# 跨导

${\displaystyle g_{m}={\Delta I_{\mathrm {out} } \over \Delta V_{\mathrm {in} }}}$

${\displaystyle g_{m}={i_{\mathrm {out} } \over v_{\mathrm {in} }}}$

${\displaystyle dI_{D}={\frac {\partial I_{D}}{\partial V_{GS}}}dV_{GS}+{\frac {\partial I_{D}}{\partial g_{m}}}dg_{m}}$

⋯⋯⋯⋯⋯

Dlt_iDrn=(iDrn/vGS)*Dlt_vGS+(iDrn/gM)*Dlt_gM

⋯⋯⋯⋯⋯

ΔiDrn=(iDrn/vGS)*ΔvGS+(iDrn/gM)*ΔgM

⋯⋯⋯⋯⋯

${\displaystyle dV_{GS}=-{\frac {\partial I_{D}/\partial V_{GS}}{\partial I_{D}/\partial g_{m}}}dg_{m}}$ ${\displaystyle =-{\frac {V_{GS}-V_{TH}}{(R_{S}+{\frac {1}{g_{m}}})^{2}}}g_{m}dI_{D}}$

⋯⋯⋯⋯⋯

${\displaystyle dV_{GS}={\frac {1}{g_{m}}}{\frac {(R_{S}+{\frac {1}{g_{m}}})^{2}}{V_{GS}-V_{TH}}}|dI_{D}|}$

## 互導公式

g_m

=sqrt(2μ_n*c_Oxd*(W/L)*i_Drn）

=2*i_Drn/(v_GS-v_Thr)

• μ_n：電子的遷移率
• c_Oxd：閘極氧化層單位面積的電容值
• W/L：閘極的寬度和長度比值
• i_Drn：汲極直流偏壓電流
• v_GS-v_Thr：（閘極Gate和源極Source電位差）-臨界電壓Þrešold

## 互導公式推演

gM=(Dlt*iDrn)/(Dlt*vGS)

=muN*cOxd*(W/L)(vGS-vThr)

=2iDrn/(vGS-vThr)

=sqrt(iDrn*2muN*cOxd(W/L))

=｛1/2*muN*cOxd*(W/L)[(vGS-vThr)^2]｝*2/(vGS-vThr)

=2iDrn/(vGS-vThr)

=sqrt(［(1/2)*muN*cOxd(W/L)(vGS-vThr)^2］*2muN*cOxd(W/L))

=sqrt(iDrn*2muN*cOxd(W/L))