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A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?
- a)42.8 m
- b)42.8 mm
- c)21.4 mm
- d)21.4 m
Correct answer is option 'C'. Can you explain this answer?
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A baseband signal of 3.5 MHz frequency is modulated with a carrier sig...
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A baseband signal of 3.5 MHz frequency is modulated with a carrier sig...
To calculate the minimum size of the antenna required to transmit the modulated signal, we need to consider the wavelength of the carrier signal.
1. Calculate the wavelength of the carrier signal:
The wavelength (λ) is given by the formula: λ = c / f, where c is the speed of light and f is the frequency.
In this case, the frequency of the carrier signal is 3.5 GHz (3.5 x 10^9 Hz).
The speed of light (c) is approximately 3 x 10^8 m/s.
Substituting these values into the formula, we get:
λ = (3 x 10^8 m/s) / (3.5 x 10^9 Hz) = 0.0857 meters or 85.7 mm
2. Calculate the length of the antenna:
The length of the antenna should be a multiple of half the wavelength to efficiently radiate the signal.
Since we are using amplitude modulation, the minimum length of the antenna should be half the wavelength.
Therefore, the minimum length of the antenna required is 0.0857 meters / 2 = 0.0428 meters or 42.8 mm.
Hence, the correct answer is option (c) 21.4 mm.
Note: It is important to mention that in practice, the actual length of the antenna may need to be slightly longer to account for factors such as impedance matching and the physical design of the antenna.
1. Calculate the wavelength of the carrier signal:
The wavelength (λ) is given by the formula: λ = c / f, where c is the speed of light and f is the frequency.
In this case, the frequency of the carrier signal is 3.5 GHz (3.5 x 10^9 Hz).
The speed of light (c) is approximately 3 x 10^8 m/s.
Substituting these values into the formula, we get:
λ = (3 x 10^8 m/s) / (3.5 x 10^9 Hz) = 0.0857 meters or 85.7 mm
2. Calculate the length of the antenna:
The length of the antenna should be a multiple of half the wavelength to efficiently radiate the signal.
Since we are using amplitude modulation, the minimum length of the antenna should be half the wavelength.
Therefore, the minimum length of the antenna required is 0.0857 meters / 2 = 0.0428 meters or 42.8 mm.
Hence, the correct answer is option (c) 21.4 mm.
Note: It is important to mention that in practice, the actual length of the antenna may need to be slightly longer to account for factors such as impedance matching and the physical design of the antenna.
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A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?a)42.8 mb)42.8 mmc)21.4 mmd)21.4 mCorrect answer is option 'C'. Can you explain this answer?
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