Data Converters MCQ Quiz - Objective Question with Answer for Data 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.

Concept:

The resolution of a Digital-to-Analog (D/A) converter is the smallest change in analog output corresponding to a one-bit change in the digital input.

It is given by: \( \text{Resolution} = \frac{V_{max}}{2^n - 1} \)

Where,

• \( V_{max} \) is the maximum output voltage
• n is the number of bits

Given:

Number of bits, n =9

Maximum output voltage, \( V_{max} = 5.12 \, V \)

Calculation:

\( \text{Resolution} = \frac{5.12}{2^9 - 1} = \frac{5.12}{511} \approx 0.01 \, V = 10 \, mV \)

Correct Answer: 1) 10 mV

Concept:

For a ladder-type D/A Converter:

Output Voltage (V0) = Resolution × Decimal Equivalent of binary input.

Where Resolution is given by:

\(Resolution=\frac{{{V}_{ref}}}{{{2}^{n}}}\)

Application:

Given n = 5 and the Digital input = 11010

∵ The Resolution will be:

\(R=\frac{{{V}_{ret}}}{{{2}^{n}}}=\frac{10}{{{2}^{5}}}=~0.3125\)

Since the decimal Equivalent of 11010 = 26

So, V0 = 26 × 0.3125

V0 = 8.125 V

Note: If the full-scale voltage is given, then:

Resolution \(=\frac{{{V}_{fs}}}{{{2}^{n}}-1}\)

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

Dual slope ADC: (2n+1 – 1) Tclk

The successive approximation A/D converter has shorter conversion time compared to the counter ramp A/D converter.

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

Resolution: It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital input.

The percentage resolution (%R) of an n-bit DAC is:

\(\%R = \frac{1}{{{2^n} - 1}} \times 100\)

The resolution of an n-bit DAC with a range of output voltage from 0 to V is given by:

\(R = \frac{V}{{{2^n} - 1}}volts\)

Calculation:

Number of bits (n) = 8

Resolution \( = \frac{{1}}{{{2^8} - 1}} = \frac{{1}}{{255}}\)

No of comparators required for n bit flash type ADC is (2ⁿ - 1)

Given that, n = 12

Resolution: It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.

The percentage resolution (%R) of an n-bit DAC is:

\(\%R = \frac{1}{{{2^n} - 1}} \times 100\)

The resolution of an n-bit DAC with a range of output voltage from 0 to V is given by:

\(R = \frac{V}{{{2^n} - 1}}volts\)

Hence the difference between analog voltage represented by two adjacent digital codes of an analog to digital converter is called resolution.

Hence option (2) is the correct answer.

Important Points

Accuracy:

• The accuracy of the A/D converter determines how close the actual digital output is to the theoretically expected digital output for given analog input.
• In other words, the accuracy of the converter determines how many bits in the digital output code represent useful information about the input signal.

% Accuracy of a n bit ADC = (1 / 2n ) × 100

Concept:

For a ladder-type D/A Converter:

Output Voltage (V0) = Resolution × Decimal Equivalent of binary input.

Where Resolution is given by:

\(Resolution=\frac{{{V}_{fs}}}{{{2}^{n}}-1}\)

Where, V_fs = Full scale voltage or maximum voltage

Application:

Given n = 6 and the Digital input = 101001

∵ The Resolution will be:

\(R=\frac{{{V}_{ret}}}{{{2}^{n}-1}}=\frac{10}{{{2}^{6}-1}}=~0.1587\)

Since the decimal Equivalent of 101001 = 41

So, V0 = 41 × 0.1587

V0 = 6.5067 V

V₀ ≈ 6.5 V

Note:  If the reference voltage is given, then:

\(Resolution=\frac{{{V}_{ref}}}{{{2}^{n}}}\)

Comparator:

• A comparator is a circuit which compares a signal voltage applied at one input of an Op-Amp with a known reference voltage at the other input.
• It produces either a high or a low output voltage, depending on which input is higher.
• Since, a comparator output has two voltage levels, either high or low. (1 or 0) So it acts as an Analog to Digital convertor.
• it is not linearly proportional to the input voltage.

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The common Analog to digital converters are:

Ramp-type:

• The principle of Ramp-type DVM is based on the measurement of the time it takes for a linear ramp voltage to rise from 0 V to the level of the input voltage (or) to decrease from the level of the input voltage to zero.
• This type of Analogue to Digital Converter is very slow (but cheap and simple).
• It is ideal for data that changes fairly slowly such as vehicle or aircraft control systems.

• Audio signals are slow enough to be converted.

Dual-slope converter:

• In the dual-slope technique, an integrator is used to integrate an accurate voltage reference for a fixed period of time. The same integrator is then used to integrate with the reverse slope, the input voltage, and the time required to return to the starting voltage is measured.
• The automatic zero correction function is performed before each conversion so that changes in the offset voltages & current will be compensated.

Successive Approximation:

• The basic principle is that binary regression, in which analog input is compared with DAC reference voltage which is repeatedly divided in half.
• A successive approximation A/D converter consists of a comparator, a successive approximation register (SAR), output latches, and a D/A converter.
• It is capable of high speed and is reliable.

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