Noise

Resistor Thermal Noise

Example
Vnr1sqr=2.3288 x 10 -19
Vnr3sqr=7.7625 x 1020
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)

𝛾 as a function of length

Noise Voltage Generated Per
Device
VDS=0.6
I1=100 uA gm/ID
5
10
15
20
25 gm(mS)
0.5
1
1.5
2
2.5
gm/gds Vn(nV/sqrt(Hz)) Gamma
12.045
84.83
1.4976
15.707
17.19
17.55
17.05
64.5
52.40
44.27
38.22
1.018
0.84
0.76
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 (f co
)

f co 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, A v 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/I =5 for M
0 gm/I
D
D
=20 for M
I1=10 uA
I2=10 uA
I(M1)=40 uA
, M
2
1
.
, M
3 and M
4
.

Source Follower with a NMOS CS
Load (Review)

Source Followers
High Input impedance, noise current source is negligible.

Cascode Stage
(At Low Frequencies)

Cascode Stage
(At High Frequencies)

Differential Pair
(negligible)

Analysis