# Math Help - Coupled differential Equations

1. ## 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?

2. 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?

3. well, the answer looks like
$g_m=gmo/(1+gmo*R_S+gdo*(R_S+R_D))$

I just don't know how to get there

4. Sorry I'm not sure. It might help if you explain what each symbol is? What is "gdo" for instance? And

$\frac{dI_d}{dV}gs=g_m$

???