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A radio receiver with 10 kHz bandwidth has a noise figure of 30 dB. The noise power at input is (take K = 1.38 x 10-23 J/Kelvin and assume room temperature of 300 K)
  • a)
    2.22 x 10-14 W
  • b)
    5.65 x 10-12 W
  • c)
    1.68 x 10-12 W
  • d)
    14 x 10-14 W
Correct answer is option 'D'. Can you explain this answer?
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A radio receiver with 10 kHz bandwidth has a noise figure of 30 dB. Th...
Noise figure,
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A radio receiver with 10 kHz bandwidth has a noise figure of 30 dB. Th...
Calculation of Noise Power at Input

Given:
- Bandwidth (B) = 10 kHz
- Noise Figure (NF) = 30 dB
- Boltzmann's constant (K) = 1.38 x 10^-23 J/K
- Room Temperature (T) = 300 K

To Find: Noise power at input

Solution:

1. Calculation of Noise Factor (F)

Noise Figure (NF) is given by:

NF = 10 log(F)

where F = (Signal-to-Noise Ratio at input) / (Signal-to-Noise Ratio at output)

In this case, Signal-to-Noise Ratio at output is assumed to be 0 dB (i.e., no noise added after the receiver).

So, F = 10^(NF/10)

F = 10^(30/10)

F = 1000

2. Calculation of Noise Temperature (Tn)

Noise Factor (F) is related to Noise Temperature (Tn) by:

F = 1 + (Tn / T)

where Tn is the equivalent noise temperature in Kelvin.

So, Tn = (F-1) x T

Tn = (1000-1) x 300

Tn = 299,700 K

3. Calculation of Noise Power at Input (Pn)

Noise power at input is given by:

Pn = k x Tn x B

Pn = 1.38 x 10^-23 x 299,700 x 10,000

Pn = 4.14 x 10^-10 W

Answer: Option (D) 14 x 10^-14 W (This is not the correct answer)

Explanation:

The calculation given in option (D) is incorrect.

The correct answer can be calculated as follows:

Pn = 10 log(Pn / 1 W)

Pn / 1 W = 10^(NF/10) x B

Pn = 1 W x 10^(NF/10) x B

Pn = 1 x 10^(-12) x 10^(30/10) x 10,000

Pn = 4.14 x 10^-10 W

Therefore, the correct answer is option (A) 2.22 x 10^-14 W.
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A radio receiver with 10 kHz bandwidth has a noise figure of 30 dB. The noise power at input is (take K = 1.38 x 10-23 J/Kelvin and assume room temperature of 300 K)a)2.22 x 10-14 Wb)5.65 x 10-12 Wc)1.68 x 10-12Wd)14 x 10-14 WCorrect answer is option 'D'. Can you explain this answer?
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