RF Module Design - [Chapter 2] Noises

RF Transceiver Module Design
Chapter 2 Noises
李健榮助理教授
Department of Electronic Engineering
National Taipei University of Technology

Outline
• Noise Sources in Electronic Components
• Antenna Noise
• Noise Temperature
• Noise Figure
• Non-frequency-converting Circuit Output Noise Power
• Frequency-converting Circuit Output Noise Power
• Output Noise Power of Cascaded Circuits
• Sensitivity
Department of Electronic Engineering, NTUT2/42

Noise Sources in Electronic Components
• The flow of charges(holes) in a electron tube or solid-state
device has the thermal fluctuation in any component at a
temperature above absolute zero. Such motions can be caused
by any of several mechanisms, leading to various sources of
noise, thermal noise, flicker noise, and shot noise.
• Noises can be picked up by the antenna, which come from
atmospheric noise, solar noise, galactic noise, ground noise,
and man-made noise.

where
is the Planck’s constant
is Boltzman’s constant
Thermal Noise
• Johnson Noise, Nyquist Noise
• Thermal agitation of charge carriers:
v(t) is a open-circuit voltage across the
resistor terminals
Department of Electronic Engineering, NTUT
( ) ( ) ( )
2
1
2 2
4
f
n rms
f
v t V kT R f P f df= = ∫
( )
1hf kT
hf kT
P f
e
=
−
34
6.546 10 J/sech −
= ×
23
1.380 10 J/Kk −
= ×
( )v t
t
( )v tR
( )o
KT
For an electron in a conductor, the probability
density function (PDF) obeys
4/42

Shot Noise
• Shot noise (Schottky noise) is first observed in vacuum tubes.
• For example, the IV curve of the Schottky Contact (metal-
semiconductor contact) is .The above results are
applicable also to p-n junction diodes, bipolar transistors,
metal-semiconductor (Schottky-barrier) diodes, and so on,
where charges are carried across potential barriers.
• In summary, shot noise has two characteristics:
1) White noise spectrum similar to that of thermal noise. This is very
useful in measuring the noise temperature or noise figure of an
amplifier or any linear receiver component for that matter.
2) The rms value of the shot noise can be easily calculated form the
measured dc current IS.
0 ( 1)qV KT
I I e= −

Flicker Noise
• Flicker noise is a low-frequency phenomenon which is
typically encountered in the device with a dc current flowing.
It is a poorly understood phenomenon and seems to be related
to surface properties of materials, and is also associated with
imperfect contact between conductors.
• Flicker noise has the interesting characteristic that its spectral
density is inversely proportional to frequency.
• Van der Ziel gives the following expression for the mean-
square noise current per unit bandwidth:
2
a
n
I
i K df
f
 
=  
 
where K : material constant, I : dc current, a : close to 2, and n : close to 1.
This expression seems hold for a variety of cases, including semiconductors,
carbon microphones, photoconductors, crystal diodes, and so on.

Antenna Noise
• Generally speaking, antenna noise includes a total of the
following noise sources:
Atmospheric noise
Solar noise
Galactic noise
Ground noise
Man-made noise

Atmospheric Noise
• This noise is greatest at the lowest frequencies and decreases
with increasing frequency.
• Below 30MHz, it is the strong
source of antenna noise,
generated mostly by lightning
discharge in thunder storms.
The noise level depends on
the frequency, the time of day,
weather, the season of the
year, and geographical
location.
NoiseFigure(dB)
140
120
100
80
60
40
20
0
Frequency (MHz)
0.1 0.3 1 3 10 30 100
Galactic noise
Atmospheric noise
(Central United States)
8/42

Solar Noise (I)
• The Sun is a powerful noise source.
• If a directional antenna is pointed at the Sun, it will see a large
antenna noise temperature (also contributes to antenna noise
through sidelobes).
• During high levels of Sun spot activity, noise temperatures
from 100 to 10,000 times greater than those of the quiet
sun may be observed for periods of seconds in what is
called solar bursts, followed by levels about 10 times the
quiet level lasting for several hours

Solar Noise (II)
• The Sun’s effective noise temperature seen by an antenna of
gain Ga is:
• For example, if the frequency is 1000 MHz and there are quiet
sun conditions, the noise temperature is about . If we
assume an antenna gain in the direction of the sun of 31 dBi
and an atmospheric loss of 1dB, the antenna noise temperature
will be
5
2 10 K×
6 5
4.75 10 1259 2 10
949.3 K
1.26
aT
−
× × × ×
= =
6
4.75 10 a s
a
A
G T
T
L
−
×
= AL : atmospheric loss (numeric)
10/42

Galactic Noise
• Typical antenna temperatures
for frequencies above 100 MHz.
• Galactic noise is the largest
natural noise between 100~400
MHz, which is most intense in
the galactic plane and reaches a
maximum in the direction of
the galactic center.
• Above 400MHz, the other
component dominate.
AntennaNoiseTemperature(K)
3000
1000
300
100
30
10
3
1
Frequency (GHz)
Cosmic noise from the galactic center
Minimum noise
10000
0.1 0.3 1 3 10 30 100
NoiseFigure(dB)
10.5
6.5
3.1
1.3
0.4
0.15
0.04
0.015
15.5
Minimum
noise
Cosmic noise from the galactic pole
11/42

Ground Noise
• The Earth is a radiator of electromagnetic noise.
• The thermal temperature of the Earth is typical about 290 K.
• In radar systems and directional communication systems, the
Earth will be viewed mainly through the sidelobes of the
antennas. The average sidelobe antenna gain typically is
about –10 dBi. A rough estimate of antenna noise temperature
in that case is 29 K.

Man-made Noise and Interference (I)
• Man-made noise is due chiefly to electric motors, neon signs,
power lines, and ignition systems located within a few hundred
yards of the receiving antenna.
• There may be radiation from hundreds of communication and
radar systems that may interfere with reception.
• Generally this type of noise is assumed to decrease with
frequency as shown in the following:
where T100 is the man-made noise temperature at 100 MHz.
2.5
100
100
a
MHz
T T
f
 
=  
 
13/42

Man-made Noise and Interference (II)
• For an example of the formula, assume an operating frequency
of 400 MHz and a man-made noise temperature at 100 MHz of
300,000 K (Fa = 30.2 dB above kT0B). The calculated antenna
noise temperature would be
The temperature is about 15.2 dB above kT0B.
2.5
100
300,000 9375 K
400
aT
 
= ⋅ = 
 
14/42

where is Boltzman’s constant
Available Thermal Noise Power
• Thermal Noise:
23
1.380 10 J/Kk −
= ×
NAP kTB=Available noise power:
Thermal noise source
,n rmsvR
( )KT
+
−
Noisy resistor
,n rmsv
Thevenin’s Equivalent Circuit
Noise-free resistor
R
2
, ?n rmsv =
R
R
Matched Load
2
,
2
n rms
NA
v
P kTB
R
 
 
 = =
,n rmsv
,
2
n rmsv
+
−
Available Noise Power
2
, 4n rmsv kTBR=
Open-circuited
noise voltage?

where is Boltzman’s constant
Thermal Noise Equivalent Circuits
• Thermal Noise:
23
1.380 10 J/Kk −
= ×
NAP kTB=Available noise power:
Thermal noise source
,n rmsv,n rmsvR
( )KT
+
−
Thevenin’s Equivalent Circuit
Noisy resistor
Noise-free resistor
Norton’s Equivalent Circuit
Noise-free resistor
R
R
2
, 4n rmsv kTBR=
,n rmsi
2
,2
,
4
4n rms
n rms
v kTB
i kTBG
R R
 
= = = 
 
2
, 4n rmsv kTBR=

Thermal Noise Power Spectrum Density
• Available noise power :
• Thermal Noise at 290 K (17 oC):
Ideal
bandpass
filter
B
R
R
,n rmsv
NAP kTB=
PSD (W/Hz, or dBm/Hz)
f (Hz)
Bandwidth B (Hz)
kT
Integrate to get noise power
0 0NAP kT B=Available noise power:
( ) ( )21
0, 0 4 10 W Hz 174 dBm HzPSDN kT −
× = −≜ ≃Power spectrum density:
17/42

Equivalent Noise Temperature (I)
• If an arbitrary source of noise (thermal or nonthermal) is
“white”, it can be modeled as an equivalent thermal noise
source, and characterized with an equivalent noise temperature.
• An arbitrary white noise source with a driving-point
impedance of R and delivers a noise power No to a load
resistor R. This noise source can be replaced by a noisy
resistor of value R, at temperature Te (equivalent temperature):
oN
R
Arbitrary
white
noise
source
R
oN
RR
eT
o
e
N
T
kB
=
18/42

Equivalent Noise Temperature (II)
• How to define the equivalent noise temperature for a two-port
component? Let’s take a noisy amplifier as an example.
• In order to know the amplifier inherent noise No, you may like
to measure the amplifier by using a noise source with 0 K
temperature. Is that possible?
Noisy amplifier
R
oN
aGR
0 KsT =
This means that the output noise No is
only generated from the amplifier.
Noiseless amplifier
R
o a iN G N=
aGR
iN
o
i e
a
N
N kT B
G
= =i o
e
a
N N
T
kB G kB
= =

Gain Method
• Use a noise source with the known noise temperature Ts.
Noiseless amplifier
R
o a iN G N=
aGR
i s eN kT B kT B= +
sT
eT
Noisy amplifier
R
_o a i o addN G N N= +
aGR
i sN kT B=
sT
( ) ( )o a s e a s eN G kT B kT B G kB T T= + = +
o
s e
a
N
T T
G
+ =
o
e s
a
N
T T
G
= −
Need to know the amplifier power gain Ga.
Due to the noise floor of the analyzer, the
gain method is suitable for measuring high
gain and high noise devices.

The Y-factor Method
• Use two loads at significantly different temperatures (hot and
cold ) to measure the noise temperature.
• Defined the Y-factor as
1 1a a eN G kT B G kT B= +
2 2a a eN G kT B G kT B= +
1 2
1
e
T YT
T
Y
−
=
−
11
2 2
1e
e
T TN
Y
N T T
+
= = >
+
R
R
1T
2T
aG
B eT 1N
2N
(hot)
(cold)
You don’t have to know Ga.
The Y-factor method is not suitable for measuring a very high noise device, since
it will make to cause some error. Thus, we may like a noise source with high
ENR for measuring high noise devices.
1Y ≈
Sometimes, you may need a pre-amplifier to lower analyzer noise for measuring a
low noise device .
21/42

Noise Figure
• The amount of noise added to a signal that is being processed
is of critical importance in most RF systems. The addition of
noise by the system is characterized by its noise figure (NF).
• Noise Factor (or Figure) is a measure of the degradation in the
signal-to-noise ratio (SNR) between the input and output:
where Si , Ni are the input and noise powers, and So, No are the output signal
and noise powers
1i i i
o o o
SNR S N
F
SNR S N
= = ≥ ( )dB 10logNF F=
Gain = 20 dB
P (dBm)
Frequency (Hz)
−100
−60
SNRi = 40 dB
NF = ?
P (dBm)
Frequency (Hz)
−80
−40
SNRo= 32 dB
−72 NF = 8 dB
Noisy Amplifier

Noise Figure (NF)
• By definition, the input noise power is assumed to be the
thermal noise power resulting from a matched resistor at T0
(=290 K); that is, , and the noise figure is given as
( )0
0 0
1 1ei i e
o i
kGB T TSNR S T
F
SNR kT B GS T
+
= = = + ≥
0iN kT B=
( ) 01eT F T= −
Noisy
Network
G B eT
R
0T
R
i i iP S N= + o o oP S N= +
23
1.380 10 J/ Kk −
= ×where is Boltzman’s constant0NAP kT B=
( ) ( )21
0 4 10 W Hz 174 dBm HzTN kT −
× = −≜ ≃
Use the concept of SNR
Use the concept of noise only
0 0
0 0 0
1 1o add e e
i
N kGBT N kGBT kGBT T
F
GN GkT B GkT B T
+ +
= = = = + ≥
23/42

Non-frequency-converting Circuit Output Noise
A. Resistive-type passive circuits
When a two-port network is a passive, lossy component (an attenuator or
lossy transmission line).
B. Reflective-type passive circuits
Assume an ideal bandpass filter response with passband insertion loss of
L (dB) and stopband attenuation of S (dB).
C. Active circuit
An active circuit is with noise figure NF and available gain G.

Resistive-type Passive Circuits (I)
• The circuit is with a matched source resistor, which is also at
temperature T.
• The output noise power :
• We can think of this power coming from the source resistor
(through the lossy line), and from the noise generated by the
line itself. Thus,
0P kTB=
0 addedP kTB GkTB GN= = +
( )
1
1added e
G
N kTB L kTB kT B
G
−
= = − =
where is the noise generated by the line.addedN
25/42

Resistive-type Passive Circuits (II)
• The lossy line equivalent noise temperature :
• The noise figure is
where T0 denotes room temperature, T is the actual physical temperature (K). Note
that the loss L may depend on frequency.
• Output noise power :
where input thermal noise power
( )
1
1e
G
T T L T
G
−
= = −
( )
0
1 1
T
F L
T
= + − ( )dB 10logNF F=
( ) ( ) ( )dBm dBm dBout inN N L NF= − +
( )WattinN kTB=
( )dBminN
f
( )dBmoutN
f
inN L NF− +

Reflective-type Passive Circuits (I)
• Assume an ideal BPF response with passband insertion loss of
L (dB) and stopband attenuation of S (dB). The filter is under
an environment of T (K)
• In the passband:
( )
0
1 1
T
F L
T
= + − ( )dB 10logNF F=
0 dB
−L dB
−S dB
BW
27/42

Reflective-type Passive Circuits (II)
• Outside the passband, the noise, the same as the signal, is
reflected back such that the output noise power is reduced by
the stopband attenuation S (dB).
( )
0 0
2 2
dBm
in
out
in
BW BW
N L NF f f f
N
N S otherwise

− + − ≤ ≤ +

= 
 −


( )dBmoutN
inN L NF− +
BW
inN S−
f
( )dBminN
f

Active Circuits
• An active circuit is with noise figure NF and available gain G.
(Note that NF and G are usually depend on frequency.)
( )dBmout inS S G= +
( )174 10log dBminN B= − +
( )dBmout inN N NF G= + +
( )dBminN
f f
( )dBmoutN
BW
( )dBminS
f
( )dBmoutS
f
BW
( )dBmin inS N+
f
( )dBmout outS N+
f
BW
( )dBG
( )dBNF
29/42

Multiple Stages Cascaded
• Multiple stages cascaded
where Fi is the noise factor and Gi is the available power gain of each stage.
1
1
0
1
1
N
i
i
i
j
j
F
F
G
−
=
=
−
= + ∑
∏
2 3
1
1 1 2 1 2 1
e e eN
eT e
N
T T T
T T
G G G G G G −
= + + + +⋯
⋯
1eT
1G 2G
2eT eNT
NG
g T addkT G N+gkT
1ekT 2ekT eNkT
gkT ( )T g eTkG T T+
eTkT
1 2T NG G G G= ⋯
1 1 1g ekT G kT G+
( )1 1 1 2 2 2g e ekT G kT G G kT G+ +
( )1 2 1 1 2 2g N e N e N eN NkT G G G kT G G kT G G kT G+ + + +⋯ ⋯ ⋯ ⋯
1
1 2
0
i
T N j
j
G G G G G
−
=
= = ∏⋯
( ) 01eT F T= −
Cascade System
Equivalent System
( ) 32
1
1 1 2 1 2 1
1 11
1 1 N
N
F FF
F F
G G G G G G −
− −−
= + − + + + +⋯
⋯
1st stage dominate less significant
30/42

Frequency-converting Circuit Output Noise
• Image Noise :
• LO Wideband Noise :
Image noise
fLO
fLO
fLO + fIFfLO − fIF
fIF
LO wideband noise
LOf
2 LOf
3 LOf
31/42

Output Noise Power of Cascaded Circuits (I)
• The total mean-square noise voltage
(Assume that the circuit is under the same physical temperature Tj=T)
• The summed open-circuit mean-square voltage at a-a' is
therefore given by ,where
( ) ( ) ( )2
1 1 1
4 4 4 4
N N N
n j j j j j T
T j j j
v kT BR kB T R kBT R kBTR
= = =
= = = =∑ ∑ ∑
( )2 2 2 2
1 2 3n
T
v v v v= + + +⋯
Noisy resistors in series
2
1ne
1R 2R
2
2ne
NR
2
nNe
2
nTe
a a′
( )
22 2
1 1 1nv v A f= ( )
22 2
2 2 2nv v A f= ( )
22 2
3 3 3nv v A f=, , and
32/42

Example – T-network
The total voltage at a-a' is the sum of the above,
where the equivalent resistance
( )
( )
( )
22 2
1 22 1 2
1 2 2
1 2 1 2
4n
kTBR Rv R
v
R R R R
= =
+ +
( )
( )
( )
22 2
2 12 2 1
2 2 2
1 2 1 2
4n
kTBR Rv R
v
R R R R
= =
+ +
2 2
3 3 34nv v kTBR= =
( ) ( ) ( )
2 2
2 1 2 2 1 1 2
3 32 2
1 21 2 1 2
4 4 4n eq
T
R R R R R R
v kBT R kBT R kTBR
R RR R R R
   
= + + = + =   
++ +    
1 2
3
1 2
eq
R R
R R
R R
= +
+
2
1ne
1R
2R
2
2ne
3R
2
3ne
a
a′
2
nTe
eqR
a
a′
( )
2
2 2
1 2
1 2
R
A
R R
=
+ ( )
2
2 1
2 2
1 2
R
A
R R
=
+
2
3 1A =, , and
33/42

Output Noise Power of Cascaded Circuits (II)
• When the noise temperature and gain of each stage are determined,
the overall noise temperature and gain of the whole system can be
obtained.
• Use the following methods to calculate the output noise ,
(1) Cascade Formula
(2) Walk-Through method
(3) Summation method
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
stage1 stage2 stage3 stage4
oN′
34/42

Cascade Formula Method
( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − =
( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − =
150 453.6 700
77.7 275.42 K
0.794 0.794 316.23 0.794 316.23 0.398
eTT = + + + =
× × ×
( ) ( )23 21
1.38 10 50 275.42 =4.5 10 Watts Hz= 173.5 dBm Hzs eTk T T − −
+ = × × + × −
0 173.5 1 25 4 30 dBm HzN = − − + − +
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
Stage 1 Teff :
Stage 3 Teff :
System equivalent noise temperature and output noise :
35/42

Walk-Through Method – Stage 1
• Calculate the noise signal from stage to stage. At first,
calculate the noise density stage by stage:
Antenna noise:
Cable 1 noise:
23 19
1.38 10 50=6.9 10 mW Hz 181.6 dBm HzskT − −
= × × × = −
( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − =
23 19
1 1.38 10 77.7=10.72 10 mW Hz 179.7 dBm HzekT − −
= × × × = −
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
Stage Input A Input B Sum Output Noise Density (dBm/Hz)
1 −181.6 −179.7 −177.5 −178.5
2 −178.5
36/42

1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
LNA Noise:
23 19
2 1.38 10 150=2.07 10 mW Hz 176.8 dBm HzekT − −
= × × × = −
1 −181.6 −179.7 −177.5 −178.5
2 −178.5 −176.8 −174.6 −149.6
3 −149.6

1 −181.6 −179.7 −177.5 −178.5
2 −178.5 −176.8 −174.6 −149.6
3 −149.6 −172.0 −149.6 −153.6
4 −153.6
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
Cable 2 Noise:
( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − =
23 19
2 1.38 10 453.6=6.26 10 mW Hz 172 dBm HzekT − −
= × × × = −

1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
Gain amplifier noise:
23 19
4 1.38 10 700=9.66 10 mW Hz 170.2 dBm HzekT − −
= × × × = −
1 −181.6 −179.7 −177.5 −178.5
2 −178.5 −176.8 −174.6 −149.6
3 −149.6 −172.0 −149.6 −152.6
4 −153.6 −170.2 −153.5 −123.5

Summation Method
• Each noise source is individually taken through the various
gains and loses to the output, and the sum of all output noises
is just the total output noise (Superposition).
For stage1:
For stage2:
For stage3:
For stage4:
181.6 1 25 4 30 131.6 dBm Hz− − + − + = −
179.7 1 25 4 30 129.7 dBm Hz− − + − + = −
176.8 25 4 30 125.8 dBm Hz− + − + = −
172 4 30 146 dBm Hz− − + = −
170.2 30 140.2 dBm Hz− + = −
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
oN′
Noise Contributor Output Noise Density (dBm/Hz)
Environment −131.6
Stage 1 −129.7
Stage 2 −125.8
Stage 3 −146.0
Stage 4 −140.2
Total −123.5
40-I/42

Noise Figure Method
1 1 dBL =
1 300 KT = 1 300 KT =
3 4 dBL =
2 150 KeT =
2 25 dBG =
4 700 KeT =
4 30 dBG =
50 KsT =
oN′
Atten1 Amp2 Atten3 Amp4
Gain (dB) -1 25 -4 30
Gain 0.79432823 316.227766 0.39810717 1000
T 300 150 300 700
F 1.26785387 1.51724138 2.56402045 3.4137931
NF (dB) 1.03069202 1.81054679 4.08921484 5.33237197
Cumumlatvie Gain 0.79432823 251.188643 100 100000
Fcas 1.26785387 1.91902219 1.92524867 1.9493866
NFcas (dB) 2.89897976
Gcas (dB) 50
Ni (Ts=50 K) (dBm) -181.611509
No=Ni+Gcas+NFcas -128.7125-128.7125-128.7125-128.7125 Wrong!Since NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 K
Fcas=1+(Te/T0)
Te 275.322114
No=Gcas(kTsB+kTeB) 4.4894E-16 -123.47807 Correct!
Department of Electronic Engineering, NTUT40-II/42

Sensitivity
•
where is the on-channel noise, including thermal, shot, flicker, antenna noise.
NIMG is the image noise, contributed from the mixing function
NLO is the LO noise, down-mixing to IF signal due to the mixing function
• The system overall noise figure is then obtained as
where includes noise, phase jittering and channel fading effects.
( ) ( ) ( ) ( )_dBm dBm dB dBout RF system
required
S
Sensitivity N NF
N
= + +
out Channel IMG LON N N N= + +
ChannelN
Module Channel IMG LOF F F F= + +
41/42

Summary
• In this chapter, we’ve introduced the thermal noise and how to
use thermal noise to define the equivalent noise temperature.
• The measuring methods of the equivalent noise temperature
(and thus the noise figure) are the practical procedure
corresponding to the noise theory. Each method has its own
pros and cons.
• The calculation of a cascade system output noise was also
introduced by using cascade formula, walk-through, and
output summation methods.

RF Module Design - [Chapter 2] Noises

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RF Module Design - [Chapter 2] Noises