Relation between Noise voltage and bandwidth

Q8. The noise voltage (V_n)and the signal bandwidth (B) are related as

Options:

a) a) V_n is directly proportional to bandwidth
b) b) V_n is directly proportional to √bandwidth
c) c) V_n is inversely proportional to absolute temperature
d) d) V_n is inversely proportional to bandwidth

Correct Answer: b) V_n is directly proportional to √bandwidth

Explanation :

Maximum Noise power is given by P_n = V²/ R



R_L = R, for maximum power transfer from V_n to load resistor R_L
In the above figure, according to voltage divider method,
V= V_n/2
P_n = V²/ R
= (V_n/2)²/ R
=V_n²/ 4R
V_n²= 4R P_n
V_n= √(4R P_n)
Noise power P_n= KTB
Where
K = 1.381×10^-23 J/K, joules per Kelvin, the Boltzmann constant
B is the bandwidth at which the power P_n is delivered.
T noise temperature
Therefore, V_n= √(4R KTB) or V_n is directly proportional to √bandwidth.