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Above-threshold transistor noise analysis.

Thermal Noise (White Noise )

\frac{ \bar{i_n^2} }{\Delta f} = 4kT r g_m and \frac{ \bar{v_n^2} }{\Delta f} = 4kT r \frac1{g_m}

  • k is Boltzmann’s constant
  • T the Temperature in Kelvins
  • r is usually 2/3, but grows larger with short channel effects

Flicker Noise

  • From Razavi - Note this does not account for bias current
    • As a voltage at the gate: \frac{ \bar{v_n^2} }{\Delta f} = \frac{K_f}{ C_{OX} W L} \frac1{f} (pp. 215)
    • As a current source parallel to the drain/source: \frac{ \bar{i_n^2} }{\Delta f} = \frac{K_f}{ C_{OX} W L} \frac1{f} g_m^2 (pp. 216)
  • \frac{ \bar{i_n^2} }{\Delta f} = \frac{K_f}{ C_{ox}} \frac1{f} \frac{ I_d }{ L_{eff}^2 }
    • Leff2 can be mapped to transistor area, if you add the gm back in
    • \frac{ \bar{i_n^2} }{\Delta f} = \frac{K_f}{ C_{OX} W L} \frac1{f} g_m^2 = \frac{K_f}{ C_{ox} W L} \frac1{f} \left( 2 \mu_n C_{ox} \frac{W}L I_d \right) = \frac{2 \mu_n K_f}{L^2} \frac{I_d}{f}
  • Kf is the flicker noise coefficient, a device constant (units: V2F or J). Values are process dependent, here are some numbers
    • Typical Values: 3x10-24 J or 10-25 J
    • 4x10-26 J (NMOS) 2x10-25 J (PMOS) for 0.5μ ( HINP16C )
  • In above-threshold, Flicker noise usually dominates over Thermal noise below 50 Hz (for 0.5μ), 500kHz-1MHz for submicron (Razavi pp. 217). This is the noise corner frequency.

Spice Models

Nlev

Depending on which simulator you are using you will probably be able to specify the noise model you wish to use when doing simulation. Some simulators use the Nlev parameter to specify the noise model. There is an excellent summary of the forumals used for Nlev here. Note that all levels below Nlev=3 are really only suited for transistors in the Saturation region.

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Last edited by DrLock. Originally by DrLock.