Electronic – JFET Vgs Calculation Equation


Does anyone know the formula to calculate the Vgs of a JFET used as a variable resistor?
Say, I have a Vds of 24v and I require a current of 20mA (just arbitrary values) I would need a 1.2k resistance, how would I calculate the Vgs to get that resistance value?

Best Answer

Following up on Andy's link, we differentiate the equation # 6.39, with respect to \$V_{DS}\$.

We want the resistance. That requires incremental \$V_\mathrm{Drain}/I_\mathrm{Drain}\$.

We end up with a constant portion: $$ \frac{\mathrm{d}I_D}{\mathrm{d} V_{DS}} = 2 K (V_{GS} - V_P) $$ and a variable portion: $$ \begin{split} \frac{\mathrm{d}I_D}{\mathrm{d} V_{DS}} &= K 2 (2 V_{DS}) \\ &= 4 K V_{DS} \end{split} $$ The constant portion is the transconductance, or the inverse of channel resistance.

The variable portion is the DISTORTION.