADC. It relies on a binary counter for bit-wise refinement of the output.
• The DAC is correctly mentioned, but the inclusion of an up-down counter makes this option invalid.

Conclusion:

The successive approximation ADC operates using N clock pulses for conversion, a binary counter to iteratively refine the digital output, and a comparator to compare the analog input signal with the reference voltage generated by the DAC. This combination ensures accurate and efficient conversion of the analog signal to a digital representation.

Understanding the essential components and processes of a successive approximation ADC is crucial for identifying its operational characteristics. The correct option (Option 2) accurately captures the requirements and functionality of this type of ADC, making it the right choice among the given options.

The correct answer is Voltage.

Key Points

• A Voltage-Controlled Oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input.
  • The output frequency of a VCO is directly proportional to the input voltage, meaning that as the input voltage changes, the output frequency changes linearly.
  • VCOs are widely used in communication systems, function generators, and phase-locked loops (PLLs).
  • The input voltage is typically applied to a varactor diode or a voltage-controlled capacitor, which adjusts the frequency of the oscillator circuit.
  • VCOs can generate a wide range of frequencies, making them versatile in various applications.

Additional Information

• VCOs can be designed using different technologies, including analog and digital circuits.
• In analog VCOs, the frequency is usually adjusted by changing the capacitance or inductance in the circuit.
• Digital VCOs use digital-to-analog converters (DACs) to convert a digital input into a corresponding voltage that controls the frequency.
• VCOs are critical components in frequency modulation (FM) and phase modulation (PM) systems.
• Modern VCOs offer high-frequency stability and low phase noise, which are essential for high-performance communication systems.

The correct answer is A Dirac delta function.

Key Points

• A Dirac delta function is a mathematical function that peaks at a single point and is zero everywhere else.
• In the context of band-limited white noise, the covariance function describes how the signal values at different times are related to each other.
• A Dirac delta function indicates that the signal values are uncorrelated at different times, meaning that there is no predictable pattern or relationship between them.
• This is characteristic of white noise, which has a flat power spectral density, implying that it contains all frequency components with equal power.

Additional Information

• The Dirac delta function is often used in signal processing and systems theory to represent an idealized impulse.
• White noise is a random signal with a constant power spectral density, used in various fields such as electronics, acoustics, and finance.
• The concept of white noise is important in the study of stochastic processes and time series analysis.
• Band-limited white noise refers to white noise that has been filtered to include only a specific range of frequencies, making it more practical for real-world applications.

The correct answer is Differential code.

Key Points

• The Differential Phase Shift Keying (DPSK) technique is a type of phase modulation technique used in digital communication systems.
  • In DPSK, the phase of the carrier signal is shifted relative to the phase of the previous signal element rather than to a fixed reference phase.
  • This technique is known for its simplicity and robustness against phase synchronization issues.
  • DPSK does not require a coherent reference signal at the receiver, making the receiver design simpler.
  • The encoding of bits in DPSK is done using differential coding, where each bit is encoded relative to the previous bit.

Additional Information

• In differential coding, a binary '1' may be represented by a phase change, while a binary '0' may be represented by no phase change.
• This method of encoding helps in overcoming the problem of phase ambiguity in the received signal.
• DPSK is widely used in various communication systems, including wireless and optical communication systems.
• Common applications of DPSK include Bluetooth technology and some forms of satellite communication.

Explanation:

Quantisation Error in an 8-bit A/D Converter

Definition: Quantisation error in an Analog to Digital (A/D) converter is the difference between the actual analog input value and the digitized output value. It arises due to the finite resolution of the A/D converter, which cannot represent all possible values of the analog input precisely.

Working Principle: An A/D converter transforms an analog voltage into a corresponding digital value. The range of the analog input is divided into discrete levels, and each level is assigned a unique digital code. The resolution of the A/D converter is determined by the number of bits it uses to represent the analog input. An 8-bit A/D converter, for instance, divides the input range into 28 = 256 discrete levels.

Calculating Quantisation Error:

The quantisation error can be approximated by determining the size of the smallest step (Least Significant Bit - LSB) that the A/D converter can resolve. For an 8-bit A/D converter with an input voltage range from -1 to +1 volt, the steps can be calculated as follows:

The total voltage range = 1 - (-1) = 2 volts

The number of discrete levels = 2⁸ = 256

The voltage step size (LSB) = Total voltage range / Number of levels = 2 volts / 256 ≈ 0.0078125 volts = 7.8125 mV

The quantisation error is typically ±1/2 LSB, hence:

Quantisation error = ± (7.8125 mV / 2) ≈ ± 3.90625 mV

Since the error is typically considered as the absolute value, the quantisation error is approximately 3.90625 mV per step for an 8-bit A/D converter. This means the correct answer is closest to 4 mV. However, since the question specifies "approximately equal to," the answer would be rounded to the closest given option.

The correct option is: Option 3: 2 mV

For n-bit conversion, the conversion time for different ADC are:

Counter type ADC: (2n – 1) Tclk

Successive approx. time ADC: n Tclk

Flash type ADC: Tclk

(Flash Type ADC is also known as Parallel comparator type)

Dual slope ADC: (2n+1 – 1) Tclk

The fastest type of Analog to Digital converter is the Flash type / Parallel comparator type.

Important points:

• Counter type ADC and successive approximate ADC uses DAC
• Counter type ADC uses linear search and successive approximation type ADC uses binary search
• Ring counter is used in successive approximation type ADC
• Flash type ADC is the fastest ADC
• Flash type ADC requires no counter
• For an n-bit ADC, flash type ADC requires (2n – 1) comparators
• Dual slope ADC is the most accurate.

The correct answer is option 3):(15)

Concept:

Flash Type ADC:

1) It is the fastest ADC among all the ADC types.

2) An n-bit flash type ADC requires: 2ⁿ -1 comparators, 2n resistors, and one 2ⁿ × n priority encoder.

Analysis: Number of bits(n) = 4

Number of comparators required = 2⁴ -1 = 15

Concept:

An ADC takes analog input and gives output corresponding to the quantized level in the discrete domain. This conversion introduces quantization error in the output. 

For 'n' bit ADC having full-scale reading as V_fs,

 \(Resolution={V_{fs}\over2^n-1}\)

Quantization error = resolution / 2

Application:

Given number of bits, n = 10

V_fs = 10.23 V  

So, Resolution

 \(=\normalsize{10.23\over 2^{10}-1}\) 

= 10 mV

Quantization error 

 \(=\frac{10}{2}\) 

= 5 mV

 Additional Information

Resolution determines the precision of a measurement.

As the number of bits of ADC is increased, quantization error decreases but the cost of ADC increases.

Integrating type ADC is the slowest.

The conversion time of different ADC is shown below.

From the above table, the fastest ADC is Flash Type ADC whose conversion time is independent of the number of bits 

Concept:

Digital ramp ADC conversion time is given as:

 \(= \left( {{2^N} - 1} \right){T_{clk}} \)

Given:

n = 10

f = 500 kHz

Analysis:

\({T_{clk}} = \frac{1}{{500\; \times \;{{10}^3}}}\) 

= 2 μs

Conversion time = (2^N – 1) T_clk

= (1024 - 1) × 2 μs = 2046 μs

Important Points

 The conversion time of different types of n-bit ADC is shown :

Concept:

A successive-approximation ADC is a type of analog-to-digital converter that converts a continuous analog waveform into a discrete digital representation using a binary search through all possible quantization levels before finally converging upon a digital output for each analog voltage conversion.

For an N-bit successive approximation ADC, the conversion time is

= N T

Where T is the time period of the clock pulse.

∴ The conversion time does not depend on the magnitude of the input voltage.

Concept:The conversion time of the countertype A/D counter is \((2^n - 1) T_ {clk}\)  1 bit =  \((​​2^1-1)T_{CLK}\) = \(T_{clk} \).

  2 bit = \((​​2^2-1)T_{CLK}\) = \(3T_{clk}\).

  From above when bit increases, conversion doubles, So the answer is counter type A/D converter.

Additional Information

• Dual slope A/D converter is \((2^{n+1}-1)T_{clk}\)
• Flash type A/D converter is \(T_{clk}\)
• Successive approximation type A/D converter is \(nT_{clk}\)

Important Points 

• Counter type ADC and successive approximate ADC uses DAC
• Counter type ADC uses linear search and successive approximation type ADC uses binary search
• Ring counter is used in successive approximation type ADC
• Flash type ADC is fastest ADC
• Flash type ADC requires no counter
• For an n-bit ADC, flash type ADC requires (2n – 1) comparators
• Dual slope ADC is most accurate

The resolution of the dual-slope ADC is determined by the length of the run-down period and by the time measurement resolution (i.e., the frequency of the controller's clock).

The resolution (in the number of bits) is the minimum length of the run-down period for a full-scale input(V_in = - V_ref).

\({t_d} = \frac{{{2^r}}}{{{f_{clk}}}}\)

Where t_d is the run-down period,

r is resolution

f_clk is the frequency of the clock.

IMPORTANT POINT:

There are limits to the maximum resolution of the dual-slope integrating ADC. It is not possible to increase the resolution of the basic dual-slope ADC to arbitrarily high values by using longer measurement times or faster clocks. 

The advantage of using a dual-slope ADC in a digital voltmeter is that its accuracy is high. 

Dual slope ADC:

1. Dual slope integration type ADC is the most accurate type of ADC because of non-dependency on variation in component values caused by noise. 

2. Dual slope ADC is the slowest ADC among all other ADC's but the advantage of dual-slope ADC is its accuracy. 

3. These are used in the precision application. 

Advantage of Dual Slope ADC:

1. High resolution can be achieved by using an accurate count.

2. Component value variations will have no effect on accuracy.

3. For instance, the capacitance may change due to temperature variation. But since the charging and discharging processes are done through the same capacitor, the net effect of this capacitance variation is negligible.

Disadvantages:

Dual slope ADC is the slowest ADC

Flash type (or) Parallel type (or) Simultaneous ADC:

The following figure shows a 3-bit flash ADC circuit.

• It is formed of a series of comparators, each one comparing the input signal to a unique reference voltage.
• The comparator outputs connect to the inputs of a priority encoder circuit, which then produces a binary output.
• Vref is a stable reference voltage provided by a precision voltage regulator as part of the converter circuit.
• As the analog input voltage exceeds the reference voltage at each comparator, the comparator outputs will sequentially saturate to a high state.
• The priority encoder generates a binary number based on the highest-order active input, ignoring all other active inputs.
• Flash type ADC is fastest ADC
• Flash type ADC requires no counter
• For an n-bit ADC, flash type ADC requires (2n – 1) comparators
• Conversion time: Tclk

Calculation:

Given that, n = 3

Number of required comparators, N = 23 – 1 = 7