The_Cambridge_Handbook_of_Physics_Formulas

5.6 Fluctuations and noise
117
Noise
Nyquist’s noise
theorem
dw = kT ·βɛ(e βɛ −1) −1 dν (5.138)
= kT N dν (5.139)
≃ kT dν (hν ≪ kT) (5.140)
Johnson
(thermal) noise v rms =(4kT N R∆ν) 1/2 (5.141)
voltage a
Shot noise
(electrical)
I rms =(2eI 0 ∆ν) 1/2 (5.142)
(
Noise figure b f dB =10log 10 1+ T )
N
T 0
Relative power
G =10log 10
(
P2
P 1
)
(5.143)
(5.144)
w
k
T
T N
βɛ
ν
h
v rms
R
∆ν
I rms
−e
I 0
f dB
T 0
a Thermal voltage over an open-circuit resistance.
b Noise figure can also be defined as f =1+T N /T 0 , when it is also called “noise factor.”
exchangeable noise power
Boltzmann constant
temperature
noise temperature
= hν/(kT)
frequency
Planck constant
rms noise voltage
resistance
bandwidth
rms noise current
electronic charge
mean current
noise figure (decibels)
ambient temperature (usually
taken as 290 K)
G decibel gain of P 2 over P 1
P 1 ,P 2 power levels
5