Noise Power, Noise Figure
and Noise Temperature
March 21, 2014
Sujeong Lee
Noise
•  Any unwanted input - UNDESIRABLE portion of
an electrical signal
•  Limits systems ability to process weak signals
Noise Power
•  Most of input noise = Thermal Noise
•  Noise power
Np = kBT B
kB = Boltzmann s constant 1.38x10 -23 J/K
T = Absolute temperature of device
B = Circuit bandwidth
Noise Power
•  Signal to Noise Ratio (SNR)
S ( f ) average − signal − power
SNR =
=
N ( f ) average − noise − power
o Soo/N
o oo
the noise figure of the receiver.
Noise
figure
has has
nothing
to do
modulation
or demodulaNoise
figure
nothing
to
do
modulation
or
Noise
figure
has
nothing
towith
do with
with
modulation
or demodulademodulation.tion.
It
is
independent
of
the
modulation
format
and
of the
It
is
independent
of
the
modulation
format
and
of
tion. It is independent of the modulation format and
of the
the
fidelity
of
modulators
and
demodulators.
Noise
figure
is,
fidelity
of
modulators
and
demodulators.
Noise
figure
fidelity of modulators and demodulators. Noise figure is,
is,
therefore,
a more
general
concept
thanthan
noise-quieting
used
to to
therefore,
aa more
general
concept
noise-quieting
used
therefore,
more
general
concept
than
noise-quieting
used
to
indicate
the
sensitivity
of
FM
receivers
or
BER
used
in
digital
indicate
the
sensitivity
of
FM
receivers
or
BER
used
in
digital
indicate the sensitivity of FM receivers or BER used in digital
communications.
communications.
communications.
Noise Figure
•  Noise Figure
Si/N
SSi/N
i ii
= ――――――――――
i/N
=
――――――――――
=
――――――――――
GSGS
/(N
+
+
i ii/(N
a aaGN
i) ii))
GS
/(N
+ GN
GN
NaN
+
i ii
N+aaGN
+ GN
GN
= ――――――
=
――――――
= GN
――――――
GN
i ii
Noise
figure
should
be thought
of as
fromfrom
gain.
Once
Noise
figure
should
be
of
as
gain.
Once
Noise
figure
should
be thought
thought
ofseparate
as separate
separate
from
gain.
Once
noise
is
added
to
the
signal,
subsequent
gain
amplifies
signal
noise
noise is
is added
added to
to the
the signal,
signal, subsequent
subsequent gain
gain amplifies
amplifies signal
signal
and and
noise
together
andand
doesdoes
not not
change
the the
signal-to-noise
noise
together
change
signal-to-noise
ratio.
available
at the
input
to the
device
u
ratio.
available
at the
input
to the
devic
represent
the
signal
and
noise
levels
represent the signal and noise le
Figure
1-2(a)
shows
an example
situation
at the
input
of an
Na is
noise
added
by the
DUT,
an
Figure
1-2(a)
shows
an example
situation
at the
input
of an
Nathe
is the
noise
added
by the
DUT
amplifier.
The
depicted
signal
is
40
dB
above
the
noise
floor:
DUT.
Equation
(1-2)
shows
the
depe
amplifier. The depicted signal is 40 dB above the noise floor:
DUT. Equation (1-2) shows the de
Figure
1-2(b)
shows
the the
situation
at the
amplifier
output.
input
Ni. The
input
noise
level
is usu
Figure
1-2(b)
shows
situation
at the
amplifier
output.
input
Ni. The
input
noise
level
is
TheThe
amplifier’s
gain
has
boosted
the
signal
by
20
dB.
It
also
source
and
is
referred
to
by
kT
B. Fr
amplifier’s gain has boosted the signal by 20 dB. It also
source and is referred to byokT
oB
boosted
the the
input
noise
levellevel
by 20
thenthen
added
its own
source
temperature
of 290K
(d
boosted
input
noise
by dB
20 and
dB and
added
its own ence
ence
source
temperature
of 290K
noise. The output signal is now only 30 dB above the noise
equivalent
to
16.8
°C
and
62.3
°F.
Th
noise. The output signal is now only 30 dB above the noise
equivalent to 16.8 °C and 62.3 °F
floor. Since the degradation in signal-to-noise ratio is 10 dB,
average temperature seen by rec
floor. Since the degradation in signal-to-noise ratio is 10 dB, the the
average temperature seen by
the amplifier has a 10 dB noise figure.
across the atmosphere at the transm
the amplifier has a 10 dB noise figure.
across the atmosphere at the tra
•  Noise figure represents the
degradation in signal/noise
6
6
ratio as the signal passes
through a device.
output
input
•  F is always greater than 1.
Noise Figure
Noise Factor
•  Noise Figure
Modern usage of “noise figure” usually is reserved
for the quantity NF, expressed in dB units:
NF = 10 log10 F [dB]
NF = (Si/Ni)dB – (So/No)dB
So/No
Si /Ni
(Si/Ni)dB = 40 dB
(So/No)dB = = 30 dB
Noise Figure = 10 dB
Noise Temperature
•  Comes from the random motion of electrons
! Thermal Noise
•  Convenient! Common basis for measuring
random electrical noise from any source
•  Relation with Noise Figure
Te = To ( F – 1 )
Te : The effective noise temperature of device
T0 : a reference temperature 290K (room temperature)
Summary
•  Noise Power
–  The magnitude of Noise
Np = kBT B
•  Noise Figure
–  Noise Factor
–  Noise Figure : the degradation of SNR
NF = 10 log10 F [dB]
•  Noise Temperature
–  Basic tool of measuring any kind of noise
–  Relation with Noise Factor
Te = To ( F – 1 )