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

Amplitude Modulation and Power Calculation

Problem Statement: A carrier signal is amplitude modulated with a modulation index of 60%, resulting in a transmitted power of 472 W. We are tasked with determining how much power can be saved by suppressing the carrier and one sideband of the modulated signal.

Solution:

To solve this problem, let us analyze the power distribution in an amplitude-modulated signal.

Step 1: Power Components in an Amplitude-Modulated Signal

In amplitude modulation (AM), the total transmitted power (P_t) consists of:

• Carrier power (P_c).
• Power in the two sidebands (P_USB and P_LSB), which are equal in magnitude.

The total transmitted power is given by:

P_t = P_c + P_USB + P_LSB

The power in each sideband is determined by the modulation index (m), and is given as:

P_USB = P_LSB = (m²/4) × P_c

Thus, the total transmitted power can be expressed as:

P_t = P_c (1 + m²/2)

Step 2: Calculate the Carrier Power (P_c)

From the problem, the modulation index (m) is 60%, or m = 0.6. The total transmitted power (P_t) is 472 W. Substituting these values into the formula for total transmitted power:

472 = P_c (1 + (0.6)²/2)

First, calculate (0.6)²/2:

(0.6)²/2 = 0.36/2 = 0.18

Now substitute this value into the equation:

472 = P_c (1 + 0.18)

472 = P_c × 1.18

P_c = 472 / 1.18

P_c ≈ 400 W

Thus, the carrier power is 400 W.

Step 3: Calculate the Sideband Power

The power in the sidebands is given by:

P_sidebands = P_USB + P_LSB = (m²/2) × P_c

Substitute m = 0.6 and P_c = 400 W:

P_sidebands = (0.6)²/2 × 400

P_sidebands = 0.36/2 × 400

P_sidebands = 0.18 × 400

P_sidebands = 72 W

The total power in the sidebands is 72 W, with each sideband contributing 36 W.

Step 4: Power Saved by Suppressing the Carrier and One Sideband

When the carrier and one sideband are suppressed, the remaining power is the power in the other sideband. Thus, the power saved is:

Power saved = P_t - P_remaining

The remaining power is the power in one sideband:

P_remaining = P_LSB or P_USB = 36 W

Substitute the values:

Power saved = 472 - 36

Power saved = 436 W

Final Answer: The power saved by suppressing the carrier and one sideband is 436 W.

Concept:

When a carrier is amplitude modulated by multiple independent modulating signals, the effective modulation index is calculated using the square root of the sum of the squares of individual modulation indices.

Effective modulation index, \( m_{eff} = \sqrt{m_1^2 + m_2^2 + m_3^2} \)

Given:

Modulation percentages are 50%, 50%, and 20%.

So, \( m_1 = 0.5, \; m_2 = 0.5, \; m_3 = 0.2 \)

Calculation:

\( m_{eff} = \sqrt{(0.5)^2 + (0.5)^2 + (0.2)^2} = \sqrt{0.25 + 0.25 + 0.04} = \sqrt{0.54} \)

Explanation:

The Purpose of Carrier Modulation:

Definition: Carrier modulation is the process of varying a high-frequency signal (called the carrier) in accordance with a lower frequency message signal (information signal). This technique is widely used in communication systems to transmit information over long distances effectively.

Correct Option Analysis:

The correct option is:

Option 2: Shift the message to higher frequency band for better radiation.

Carrier modulation plays a crucial role in communication systems by shifting the message signal to a higher frequency band. This is done for several essential reasons:

• Efficient Radiation: Low-frequency signals are not efficiently radiated by antennas due to their long wavelengths. Antennas need to be comparable in size to the wavelength of the signal for effective radiation, and low-frequency signals would require impractically large antennas. By modulating the signal to a higher frequency band, antennas of reasonable size can be used for efficient radiation.
• Reduced Interference: Shifting the message signal to a higher frequency band allows multiple signals to coexist in different frequency ranges without overlapping. This reduces interference and enables the simultaneous transmission of multiple signals through multiplexing techniques.
• Improved Signal Quality: High-frequency signals are less prone to attenuation and distortion during transmission, ensuring better signal quality over long distances.
• Ease of Signal Processing: High-frequency signals are easier to process and amplify using available electronic components, making the design of communication systems more practical and cost-effective.

Detailed Working:

In carrier modulation, the message signal modulates certain characteristics of the carrier signal (such as amplitude, frequency, or phase). Depending on the method of modulation used, the message signal is encoded into the carrier signal, which is then transmitted through the medium (e.g., air, cable). At the receiver end, the original message signal is extracted from the modulated carrier signal using demodulation techniques.

Types of Modulation:

• Amplitude Modulation (AM): The amplitude of the carrier signal is varied in proportion to the message signal.
• Frequency Modulation (FM): The frequency of the carrier signal is varied according to the message signal.
• Phase Modulation (PM): The phase of the carrier signal is varied based on the message signal.

Applications:

• Radio and television broadcasting.
• Satellite communication.
• Mobile telephony and wireless communication systems.
• Data transmission over networks.

Additional Information

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

Option 1: Reduce the amplitude of the message for better radiation.

This option is incorrect. Reducing the amplitude of the message signal does not improve radiation. In fact, reducing the amplitude could lead to weaker transmission and poorer signal reception. The primary purpose of carrier modulation is not to alter the amplitude of the message signal for radiation but rather to shift it to a higher frequency band, which facilitates efficient radiation.

Option 3: Result in reduced performance in noise in some of the systems.

This option is misleading. Carrier modulation often improves the system's performance against noise, especially in techniques like frequency modulation (FM), which is known for its noise immunity. While certain modulation methods may be more susceptible to noise, the primary purpose of modulation is not related to reducing performance in noise but rather ensuring efficient transmission and reception of signals.

Option 4: Shift the message to lower frequency band for better radiation.

This option is incorrect. Shifting the message to a lower frequency band would result in poorer radiation efficiency due to the requirement for large antennas and increased susceptibility to attenuation and distortion. Carrier modulation is specifically used to shift the message signal to a higher frequency band to overcome these issues.

Conclusion:

Carrier modulation is a fundamental technique in communication systems, enabling efficient transmission and reception of signals over long distances. By shifting the message signal to a higher frequency band, it facilitates better radiation, reduces interference, and improves signal quality. Understanding the purpose and benefits of carrier modulation is essential for designing and analyzing modern communication systems.

Explanation:

Given Problem:

An antenna has an impedance of 40 Ω. An unmodulated AM signal produces a current of 5 A. The total power of the AM signal is given as 1295 W. The task is to determine the sideband power (PSB).

Solution:

In amplitude modulation (AM), the total power (PT) is the sum of the carrier power (PC) and the sideband power (PSB). Mathematically, this can be expressed as:

PT = PC + PSB

Where:

• PT = Total power
• PC = Carrier power
• PSB = Sideband power

To solve the problem, let us calculate the carrier power first.

Step 1: Calculate the Carrier Power (PC)

The carrier power is given by the formula:

PC = I² × R

Where:

• I = Carrier current (in amperes)
• R = Impedance of the antenna (in ohms)

Substitute the given values:

PC = 5² × 40

PC = 25 × 40

PC = 1000 W

Thus, the carrier power is 1000 W.

Step 2: Calculate the Sideband Power (PSB)

The total power (PT) is provided as 1295 W. From the total power formula, we know:

PT = PC + PSB

Rearranging for PSB:

PSB = PT - PC

Substitute the known values:

PSB = 1295 - 1000

PSB = 295 W

Thus, the sideband power is 295 W.

Final Answer:

The sideband power is 295 W, which corresponds to Option 4.

Additional Information

To further analyze the correctness of the other options, let's review them based on the solution:

Option 1 (800 W):

This option is incorrect. The sideband power (PSB) is calculated as 295 W, not 800 W. The value of 800 W is far too high and does not match the given total power or the calculated carrier power.

Option 2 (2800 W):

This option is also incorrect. A sideband power of 2800 W exceeds the given total power (1295 W), which is not feasible. Such a value is physically inconsistent with the problem's parameters.

Option 3 (2295 W):

This option is incorrect as well. A sideband power of 2295 W is unrealistic and does not align with the calculated values. The total power is only 1295 W, so the sideband power cannot exceed this value.

Option 4 (295 W):

This is the correct option. As derived above, the sideband power is 295 W, which matches the calculations based on the given data.

Option 5 (No value provided):

This option is invalid as it does not provide any numerical value for the sideband power.

Conclusion:

In amplitude modulation, the total power is the sum of the carrier power and the sideband power. Using the given data, the carrier power was calculated as 1000 W, and the sideband power was determined to be 295 W. Therefore, the correct answer is Option 4.

Explanation:

Signal Sampling and Overlapping Terms

Definition: When analyzing signals, sampling is the process of converting a continuous-time signal into a discrete-time signal by taking periodic samples. The Nyquist rate, named after Harry Nyquist, is the minimum rate at which a signal can be sampled without introducing errors, which is twice the highest frequency present in the signal. If the sampling rate is lower than this threshold, it can lead to a phenomenon called aliasing, where different signals become indistinguishable from each other.

Correct Option Analysis:

The correct option is:

Option 4: under sampled

During the message recovery, if terms (or components) of the signal are observed to be overlapping, it indicates that the signal has been under sampled. Under sampling means that the sampling rate is less than the Nyquist rate, which leads to aliasing. Aliasing occurs when higher frequency components of the signal are misrepresented as lower frequencies, causing overlap and distortion in the recovered signal.

Additional Information

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

Option 1: sampled at twice the Nyquist rate

If the signal were sampled at twice the Nyquist rate, it would be sampled at a rate higher than necessary to avoid aliasing. This would result in a well-defined and clear signal recovery without any overlapping terms. Over sampling at this rate would not cause any overlap or distortion.

Option 2: over sampled

Over sampling refers to sampling at a rate higher than the Nyquist rate. While over sampling is generally beneficial as it can reduce noise and improve signal accuracy, it does not cause overlapping terms. Instead, it provides more data points than necessary, making the signal recovery more accurate and less prone to aliasing.

Option 3: sampled at the Nyquist rate

Sampling at the Nyquist rate means sampling at exactly twice the highest frequency present in the signal. This is the minimum rate required to avoid aliasing. When sampled at the Nyquist rate, the signal can be perfectly reconstructed without any overlapping terms, provided that the sampling and reconstruction processes are ideal.

Conclusion:

Understanding the concept of the Nyquist rate and the effects of under sampling is crucial in signal processing. Under sampling leads to aliasing, where different frequency components overlap and distort the original signal during recovery. This phenomenon highlights the importance of sampling at or above the Nyquist rate to ensure accurate signal representation and recovery. By examining the options, it is clear that the presence of overlapping terms during message recovery indicates under sampling, as described in option 4.

Concept:

A single tone modulated signal is given as:

Maximum envelope Amax : Ac (1+μ)

Minimum envelope Amin : Ac (1-μ)

\(\frac{{{A_{max}}}}{{{A_{min}}}} = \frac{{1 + μ}}{{1 - μ}}\)

The above can be written as:

\(μ = \frac{{{A_{max}} - {A_{min}}}}{{{A_{max}} + {A_{min}}}}\)

Calculation:

Given:  Amax = 3 V and Amin = 1 V

The modulation index will be:

\(μ = \frac{{{3} - 1}}{{3 + 1}}\)

μ = 0.5

Amplitude Modulation (AM) is preferred for picture transmission in TV because of the following reasons:

• The distortion which arises due to interference between multiple signals is more in FM than AM because the frequency of the FM signal continuously changes.
• Steady production of the picture is affected because of this.
• If AM were used, the ghost image, if produced is steady.
• Also, the circuit complexity and bandwidth requirements are much less in AM than in FM.

On the other hand, FM is preferred for sound because of the following reasons:

• The bandwidth assigned to the FM sound signal is about 200 kHz, of which not more than 100 kHz is occupied by significant side bands.
• This is only 1.4 % of the total channel bandwidth of 7 MHz. This results in efficient utilization of the channel.

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:

The generalized AM expression is represented as:

s(t) = Ac [1 + μa mn (t)] cos ωc t

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)

Pc = Carrier Power

μ = Modulation Index

The above expression can be expanded to get:

\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)

The total power is the sum of the carrier power and the sideband power, i.e.

\({P_s} = P_c\frac{{{μ^2}}}{2}\)

Analysis:

Total sideband power is calculated as:

\({P_s} = P_c\frac{{{μ^2}}}{2}\)

% of sideband power is given as:

⇒ \( \frac{P_c \frac{μ^2}{2}}{{P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)}\)

⇒ \( \frac{μ^2}{μ^2+2}\)

putting μ = 0.4, we get

⇒ \( \frac{0.4^2}{0.4^2\;+\;2} \times 100 = 0.074 \times 100\)

= 7.4 %

Concept:

The generalized AM expression is represented as:

s(t) = Ac [1 + μa mn (t)] cos ωc t

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)

Pc = Carrier Power

μ = Modulation Index

The above expression can be expanded to get:

\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)

The total power is the sum of the carrier power and the sideband power, i.e.

\({P_s} = P_c\frac{{{μ^2}}}{2}\)

The power in a single sideband will be:

\({P_s} = \frac{1}{2}\times P_c\frac{{{μ^2}}}{2}\)

With \(P_c=\frac{A^2}{2}\), the above can be written as:

\({P_s} = \frac{1}{2}\times \frac{A_c^2}{2}\frac{{{μ^2}}}{2}\)

\({P_s} = \frac{{{A_c^2μ^2}}}{8}\)   

\(Power Saved=\frac{P_c}{P_{total}}\)  ---(1)

Power Saved = Pc in DSB - SC

\(Power \ Saved=\frac{2}{2 \ + \ μ^2}\)

Analysis:

When μ = 1, the transmitted power will be:

\({P_t} = {P_c}\left( {1 + \frac{{{1^2}}}{2}} \right)=\frac{3}{2}P_c\)

\(Power Saved=\frac{P_c}{P_c(1 \ + \ \frac{μ^2}{2})}\)

As μ = 1

\(Power \ Saved=\frac{2}{2 \ + \ 1^2}\times 100\)

Power Saved = 66 %

Concept:

The frequency spectrum of an Amplitude Modulated wave is given by:

Bandwidth in AM = (f_c + f_m) - (fc - fm)

Bandwidth in AM = 2fm

Calculation:

fc = 10 kHz

Upper sideband = fc + fm = 11 kHz

∴ The message frequency is:

fm = 11 – 10 = 1 kHz

Hence, Bandwidth is:

= 2f_m = 2 × 1 kHz = 2 kHz

Concept:

The transmission efficiency of an AM wave is defined as the percentage of total power contributed by the sidebands.

For a sinusoidal AM signal, it is given by:

\(η=\frac{{{μ ^2}}}{{2 + {μ ^2}}} \times 100\)

μ = Modulation index

The maximum efficiency is obtained for μ = 1, i.e.

\(η_{max}=\frac{{{1}}}{{2 + {1}}} \times 100\)

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

\(\eta = \frac{{{P}_{SB}}}{{{P_t}}} \times 100\%\)

For sinusoidal input

PSB = Sideband power given by:

\({P_{SB}} = \frac{{{P_c}\;{\mu ^2}}}{2}\)

Pt = Total power given by:

\({P_t} = {P_c}\;\left( {1 + \frac{{{\mu ^2}}}{2}} \right)\),

\(\eta = \frac{{{P_c}{\mu ^2}}}{{2\left( {{P_c}\left( {1 + \frac{{{\mu ^2}}}{2}} \right)} \right)}}\)

\(\eta = \frac{{{P_c}{\mu ^2}}}{{{P_c}\left( {2 + {\mu ^2}} \right)}} = \frac{{{\mu ^2}}}{{2 + {\mu ^2}}} \times 100\)

Explanation:

In AM modulation Index is defined as:

\(μ = \frac{{{A_m}}}{{{A_c}}} = \frac{{{A_{max}} - {A_{min}}}}{{{A_{max}} + {A_{min}}}}\)

Where Am = amplitude of modulating wave

Ac = amplitude of carrier wave

Clearly, it is independent of fm.

• The value of modulation varies from 0 to 1.   0 ≤ μ ≤ 1
• For μ < 1, the AM wave is said to be under modulated.
• For μ > 1, the AM wave is said to be over-modulated.
• For μ = 1, the AM wave is said to be critically modulated.
• 100% modulation is where the modulating signal drives the carrier to zero and is theoretically the maximum modulation that can be successfully demodulator by a regular AM envelope detector.

A general Amplitude modulation process is as shown:

Modulation:

The process in which the characteristics of carrier signal is varied in accordance with baseband message signal to make bandpass signal.

Sampling :

The process of conversion of continuous time signals into discrete time signal.

Encoding :

The process of putting the message in the form in which it is to be communicated.

ex: Analog signal into digital form.

Demodulation :

The process of recovery of message signal from modulated signal.

Hence correct option is "3"

Concept:

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)

Pc = Carrier Power

μ = Modulation Index

Calculation:

With PC = 500 W and μ = 0.80, the total power in the modulated wave will be:

\({P_t} = {500}\left( {1 + \frac{{{(0.8)^2}}}{2}} \right)\)

Pt = 660 W

Note: The transmitted power is independent of the modulation index in the case of FM and PM.

Amplitude Modulation (AM) is preferred for picture transmission on TV because of the following reasons:

• The distortion which arises due to interference between multiple signals is more in FM than AM because the frequency of the FM signal continuously changes.
• Steady production of the picture is affected because of this.
• If AM were used, the ghost image, if produced is steady.
• Also, the circuit complexity and bandwidth requirements are much less in AM than in FM.

On the other hand, FM is preferred for sound because of the following reasons:

• The bandwidth assigned to the FM sound signal is about 200 kHz, of which not more than 100 kHz is occupied by significant sidebands.
• This is only 1.4 % of the total channel bandwidth of 7 MHz. This results in efficient utilization of the channel.

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.