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White noise with power density N0 /2 is applied to a low pass network for which |H(0)| = 2. It has a noise bandwidth of 2 MHz. If the average output noise power is 0.1 W in a 1 - Ω( resistor, the value of N0 is
- a)12.5 nW/Hz
- b)12.5 μW/Hz
- c)25 nW/Hz
- d)25 μW/Hz
Correct answer is option 'A'. Can you explain this answer?
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White noise with power density N0 /2 is applied to a low pass network ...
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White noise with power density N0 /2 is applied to a low pass network ...
Given information:
- White noise with power density N0/2 is applied to a low pass network.
- |H(0)| = 2, where H(0) is the transfer function of the low pass network at frequency 0.
- The noise bandwidth of the low pass network is 2 MHz.
- The average output noise power is 0.1 W in a 1-ohm resistor.
To find: The value of N0
Solution:
1. The power spectral density (PSD) of white noise is given by N0/2.
2. The transfer function of the low pass network is given by H(f), where f is the frequency.
3. The magnitude of the transfer function at frequency 0, |H(0)|, represents the gain of the low pass network at DC.
4. The noise bandwidth of the low pass network is the frequency range over which the noise power is considered.
5. The average output noise power in the 1-ohm resistor can be calculated using the formula:
Average Output Noise Power = Noise Power Density * Noise Bandwidth * |H(0)|^2
Calculation:
Given: Average Output Noise Power = 0.1 W
Noise Bandwidth = 2 MHz
|H(0)| = 2
Using the formula, we can calculate the value of N0:
0.1 = N0/2 * 2 MHz * (2)^2
0.1 = N0 * 8 MHz
N0 = 0.1 / (8 MHz)
N0 = 0.1 / (8 x 10^6) W/Hz
Converting to nW/Hz:
N0 = 0.1 x 10^9 / (8 x 10^6) nW/Hz
N0 = 12.5 nW/Hz
Therefore, the value of N0 is 12.5 nW/Hz, which corresponds to option A.
- White noise with power density N0/2 is applied to a low pass network.
- |H(0)| = 2, where H(0) is the transfer function of the low pass network at frequency 0.
- The noise bandwidth of the low pass network is 2 MHz.
- The average output noise power is 0.1 W in a 1-ohm resistor.
To find: The value of N0
Solution:
1. The power spectral density (PSD) of white noise is given by N0/2.
2. The transfer function of the low pass network is given by H(f), where f is the frequency.
3. The magnitude of the transfer function at frequency 0, |H(0)|, represents the gain of the low pass network at DC.
4. The noise bandwidth of the low pass network is the frequency range over which the noise power is considered.
5. The average output noise power in the 1-ohm resistor can be calculated using the formula:
Average Output Noise Power = Noise Power Density * Noise Bandwidth * |H(0)|^2
Calculation:
Given: Average Output Noise Power = 0.1 W
Noise Bandwidth = 2 MHz
|H(0)| = 2
Using the formula, we can calculate the value of N0:
0.1 = N0/2 * 2 MHz * (2)^2
0.1 = N0 * 8 MHz
N0 = 0.1 / (8 MHz)
N0 = 0.1 / (8 x 10^6) W/Hz
Converting to nW/Hz:
N0 = 0.1 x 10^9 / (8 x 10^6) nW/Hz
N0 = 12.5 nW/Hz
Therefore, the value of N0 is 12.5 nW/Hz, which corresponds to option A.
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