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Noise

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Resistor Thermal Noise

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Example

Vnr1sqr=2.3288 x 10-19

Vnr3sqr=7.7625 x 10-20

Vnoutsqr=3.1050 x10-19

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Popular Interview Question

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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.

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Alternative Representation of

Resistor Thermal Noise

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MOSFETS

(Typically 2/3, not to be confused withbody effect coefficient)

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as a function of length

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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

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Flicker Noise

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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.

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Corner Frequency

Definition: the frequency at which thethermal noise equals the flicker noise.

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Corner Frequency (fco)

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fco as a function of length

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Representation of Noise in

Circuits

Output noise

Input noise

Voltage noise source

Current noise source

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Output Noise

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Problem of Output Noise

Output noise depends on the gain ofthe amplifier, for example.

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Input-Referred Noise Voltage

Problem: only valid for when source impedance is low.

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Input Voltage Calculation

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Calculation of Input-Referred

NoiseLow sourceimpedance

High source impedance

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Input Current

More significant atHigh frequencies!

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Noise in Single Stage Amplifier

Equivalent CS Stages

CS

CG SF

Cascode

Differential Pairs

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Equivalent CS Stages

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Common Source Amplifier

The transconductance of M1 must be maximized in order tominimize input-referred noise.

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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.

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Noise Simulation

Thermalnoise

3.758 nV/sqrt(Hz)

Av=28.711

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Noise Simulation

3.126 nV/sqrt(Hz)

Av=33.42

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Comparison

Av=33.42

(simulated input-referredthermal noise)

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Flicker Noise

Dominated byFlicker noise Dominated byThermal noise

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Common Gate Amplifier

Need to consider

Input referred voltage source

Input referred current source

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Gain of CG

If RS=0 and channel length modulation is ignored, Av is

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Input-Referred Voltage Source

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Input-Referred Current Source

Does not producea current to the output

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Input-Referred Thermal Noise

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Input-Referred Flicker Noise

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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

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Source Follower with a NMOS CS

Load (Review)

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Source Followers

High Input impedance,noise current source is negligible.

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Cascode Stage

(At Low Frequencies)

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Cascode Stage

(At High Frequencies)

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Differential Pair

(negligible)

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Analysis