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A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 50 KHz and the message signal is band limited to 500 KHz. The generated FM signal is amplitude modulated using carrier of 1 GHz.
Q. The bandwidth of the generated signal is
- a)1 MHz
- b)1.5 MHz
- c)1.1 MHz
- d)2 MHz
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signa...
It is a narrow band FM
Most Upvoted Answer
A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signa...
The given problem involves frequency modulation (FM) and amplitude modulation (AM) techniques. Let's break down the problem and solve it step by step.
Given information:
- Carrier power (Pc) = 20 kW
- Carrier frequency (fc) = 1 MHz
- Maximum frequency deviation (Δf) = 50 kHz
- Message signal bandwidth (Bm) = 500 kHz
- Carrier frequency for AM modulation (fca) = 1 GHz
Step 1: Determine the bandwidth of the FM signal.
The bandwidth of an FM signal can be calculated using Carson's rule:
Bandwidth (B) = 2(Δf + Bm)
Substituting the given values:
B = 2(50 kHz + 500 kHz)
B = 2(550 kHz)
B = 1.1 MHz
So, the bandwidth of the FM signal is 1.1 MHz.
Step 2: Determine the bandwidth of the AM signal.
The bandwidth of an AM signal is given by:
Bandwidth (Ba) = 2Bm
Substituting the given value:
Ba = 2(500 kHz)
Ba = 1 MHz
So, the bandwidth of the AM signal is 1 MHz.
Step 3: Determine the total bandwidth of the generated signal.
Since the generated signal is the result of AM modulation on the FM signal, the total bandwidth is the sum of the individual bandwidths.
Total bandwidth = B + Ba
Total bandwidth = 1.1 MHz + 1 MHz
Total bandwidth = 2.1 MHz
However, the problem states that the carrier frequency for the AM modulation is 1 GHz (1,000 MHz). Since the total bandwidth cannot exceed twice the carrier frequency due to the Nyquist theorem, the maximum bandwidth is limited to 1 GHz.
Therefore, the correct answer is option A) 1 MHz.
In summary, the FM signal has a bandwidth of 1.1 MHz, but when it is amplitude modulated using a carrier frequency of 1 GHz, the total bandwidth is limited to 1 MHz.
Given information:
- Carrier power (Pc) = 20 kW
- Carrier frequency (fc) = 1 MHz
- Maximum frequency deviation (Δf) = 50 kHz
- Message signal bandwidth (Bm) = 500 kHz
- Carrier frequency for AM modulation (fca) = 1 GHz
Step 1: Determine the bandwidth of the FM signal.
The bandwidth of an FM signal can be calculated using Carson's rule:
Bandwidth (B) = 2(Δf + Bm)
Substituting the given values:
B = 2(50 kHz + 500 kHz)
B = 2(550 kHz)
B = 1.1 MHz
So, the bandwidth of the FM signal is 1.1 MHz.
Step 2: Determine the bandwidth of the AM signal.
The bandwidth of an AM signal is given by:
Bandwidth (Ba) = 2Bm
Substituting the given value:
Ba = 2(500 kHz)
Ba = 1 MHz
So, the bandwidth of the AM signal is 1 MHz.
Step 3: Determine the total bandwidth of the generated signal.
Since the generated signal is the result of AM modulation on the FM signal, the total bandwidth is the sum of the individual bandwidths.
Total bandwidth = B + Ba
Total bandwidth = 1.1 MHz + 1 MHz
Total bandwidth = 2.1 MHz
However, the problem states that the carrier frequency for the AM modulation is 1 GHz (1,000 MHz). Since the total bandwidth cannot exceed twice the carrier frequency due to the Nyquist theorem, the maximum bandwidth is limited to 1 GHz.
Therefore, the correct answer is option A) 1 MHz.
In summary, the FM signal has a bandwidth of 1.1 MHz, but when it is amplitude modulated using a carrier frequency of 1 GHz, the total bandwidth is limited to 1 MHz.
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A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 50 KHz and the message signal is band limited to 500 KHz. The generated FM signal is amplitude modulated using carrier of 1 GHz.Q. The bandwidth of the generated signal isa)1 MHzb)1.5 MHzc)1.1 MHzd)2 MHzCorrect answer is option 'A'. Can you explain this answer?
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A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 50 KHz and the message signal is band limited to 500 KHz. The generated FM signal is amplitude modulated using carrier of 1 GHz.Q. The bandwidth of the generated signal isa)1 MHzb)1.5 MHzc)1.1 MHzd)2 MHzCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 50 KHz and the message signal is band limited to 500 KHz. The generated FM signal is amplitude modulated using carrier of 1 GHz.Q. The bandwidth of the generated signal isa)1 MHzb)1.5 MHzc)1.1 MHzd)2 MHzCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 20 KW and 1 MHz carrier is frequency modulated by a sinusoidal signal so that the maximum frequency deviation is 50 KHz and the message signal is band limited to 500 KHz. The generated FM signal is amplitude modulated using carrier of 1 GHz.Q. The bandwidth of the generated signal isa)1 MHzb)1.5 MHzc)1.1 MHzd)2 MHzCorrect answer is option 'A'. Can you explain this answer?.
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