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## Noise

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**Example**Vnr1sqr=2.3288 x 10-19 Vnr3sqr=7.7625 x 10-20 Vnoutsqr=3.1050 x10-19**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.**MOSFETS**(Typically 2/3, not to be confused with body effect coefficient)**Noise Voltage Generated Per Device**VDS=0.6 I1=100 uA**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.**Representation of Noise in Circuits**• Output noise • Input noise • Voltage noise source • Current noise source**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.**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**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**(simulated input-referred thermal noise) Av=33.42**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 Current Source**Does not produce a current to the output**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 Followers**High Input impedance, noise current source is negligible.**Differential Pair**(negligible)