Noise voltage and absolute temperature

Q.  Noise voltage Vn and absolute temperature T are related as
- Published on 15 Oct 15

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

ANSWER: Vn = √(4RKTB)
 
In the following figure the maximum Noise power is given by Pn = V2/ R

Noise voltage

RL = R, for maximum power transfer from Vn to load resistor RL
In the above figure, according to voltage divider method,
V = Vn/2
Pn = V2/ R
= (Vn/2)2/ R
= Vn2/ 4R
Vn2 = 4R Pn
Vn = √(4R Pn)
Noise power Pn = KTB
Where
K = 1.381 × 10-23 J/K, joules per Kelvin, the Boltzmann constant
B is the bandwidth at which the power Pn is delivered.
T noise temperature
Therefore, Vn = √(4R KTB)

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