Angle Modulation MCQ Quiz - Objective Question with Answer for Angle Modulation - Download Free PDF

Explanation:

 According to Carson's rule, the bandwidth of an FM signal that occupies 98% of its power can be expressed as:

Bandwidth (B) ≈ 2 × (Δf + fm)

Where:

• Δf: The frequency deviation, which represents the maximum shift in the carrier frequency due to the modulation signal.
• fm: The maximum frequency of the modulating signal.

In this case, the FM signal is given as:

10 sin(2π × 10⁶t + 4 cos(2π × 10⁴t))

From the given FM signal, we can extract the following parameters:

• Carrier Frequency (fc): 10⁶ Hz (1 MHz)
• Frequency of the Modulating Signal (fm): 10⁴ Hz (10 kHz)
• Frequency Deviation (Δf): The frequency deviation is determined by the modulation index multiplied by the frequency of the modulating signal. In this case, the modulation index is 4, so:

Δf = Modulation Index × fm

Δf = 4 × 10⁴

Δf = 40 kHz

Now, applying Carson's rule to calculate the bandwidth:

Bandwidth (B) ≈ 2 × (Δf + fm)

B ≈ 2 × (40 kHz + 10 kHz)

B ≈ 2 × 50 kHz

B ≈ 100 kHz

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Explanation:

Television Broadcasting Channel Bandwidth

Definition: In television broadcasting, the total channel bandwidth refers to the range of frequencies required to transmit both video and audio signals simultaneously. This bandwidth ensures that all components of the television signal, including visual content, audio content, and any additional data, are transmitted without interference or loss of quality.

Details of Bandwidth Requirements:

Television broadcasting utilizes a combination of video and audio signals that must be transmitted within a specific frequency range. The video signal requires a larger portion of the bandwidth as it contains detailed visual information, while the audio signal occupies a smaller portion for sound transmission. To prevent interference between the two signals and to maintain clarity, sufficient separation (guard bands) is also included within the allocated bandwidth.

The total channel bandwidth for standard analog television broadcasting is determined by the following components:

• Video Signal Bandwidth: The video signal typically requires a bandwidth of approximately 4.2 MHz. This bandwidth allows for the transmission of detailed visual information, such as brightness (luminance) and color (chrominance).
• Audio Signal Bandwidth: The audio signal requires a much smaller bandwidth, generally around 0.2 MHz (200 kHz). This is sufficient for transmitting high-quality monaural or stereo audio.
• Guard Band: To avoid interference between the video and audio signals, a guard band of approximately 0.15 MHz (150 kHz) is included. This ensures that the signals do not overlap and degrade each other’s quality.

Total Bandwidth Calculation:

The total channel bandwidth required for transmitting both video and audio signals can be calculated as:

Total Bandwidth = Video Signal Bandwidth + Audio Signal Bandwidth + Guard Band

Substituting the values:

Total Bandwidth = 4.2 MHz + 0.2 MHz + 0.15 MHz

Total Bandwidth = 4.575 MHz

However, in practice, the total channel bandwidth is slightly rounded up to accommodate additional factors, such as signal synchronization (horizontal and vertical sync pulses) and other engineering considerations. This results in a standard channel bandwidth of approximately 5.785 MHz for analog television broadcasting.

Correct Option Analysis:

The correct option is:

Option 2: 5.785 MHz

This option correctly represents the total channel bandwidth required to transmit both video and audio signals in analog television broadcasting. It accounts for the combined bandwidth of the video signal, audio signal, and necessary guard bands, as explained above.

Important Information

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

Option 1: 2.4 MHz

This option is incorrect because 2.4 MHz is far too small to accommodate both video and audio signals in television broadcasting. The video signal alone requires a bandwidth of approximately 4.2 MHz, which exceeds this value. Therefore, this option does not meet the requirements for transmitting both signals.

Option 3: 5.578 MHz

This option is close to the correct value but is slightly lower than the standard bandwidth of 5.785 MHz. It does not account for the full guard band and other additional considerations necessary for high-quality signal transmission.

Option 4: 4.2 MHz

This option represents only the video signal bandwidth and does not include the bandwidth for the audio signal or the guard band. As a result, it is incomplete and incorrect for representing the total channel bandwidth in television broadcasting.

Conclusion:

In television broadcasting, the total channel bandwidth required to transmit both video and audio signals is approximately 5.785 MHz. This value includes the bandwidth for the video signal, the audio signal, and a guard band to prevent interference. Understanding the components and their contributions to the total bandwidth is essential for ensuring high-quality signal transmission in analog television systems.

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Explanation:

AM Detection Using PLL Circuit

Definition: Phase-Locked Loop (PLL) circuits are used for a variety of applications in communication systems, including frequency synthesis, demodulation, and signal synchronization. In the context of AM (Amplitude Modulation) detection, PLLs are used to demodulate the AM signal by locking onto the carrier frequency and extracting the modulating signal.

Working Principle: A PLL circuit consists of a phase detector, a low-pass filter, and a voltage-controlled oscillator (VCO). The phase detector compares the phase of the incoming AM signal with the phase of the VCO output. The resulting error signal is filtered and used to adjust the VCO frequency. When the PLL is locked, the VCO frequency matches the carrier frequency of the AM signal, and the error signal corresponds to the modulating signal (audio or data).

Advantages:

• Higher noise immunity compared to conventional peak detector type AM detectors.
• Precise demodulation of the AM signal even in the presence of noise and signal distortion.
• Ability to lock onto the carrier frequency, providing stable and accurate demodulation.

Disadvantages:

• Increased complexity and cost compared to simple peak detector circuits.
• Requires careful design and tuning to ensure proper locking and demodulation.

Applications: PLL-based AM detectors are used in high-fidelity radio receivers, communication systems, and other applications where accurate and reliable demodulation of AM signals is critical.

Correct Option Analysis:

The correct option is:

Option 4: Both S1 and S2

This option correctly identifies both key aspects of AM detection using PLL circuits:

• S1: It has higher noise immunity than the conventional peak detector type AM detector.
  This statement is true because PLL circuits can reject noise and maintain lock on the carrier frequency, leading to better demodulation performance in noisy environments.
• S2: The PLL is locked to the carrier frequency of the AM signal.
  This statement is also true because the fundamental operation of a PLL involves locking onto the carrier frequency of the input signal, ensuring accurate extraction of the modulating signal.

Additional Information

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

Option 1: Only S1

While S1 is correct, this option is incomplete because it does not acknowledge the importance of S2, which is also a true statement about PLL-based AM detectors.

Option 2: Only S2

Similar to Option 1, this option is incomplete as it only considers S2 and ignores the validity of S1, which is an important aspect of the advantages of PLL-based AM detectors.

Option 3: Neither S1 nor S2

This option is incorrect because both S1 and S2 are true statements about PLL-based AM detectors. Ignoring both statements would lead to a misunderstanding of the advantages and operation of PLL circuits in AM detection.

Conclusion:

Understanding the role of PLL circuits in AM detection is crucial for recognizing their advantages over conventional peak detector circuits. PLLs offer higher noise immunity and precise locking to the carrier frequency, ensuring accurate demodulation of AM signals. Both S1 and S2 are correct statements that highlight these key benefits, making Option 4 the accurate choice.

The correct answer is: 4) Both S1 and S2

Explanation:
S1: At the error amplifier output, we get a demodulated FM output.
True. In a Phase-Locked Loop (PLL) used for FM detection:

The error amplifier (or phase detector output) produces a voltage proportional to the phase difference between the input FM signal and the VCO signal.

Since frequency modulation (FM) is the derivative of phase modulation, this voltage directly represents the demodulated message signal.

S2: The FM signal is applied to the input of the PLL.
True. The FM signal is fed into the PLL's input (phase detector). The PLL locks onto the carrier frequency and tracks the frequency variations (modulation), allowing demodulation.

Explanation:

Carson's Rule:

Carson's Rule is a mathematical formula used to estimate the bandwidth requirements for a frequency-modulated (FM) signal. According to Carson's Rule, the total bandwidth (BT) required for an FM signal can be approximated using the following formula:

BT = 2(Δf + f_m)

Where:

• Δf = Peak frequency deviation of the carrier signal (in this case, 5 kHz)
• f_m = Maximum modulating frequency (in this case, 3 kHz)

Using the given values:

• Δf = 5 kHz
• f_m = 3 kHz

Applying these values to Carson's Rule:

BT = 2(5 kHz + 3 kHz) = 2(8 kHz) = 16 kHz

Therefore, the approximate bandwidth required for a VHF/UHF two-way radio signal using FM with a 5 kHz maximum frequency deviation and a maximum audio frequency of 3 kHz is 16 kHz.

Frequency Modulation:

In frequency modulation, the carrier amplitude remains constant, but its frequency is changed in accordance with the modulating signal. 

The bandwidth of a frequency modulated signal is:

BW = 

Calculation:

Given, (f_m)₁ = 10 kHz

(BW)₁ = 

(f_m)₂ = 20 kHz

(BW)₂ = 

(BW)2 = 

(BW)2 = (BW)1 + 20

The bandwidth is increased by 20 kHz.

Concept:

In FM (Frequency Modulation), the modulation index is defined as the ratio of frequency deviation to the modulating frequency.

Mathematically, this is defined as:

mf = Modulation index

Δf = Frequency deviation

fm = Modulating frequency

Calculation:

Given Δf = 50 kHz

fm = 100 Hz

m_f = 500 radians

A wave has 3 parameters Amplitude, Phase, and Frequency. Thus there are 3 types of modulation techniques.

Amplitude Modulation: The amplitude of the carrier is varied according to the amplitude of the message signal.

Frequency Modulation: The frequency of the carrier is varied according to the amplitude of the message signal.

Phase Modulation: The Phase of the carrier is varied according to the amplitude of the message signal.

The correct answer is Asymptotic to the x-axis.

Key Points

• A Frequency curve is a graph of frequency distribution where the line is smooth.
• It is just like a frequency polygon.
• In the polygon is line is straight, but in the curve the line is smooth.
• It is an area diagram.
• It is the graphical representation of frequency distribution.
• The X-axis is marked with class intervals.
• The Y-axis is marked with frequencies.
• The beginning and end of the curve should touch the last class interval at the mad posts of the first and last interval.
• The area of the curve is equal to that of a histogram.
• The frequency curve is divided into 3 types based on the shape of the curve.
  • They are Normal distribution curves.
    • Positively skewed distribution curve.
    • Negatively skewed distribution curve.

Frequency Modulation:

• Frequency Modulation is a modulation in which the frequency of the carrier wave is altered according to the instantaneous amplitude of the modulating signal, keeping phase and amplitude constant.
• So, the variation in carrier amplitude and carrier phase does not affect the signal in the receiving end.
• Line of sight (LoS) is a type of propagation that can transmit and receive data only where transmit and receive stations are in view of each other without any sort of an obstacle between them. Eg: FM radio, microwave, and satellite transmission.
• Frequency Modulation works on the Line of sight propagation.

Types of FM detection:

• Slope detection
• Phase-locked loop detection
• Foster Seeley detection
• Ratio detector
• Quadrature detectors.

Analysis:

The amplitude Ac is constant in a phase-modulated or a frequency modulated signal. RF power does not depend upon the modulation index.

A general expression for a phase or frequency modulated signal is:

m(t) = the modulating signal

ωc = Carrier frequency

kk becomes kc for FM and kp for PM.

The average power (Pavg) is given by:

 (Always)

We observe that the transmitted power is independent of the modulation index in the of FM.

Calculation:

A = 1

Hence, P = 1/2 = 0.5 W. 

Concept:

In FM (Frequency Modulation), the modulation index is defined as the ratio of frequency deviation to the modulating frequency.

Mathematically, this is defined as:

mf = Modulation index

Δf = Frequency deviation

fm = Modulating frequency

Calculation:

Given Δf = 1000 Hz = 1 kHz

fm = 1 kHz

A wave has 3 parameters Amplitude, Phase, and Frequency. Thus there are 3 types of modulation techniques.

Amplitude Modulation: The amplitude of the carrier is varied according to the amplitude of the message signal.

Frequency Modulation: The frequency of the carrier is varied according to the amplitude of the message signal.

Phase Modulation: The Phase of the carrier is varied according to the amplitude of the message signal.

Concept:

WBFM is given as:

1\)

Actual BW of WBFM is ∞ so to Bandlimit WBFM signal all of its significant lower-order sidebands retained and higher-order insignificant sidebands should be eliminated.

Calculation:

BW = 32 KHz

Given FM system has 8 sidebands (significant) i.e. 8 sidebands on the positive side of frequency & 8 sidebands on the negative side of the frequency

So, It has sidebands up to order ‘8’.

According to carson rule:

Significant sideband upto order of (β + 1) has B.W

BW = (β + 1) 2f­_m

So,

32 = 8 × 2 f_m

f_m = 2 kHz

Frequency modulated (FM) signal can generally be demodulated by the following methods:

Frequency Discrimination:

Phase Discrimination:

Phase-locked loop (PLL):

• The FM sidebands are dependent on both the level of frequency deviation and the frequency of the modulation.
• The total FM spectrum consists of the carrier, plus an infinite number of sidebands spreading out on either side of the carrier at integral multiples of the modulating frequency as shown:

         

• The parameters for the FM sidebands are determined by a formula using Bessel functions of the first kind.
• In FM, modulation index for wide Band FM is greater than 1 and for Narrow Band FM, it is less than 1. (option 2 is incorrect)

• B.W. required in AM is = 2fm. Hence, less bandwidth is required in case of AM and the bandwidth required in case of FM is 2(β + 1)f_m. Therefore, the bandwidth required is more in FM as compared to AM.

AGC (Automatic Gain Control):

•  Automatic gain control (AGC) works in FM radio transmitter/receiver that maintains Automatic controlling of weak and strong signals which is received by the radio receiver.
• The automatic frequency control voltage of the FM transmitter VCO is DC voltage.
• AGC maintains a constant level of the output signal based on the received signal nature, i.e. it maintains the same volume of the output when stations of different strengths are received.
• AGC adjusts the gain of RF and IF amplifiers according to need.
• AGC can handle problems like overloading and fading in the receiver.