### Noise Analysis

```Noise
Resistor Thermal Noise
Example
Vnr1sqr=2.3288 x 10-19
Vnr3sqr=7.7625 x 10-20
Vnoutsqr=3.1050 x10-19
Analytical Versus Simulation
Popular Interview Question
Noise Spectrum Shaping by a
Low Pass Filter
As R increases, 4kTR increases, but the bandwidth decreases.
Therefore, the bandwidth is constant.
Pn,out can only be decreased by increasing C.
Alternative Representation of
Resistor Thermal Noise
MOSFETS
(Typically 2/3, not to be confused with
body effect coefficient)
as a function of length
Noise Voltage Generated Per
Device
VDS=0.6
I1=100 uA
gm/ID
gm(mS)
gm/gds
Vn(nV/sqrt(Hz))
Gamma
5
0.5
12.045
84.83
1.4976
10
1
15.707
64.5
1.018
15
1.5
17.19
52.40
0.84
20
2
17.55
44.27
0.76
25
2.5
17.05
38.22
0.76
Flicker Noise
Flicker Noise Model
The flicker noise is modeled as a voltage source in series with the gate:
The trap-and-release phenomenon associated with the dangling
bond occurs at low frequencies more often.
Device area can be increased to
decrease noise due to flicker noise.
Corner Frequency
• Definition: the frequency at which the
thermal noise equals the flicker noise.
Corner Frequency (fco)
fco as a function of length
Representation of Noise in
Circuits
• Output noise
• Input noise
– Voltage noise source
– Current noise source
Output Noise
Problem of Output Noise
• Output noise depends on the gain of
the amplifier, for example.
Input-Referred Noise Voltage
Problem: only valid for when source impedance is low.
Input Voltage Calculation
Calculation of Input-Referred
Noise
Low source
impedance
High source impedance
Input Current
More significant at
High frequencies!
Noise in Single Stage Amplifier
•
•
•
•
•
•
Equivalent CS Stages
CS
CG
SF
Cascode
Differential Pairs
Equivalent CS Stages
Common Source Amplifier
The transconductance of M1 must be maximized in order to
minimize input-referred noise.
Input Referred Thermal Noise
Voltage
M2 acts as the current source.
The gm of M2 should be minimized.
M1 acts as the amplifier.
The gm of M1 should be maximized.
Noise Simulation
Thermal
noise
3.758 nV/sqrt(Hz)
Av=28.711
Noise Simulation
3.126 nV/sqrt(Hz)
Av=33.42
Comparison
Av=33.42
(simulated input-referred
thermal noise)
Flicker Noise
Dominated by
Flicker noise
Dominated by
Thermal noise
Common Gate Amplifier
• Need to consider
– Input referred voltage source
– Input referred current source
Gain of CG
If RS=0 and channel length modulation is ignored, Av is
Input-Referred Voltage Source
Input-Referred Current Source
Does not produce
a current to the output
Input-Referred Thermal Noise
Input-Referred Flicker Noise
Design Example
Design criteria:
gm/ID=5 for M0, M2, M3 and M4.
gm/ID=20 for M1.
I1=10 uA
I2=10 uA
I(M1)=40 uA
Source Follower with a NMOS CS