# Coupled differential Equations

• October 13th 2008, 03:13 PM
WantMath
Coupled differential Equations
$Vds=(R_S+R_d)*I_d+VDS$
$Vgs=VGS+R_S*I_d$
$dI_d/dVgs=g_m$
$dI_d/dVGS=gmo$
$dI_d/dVDS=gdo$

Hi,
I have a problem with finding $g_m$ in terms of gmo, gdo, $R_s$ and $R_d$. Does anyone know how to do this?
• October 13th 2008, 03:22 PM
Jason Bourne
Quote:

Originally Posted by WantMath
$Vds=(R_S+R_d)*I_d+VDS$
$Vgs=VGS+R_S*I_d$
$dI_d/dVgs=g_m$
$dI_d/dVGS=gmo$
$dI_d/dVDS=gdo$

Hi,
I have a problem with finding $g_m$ in terms of gmo, gdo, $R_s$ and $R_d$. Does anyone know how to do this?

• October 13th 2008, 03:26 PM
WantMath
$g_m=gmo/(1+gmo*R_S+gdo*(R_S+R_D))$
$\frac{dI_d}{dV}gs=g_m$