Noise voltage and absolute temperature

Q14. Noise voltage V_n and absolute temperature T are related as

Options:

a) V_n =1/ √(4RKTB)
b) V_n = √(4RK)/ (TB)
c) V_n = √(4RKTB)
d) V_n = √(4KTB)/R

Correct Answer: c) V_n = √(4RKTB)

Explanation :

In the following figure the 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)