Large Signal Operation

Drain current (saturation region)

I D = 1 2 μ C o x W L (V G S - V T H) 2 (1 + λ V D S)

$I_D = {1 \over 2} \mu C_{ox} {W \over L}(V_{GS} - V_{TH})^2(1+\lambda V_{DS})$

Drain current (triode region)

I D = 1 2 μ C o x W L [2 (V G S - V T H) V D S - V 2 D S)

$I_D = {1 \over 2} \mu C_{ox} {W \over L}[2(V_{GS} - V_{TH})V_{DS} - V_{DS}^2)$

Threshold Voltage

V T H = V T H 0 + γ [2 ϕ f + V S B ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ \sqrt - 2 ϕ f ‾ ‾ ‾ ‾ \sqrt]

$V_{TH} = V_{TH0} + \gamma [\sqrt{2\phi_f + V_{SB}} - \sqrt{2\phi_f}]$

Threshold Voltage parameter

γ = 1 C o x 2 q ϵ N A ‾ ‾ ‾ ‾ ‾ ‾ \sqrt

$\gamma = {1 \over C_{ox}} \sqrt{2q\epsilon N_A}$

Oxide capacitance

C o x = ϵ o x t o x

$C_{ox} = \frac{\epsilon_{ox}}{t_{ox}}$

Small Signal Operation

Transconductance

g m = μ C o x W L (V G S - V T H) = 2 I D μ C o x W L ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ \sqrt = 2 I D V o v

$g_m = \mu C_{ox} {W \over L} (V_{GS} - V_{TH}) = \sqrt{2 I_D \mu C_{ox} {W \over L}} = {2I_D \over V_{ov}}$

Transconductance efficiency

g m I D = 2 V G S - V T H

$\frac{g_m}{I_D} = \frac{2}{V_{GS} - V_{TH}}$

Overdrive Voltage

V o v = V G S - V T H = 2 I D μ C o x ( W / L ) ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ \sqrt

$V_{ov} = V_{GS} - V_{TH} = \sqrt{\frac{2I_D}{\mu C_{ox}(W / L)}}$

Body effect transconductance

g m b = γ 2 2 ϕ f + V S B ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ \sqrt g m = χ g m = γ k ‘ ( W / L ) I D 2 ( 2 ϕ f + V S B ) ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ ‾ \sqrt

$g_{mb} = \frac{\gamma}{2\sqrt{2\phi_f + V_{SB}}}g_m = \chi g_m = \gamma \sqrt{\frac{k^` (W / L)I_D}{2(2\phi_f + V_{SB})}}$

Channel Length Modelation parameter

λ = 1 V A = 1 L e f f d X d d V D S \propto 1 L

$\lambda = {1 \over V_A} = {1 \over L_{eff}} \frac{dX_d}{dV_{DS}} \propto {1 \over L}$

Output resistance

r o = 1 λ I D = L e f f I D (d X d d V D S) - 1

$r_o = {1 \over \lambda I_D} = {L_{eff} \over I_D} (\frac{dX_d}{dV_{DS}})^{-1}$

Intrinsic Gain

g m r o = g m g d s = 1 λ 2 V o v = 2 V A V o v \propto W L I D ‾ ‾ ‾ ‾ \sqrt

$g_m r_o ={g_m \over g_{ds}} = {1 \over \lambda} \frac{2}{V_{ov}} = \frac{2V_A}{V_{ov}} \propto \sqrt{{WL \over I_D}}$

Transition Frequency

f T = g m 2 π ( C g s + C g d + C g b ) \approx 3 2 1 2 π g m C g s = 3 2 μ 2 π V o v L 2

$f_T = \frac{g_m}{2 \pi (C_{gs} + C_{gd} + C_{gb})} \approx {3 \over 2}{1 \over 2\pi}{g_m \over C_{gs}} = {3 \over 2}{\mu \over 2\pi}{V_{ov} \over L^2}$

Capacitance

C s b = C s b 0 ( 1 + V S B Ψ 0 ) 0 .5

$C_{sb} = \frac{C_{sb0}}{(1+{V_{SB} \over \Psi_0})^0.5}$

C d b = C d b 0 ( 1 + V D B Ψ 0 ) 0 .5

$C_{db} = \frac{C_{db0}}{(1+{V_{DB} \over \Psi_0})^0.5}$

MOS器件公示总结

Large Signal Operation

Small Signal Operation

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