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A carrier wave has power of 1675 kW. If the side band power of a modulated wave subjected to 60%. Then find the amplitude modulation level
- a)301.5 kW
- b)942 kW
- c)1392 kW
- d)1884 kW
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A carrier wave has power of 1675 kW. If the side band power of a modul...
As you know that, sideband power is, 
Where PC is power of carrier wave, PS s sideband power and ‘m’ is modulation rate,
Where PC is power of carrier wave, PS s sideband power and ‘m’ is modulation rate,Most Upvoted Answer
A carrier wave has power of 1675 kW. If the side band power of a modul...
Understanding the Problem
In this problem, we need to calculate the amplitude modulation level given the power of the carrier wave and the sideband power.
Given Values
- Carrier Wave Power (Pc) = 1675 kW
- Sideband Power (Psb) = 60% of the carrier power
Calculating Sideband Power
To find the sideband power (Psb):
- Psb = 60% of Pc
- Psb = 0.60 * 1675 kW
- Psb = 1005 kW
Calculating Total Power of Modulated Wave
The total power (Pt) of the modulated wave is the sum of the carrier power and the sideband power.
- Pt = Pc + Psb
- Pt = 1675 kW + 1005 kW
- Pt = 2680 kW
Finding the Amplitude Modulation Level
The amplitude modulation level can be calculated using the formula that relates the total power, carrier power, and sideband power. The sideband power can also be related to the modulation index (m) as follows:
- Psb = (m^2/2) * Pc
From the earlier calculation of Psb, we can rearrange the formula to find m:
- m^2 = (2 * Psb) / Pc
- m^2 = (2 * 1005 kW) / 1675 kW
- m^2 = 1206/1675
- m ≈ 0.3015 (taking the square root)
Now, to find the amplitude modulation level in terms of power:
- Amplitude Modulation Level = m * Pc
- Amplitude Modulation Level = 0.3015 * 1675 kW ≈ 301.5 kW
Conclusion
Thus, the correct answer is option 'A' which is 301.5 kW.
In this problem, we need to calculate the amplitude modulation level given the power of the carrier wave and the sideband power.
Given Values
- Carrier Wave Power (Pc) = 1675 kW
- Sideband Power (Psb) = 60% of the carrier power
Calculating Sideband Power
To find the sideband power (Psb):
- Psb = 60% of Pc
- Psb = 0.60 * 1675 kW
- Psb = 1005 kW
Calculating Total Power of Modulated Wave
The total power (Pt) of the modulated wave is the sum of the carrier power and the sideband power.
- Pt = Pc + Psb
- Pt = 1675 kW + 1005 kW
- Pt = 2680 kW
Finding the Amplitude Modulation Level
The amplitude modulation level can be calculated using the formula that relates the total power, carrier power, and sideband power. The sideband power can also be related to the modulation index (m) as follows:
- Psb = (m^2/2) * Pc
From the earlier calculation of Psb, we can rearrange the formula to find m:
- m^2 = (2 * Psb) / Pc
- m^2 = (2 * 1005 kW) / 1675 kW
- m^2 = 1206/1675
- m ≈ 0.3015 (taking the square root)
Now, to find the amplitude modulation level in terms of power:
- Amplitude Modulation Level = m * Pc
- Amplitude Modulation Level = 0.3015 * 1675 kW ≈ 301.5 kW
Conclusion
Thus, the correct answer is option 'A' which is 301.5 kW.
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A carrier wave has power of 1675 kW. If the side band power of a modulated wave subjected to 60%. Then find the amplitude modulation levela)301.5 kWb)942 kWc)1392 kWd)1884 kWCorrect answer is option 'A'. Can you explain this answer?
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