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

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

VDS=0.6I1=100 uA

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 danglingbond occurs at low frequencies more often.

Device area can be increased todecrease 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 sourceimpedance

High source impedance

Input Current

More significant atHigh 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 tominimize 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 byFlicker 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 producea 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 uAI2=10 uAI(M1)=40 uA

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