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

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.

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:

$\eta =\frac{{\mu }^2}{2+{\mu }^2}\times 100$

μ = Modulation index

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

${\eta }_{max}=\frac{1}{2+1}\times 100$

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

$\eta =\frac{P_{SB}}{P_t}\times 100\mathrm{\%}$

For sinusoidal input

PSB = Sideband power given by:

$P_{SB}=\frac{P_c{\mu }^2}{2}$

Pt = Total power given by:

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

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

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

Concept:

The AM signal is (A_c cos ω_c t + m(t) cos ω_ct)

Efficiency is defined as:

$\left(\eta \right)=\frac{\frac{P_{m\left(t\right)}}{2}}{\frac{P_{m\left(t\right)}}{2}+P_c}$

Where P_m(t) is the message signal power and P_c is carrier power.

Calculation:

$P_{m\left(t\right)}=\frac{1}{4}{\int }_0^4{\left|m\left(t\right)\right|}^{2}dt=6$

With $\mu =\frac{A_m}{A_c}$, the carrier power for the given modulation index of 0.62 will be:

$A_c=\frac{A_m}{\mu }=\frac{3}{0.62}$

A_c = 4.83

$P_c=\frac{A_c^2}{2}=11.70$

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:

$\eta =\frac{{\mu }^2}{2+{\mu }^2}\times 100$

μ = Modulation index

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

${\eta }_{max}=\frac{1}{2+1}\times 100$

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

$\eta =\frac{P_{SB}}{P_t}\times 100\mathrm{\%}$

For sinusoidal input

PSB = Sideband power given by:

$P_{SB}=\frac{P_c{\mu }^2}{2}$

Pt = Total power given by:

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

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

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

Standard form of AM:

$A_c\left[1+\mu \cos {\omega }_{m}t\right]\cos {\omega }_{c}t$

$=20\left[1+\frac{1}{10}\cos 3000\pi t+\frac{1}{2}\cos 6000\pi t\right]$

μ₁ = 0.1 , μ₂ = 0.5

${\mu }_{total}=\sqrt{{0.1}^2+{0.5}^2}$

μ_total = 0.51

Ratio of power in sideband to total power

$Power=\frac{{\mu }^2}{{\mu }^2+2}$

$\Rightarrow \frac{{\left(0.51\right)}^2}{{\left(0.51\right)}^2+2}=0.115$

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:

$\eta =\frac{{\mu }^2}{2+{\mu }^2}\times 100$

μ = Modulation index

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

${\eta }_{max}=\frac{1}{2+1}\times 100$

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

$\eta =\frac{P_{SB}}{P_t}\times 100\mathrm{\%}$

For sinusoidal input

PSB = Sideband power given by:

$P_{SB}=\frac{P_c{\mu }^2}{2}$

Pt = Total power given by:

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

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

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

Concept: power efficiency of AM is defined as $\left(\eta \right)=\frac{{\mu }^2}{2+\mu }\times 100\mathrm{\%}$

Where μ = modulation index = $\frac{A_m}{A_c}$

Solution:

$m\left(t\right)=\frac{1}{2}\cos {\omega }_1\left(t\right)-\frac{1}{2}\sin {\omega }_{2}t$

Since in msg signal, two different frequencies ω₁ ⋅ ω₂ are present So it is a multitone signal.

$A_{m_1}=\frac{1}{2}$

$A_{m_2}=\frac{1}{2}$

$s\left(t\right)=\left[1+m\left(t\right)\right]\cos {\omega }_{c}t$

Comparing with standard

AM signal equation $s\left(t\right)=A_c\left[+K_{a}m\left(t\right)\right]\cos {\omega }_{c}t$

A_c = 1, K_a = 1

${\mu }_1=\frac{A_{m_1}}{A_c}=\frac{1}{2}$

${\mu }_2=\frac{A_{m_2}}{A_c}=\frac{1}{2}$

$\mu =\sqrt{{\mu }_1^2+{\mu }_2^2}=\sqrt{{\frac{1}{2}}^2+{\frac{1}{2}}^2}=\sqrt{\frac{1}{2}}$

$\eta =\frac{{\mu }^2}{2+\mu }\times 100\mathrm{\%}=\frac{\frac{1}{2}}{2+\frac{1}{2}}\times 100\mathrm{\%}=\frac{1}{5}\times 100\mathrm{\%}$

η = 20%

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.

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:

$\eta =\frac{{\mu }^2}{2+{\mu }^2}\times 100$

μ = Modulation index

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

${\eta }_{max}=\frac{1}{2+1}\times 100$

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

$\eta =\frac{P_{SB}}{P_t}\times 100\mathrm{\%}$

For sinusoidal input

PSB = Sideband power given by:

$P_{SB}=\frac{P_c{\mu }^2}{2}$

Pt = Total power given by:

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

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

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

Concept:

The AM signal is (A_c cos ω_c t + m(t) cos ω_ct)

Efficiency is defined as:

$\left(\eta \right)=\frac{\frac{P_{m\left(t\right)}}{2}}{\frac{P_{m\left(t\right)}}{2}+P_c}$

Where P_m(t) is the message signal power and P_c is carrier power.

Calculation:

$P_{m\left(t\right)}=\frac{1}{4}{\int }_0^4{\left|m\left(t\right)\right|}^{2}dt=6$

With $\mu =\frac{A_m}{A_c}$, the carrier power for the given modulation index of 0.62 will be:

$A_c=\frac{A_m}{\mu }=\frac{3}{0.62}$

A_c = 4.83

$P_c=\frac{A_c^2}{2}=11.70$

Concept:

The general expression for an amplitude modulated signal, with single tone modulating signal, is defined as:

S_AM(t) = A_C (1 + cos ω_mt) cos ω_c t

= A_c cos ω_c + A_c cos ω_mt cos ω_ct

$=A_C\cos {\omega }_{c}t+\frac{A_c}{2}\cos \left({\omega }_c-{\omega }_m\right)t+\frac{A_c}{2}\cos \left({\omega }_c+{\omega }_m\right)t$ 

Also, the modulation efficiency of an AM signal is defined as the ratio of the power with the sidebands to the total power i.e.

$\eta =\frac{P_{sb}}{P_t}\times 100$ 

Analysis:

Given:

x_AM(t) = A cos (400πt) + B cos (380 πt) + B cos (420 πt) 

Comparing this with the general expression, the above can be written as:

x_AM(t) = A cos 400 πt + B cos (400 π – 20 π)t + B cos (400 π + 20 π)t

The carrier signal is, therefore:

c(t) = A cos 400πt

And the two sidebands are:

Sideband 1: B cos (380 πt)

Sideband 2: B cos (420 πt)

The carrier power will be:

$P_c=\frac{A^2}{2}$ 

Given P_c = 100, we can write:

$100=\frac{A^2}{2}$ 

A² = 200

A = 14.14

Now, the total sideband power will be:

$P_{sb}=\frac{B^2}{2}+\frac{B^2}{2}$ 

P_SB = B²

Given modulation efficiency = 40% = 0.4

We can write:

$0.4=\frac{P_{SB}}{P_t}=\frac{P_{SB}}{P_C+P_{SB}}$ 

$0.4=\frac{B^2}{100+B^2}$ 

40 + 0.4 B² = B²

40 = 0.6 B²

$B^2=\frac{400}{6}$ 

B = 8.16

Alternate method:

The power efficiency of an AM signal with single tone modulation is given by:

${\eta }_{AM}=\frac{{\mu }^2}{2+{\mu }^2}$ 

μ = Modulation index

Given output of AM modulator is:

x(t) = A cos (400 πt) + B cos (380 πt) + B cos (240 πt)

Appying trigonometric property, the above equation becomes:

x(t) = A cos (400 πt) + 2 B cos (400 πt) cos (20 πt)

$=A\left[1+\frac{2B}{A}\cos \left(20\pi t\right)\right]\cos \left(400\pi t\right)$ 

From the above, we get the carrier power as:

$P_C=\frac{A^2}{2}$ 

And the modulation index (μ) as:

$\mu =\frac{2B}{A}$         ---(1)

Now,

P_C = 100 W (Given)

$\therefore 100=\frac{A^2}{2}$ 

A = 14.14

η_AM = 40% = 0.4

$0.4=\frac{{\mu }^2}{2+{\mu }^2}$ 

0.8 + 0.4 μ² = μ²

0.8 = 0.6 μ²

${\mu }^2=\frac{4}{3}$ 

$\mu =\frac{2}{\sqrt{3}}$ 

Substituting this in equation (1), we get:

$\frac{2}{\sqrt{3}}=\frac{2B}{A}$ 

$B=\frac{A}{\sqrt{B}}=\frac{14.14}{\sqrt{3}}$ 

Concept: power efficiency of AM is defined as $\left(\eta \right)=\frac{{\mu }^2}{2+\mu }\times 100\mathrm{\%}$

Where μ = modulation index = $\frac{A_m}{A_c}$

Solution:

$m\left(t\right)=\frac{1}{2}\cos {\omega }_1\left(t\right)-\frac{1}{2}\sin {\omega }_{2}t$

Since in msg signal, two different frequencies ω₁ ⋅ ω₂ are present So it is a multitone signal.

$A_{m_1}=\frac{1}{2}$

$A_{m_2}=\frac{1}{2}$

$s\left(t\right)=\left[1+m\left(t\right)\right]\cos {\omega }_{c}t$

Comparing with standard

AM signal equation $s\left(t\right)=A_c\left[+K_{a}m\left(t\right)\right]\cos {\omega }_{c}t$

A_c = 1, K_a = 1

${\mu }_1=\frac{A_{m_1}}{A_c}=\frac{1}{2}$

${\mu }_2=\frac{A_{m_2}}{A_c}=\frac{1}{2}$

$\mu =\sqrt{{\mu }_1^2+{\mu }_2^2}=\sqrt{{\frac{1}{2}}^2+{\frac{1}{2}}^2}=\sqrt{\frac{1}{2}}$

$\eta =\frac{{\mu }^2}{2+\mu }\times 100\mathrm{\%}=\frac{\frac{1}{2}}{2+\frac{1}{2}}\times 100\mathrm{\%}=\frac{1}{5}\times 100\mathrm{\%}$

η = 20%

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.

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:

$\eta =\frac{{\mu }^2}{2+{\mu }^2}\times 100$

μ = Modulation index

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

${\eta }_{max}=\frac{1}{2+1}\times 100$

η_max = 33.33 %

Derivation:

Mathematically, the efficiency can be expressed as:

$\eta =\frac{P_{SB}}{P_t}\times 100\mathrm{\%}$

For sinusoidal input

PSB = Sideband power given by:

$P_{SB}=\frac{P_c{\mu }^2}{2}$

Pt = Total power given by:

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

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

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

Standard form of AM:

$A_c\left[1+\mu \cos {\omega }_{m}t\right]\cos {\omega }_{c}t$

$=20\left[1+\frac{1}{10}\cos 3000\pi t+\frac{1}{2}\cos 6000\pi t\right]$

μ₁ = 0.1 , μ₂ = 0.5

${\mu }_{total}=\sqrt{{0.1}^2+{0.5}^2}$

μ_total = 0.51

Ratio of power in sideband to total power

$Power=\frac{{\mu }^2}{{\mu }^2+2}$

$\Rightarrow \frac{{\left(0.51\right)}^2}{{\left(0.51\right)}^2+2}=0.115$