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Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.?
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Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the car...
1. Expression for the Modulated Signal u(t)
The modulated signal can be expressed using the formula for frequency modulation (FM):
u(t) = Ac cos(2πfct + β sin(2πfmt))
Where:
- Ac = 100 (amplitude of the carrier)
- fc = fe (carrier frequency)
- β = modulation index (6)
- fm = 400 Hz (message frequency derived from sinc function)
Thus, the expression becomes:
u(t) = 100 cos(2πfct + 6 sin(2π(400)t))
2. Maximum Frequency Deviation
The maximum frequency deviation (Δf) can be calculated using the modulation index:
Δf = β * fm
Given:
- β = 6
- fm = 400 Hz
Calculating Δf:
Δf = 6 * 400 = 2400 Hz
3. Power Content of the Modulated Signal
The power content (P) of an FM signal is given by:
P = (Ac^2) / 2
Substituting the values:
P = (100^2) / 2 = 5000 Watts
4. Bandwidth of the Modulated Signal
The bandwidth (BW) of an FM signal can be estimated using Carson's Rule:
BW = 2(Δf + fm)
Substituting the values:
BW = 2(2400 + 400) = 2 * 2800 = 5600 Hz
In summary, the modulated signal is represented as u(t), with a maximum frequency deviation of 2400 Hz, power content of 5000 Watts, and a bandwidth of 5600 Hz.
The modulated signal can be expressed using the formula for frequency modulation (FM):
u(t) = Ac cos(2πfct + β sin(2πfmt))
Where:
- Ac = 100 (amplitude of the carrier)
- fc = fe (carrier frequency)
- β = modulation index (6)
- fm = 400 Hz (message frequency derived from sinc function)
Thus, the expression becomes:
u(t) = 100 cos(2πfct + 6 sin(2π(400)t))
2. Maximum Frequency Deviation
The maximum frequency deviation (Δf) can be calculated using the modulation index:
Δf = β * fm
Given:
- β = 6
- fm = 400 Hz
Calculating Δf:
Δf = 6 * 400 = 2400 Hz
3. Power Content of the Modulated Signal
The power content (P) of an FM signal is given by:
P = (Ac^2) / 2
Substituting the values:
P = (100^2) / 2 = 5000 Watts
4. Bandwidth of the Modulated Signal
The bandwidth (BW) of an FM signal can be estimated using Carson's Rule:
BW = 2(Δf + fm)
Substituting the values:
BW = 2(2400 + 400) = 2 * 2800 = 5600 Hz
In summary, the modulated signal is represented as u(t), with a maximum frequency deviation of 2400 Hz, power content of 5000 Watts, and a bandwidth of 5600 Hz.
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Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.?
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Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.?.
Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.?.
Solutions for Q.1) The message signal m(1) 10 sinc(400r) frequency modulates the carrier c(t)= 100 cos 2 fet. The modulation index is 6. 1. Write an expression for the modulated signal u(t). 2. What is the maximum frequency deviation of the modulated signal? 3. What is the power content of the modulated signal? 4. Find the bandwidth of the modulated signal.? in English & in Hindi are available as part of our courses for UPSC.
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