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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 VDS=0.6 I1=100 uA 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 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 (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 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, Av 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/ID=5 for M0, M2, M3 and M4. gm/ID=20 for M1. I1=10 uA I2=10 uA I(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