Electrical – Is this equation for transconductance correct


\$\frac{1}{g_m} = \frac{r_\pi}{(1+\beta)}\$

Is this equation correct? If so, how are they equivalent?

In words: inverse of the transconductance = \$\frac{r_\pi}{(1+\beta)}\$

Small-Signal model

Best Answer

I suppose, we are speaking about bipolar transistors, right? The following definitions apply:

  • Transconductance (slope of the Ic=f(Vbe) function): gm=d(Ic)/d(Vbe)

  • Input resistance (inverse slope of the Ib=f(Vbe) function): rbe=d(Vbe)/d(Ib)

  • From this: gm=d(Ic)/[d(Ib)rbe]=beta/rbe.