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Published byJett Windell Modified about 1 year ago

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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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Analytical Versus Simulation

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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 with body effect coefficient)

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Noise Voltage Generated Per Device gm/IDgm(mS)gm/gdsVn(nV/sqrt(Hz))Gamma 50.512.04584.831.4976 10115.70764.51.018 151.517.1952.400.84 20217.5544.270.76 252.517.0538.220.76 VDS=0.6 I1=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 dangling bond occurs at low frequencies more often. Device area can be increased to decrease noise due to flicker noise.

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Corner Frequency Definition: the frequency at which the thermal noise equals the flicker noise.

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Corner Frequency (f co )

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f co 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 of the 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 Noise Low source impedance High source impedance

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Input Current More significant at High 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 to minimize 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 Thermal noise 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-referred thermal noise)

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Flicker Noise Dominated by Flicker noise Dominated by Thermal 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, A v is

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Input-Referred Voltage Source

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Input-Referred Current Source Does not produce a 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/I D =5 for M 0, M 2, M 3 and M 4. gm/I D =20 for M 1. I1=10 uA I2=10 uA I(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

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