Unipolar transistor basic variable transconductance is commonly marked by:

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It is commonly used in calculations where we need drain current, Ugs, rds(on), and similar.

I have also seen many equations for calculating upper variables but here mostly used variable is known as "conduction parameter" (unit: mA/V square). It says (in the pdf file) that "K" should be given by manufacturer. But none datasheet till now had any value like this one.

Question: Do these two (transconductance & conduction parameter) have something in common? Can one replaced with another (probably not)? Are these equations with conduction parameter even used in practice?

enter image description here


1 Answer 1


The relation between transconductance (\$g_m\$) and the conduction parameter (\$K_n\$) may be found from the definition of \$g_m\$:

$$ g_m = \frac{\partial i_D}{\partial v_{GS}} = 2K_n\left(v_{GS}-V_{TN}\right) \\ \implies K_n=g_m/\left(2\left(v_{GS}-V_{TN}\right)\right) $$

In other words, the conduction parameter may be found from the transconductance when given the overdrive voltage at which \$g_m\$ was measured.

It is also possible to find \$K_n\$ from \$g_m\$ when given the drain current at which \$g_m\$ was measured:

$$ g_m = 2K_n\left(v_{GS}-V_{TN}\right) = 2\sqrt{K_n}\sqrt{K_n\left(v_{GS}-V_{TN}\right)^2} = 2\sqrt{K_ni_D} \\ \implies K_n=g_m^2/\left(4i_D\right) $$

In practice, the conduction parameter may be useful for back-of-the-envelope, or approximate, calculations.

Reference: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-012-microelectronic-devices-and-circuits-fall-2005/lecture-notes/lec11.pdf. See slide 11-6 and apply definition \$K_n = W\mu_nC_{ox}/\left(2L\right)\$.

  • \$\begingroup\$ I hope these equations are true. Could you define the source of information written here? \$\endgroup\$
    – MucaGinger
    Mar 24, 2017 at 8:55
  • \$\begingroup\$ You said "back-of-the-envelope calculations". What does that mean? \$\endgroup\$
    – MucaGinger
    Mar 24, 2017 at 8:56
  • 1
    \$\begingroup\$ Updated response to address your questions. Note that the same variable, \$K_n\$, is sometimes defined as \$W\mu_nC_{ox}/L\$. As a result, you must be careful when applying formulas using \$K_n\$ to ensure the meaning of this variable is consistent. \$\endgroup\$
    – SGH
    Mar 24, 2017 at 15:17
  • \$\begingroup\$ Yes, I totally forgot to write that "n" near to it. "Kn" applies for NMOSFET and "Kp" for PMOSFET (n-electrons, p-holes). \$\endgroup\$
    – MucaGinger
    Mar 24, 2017 at 20:25
  • \$\begingroup\$ I also forgot to write down which unipolar transistor I am reffering to: the equations from my question are reffering to MOSFET (as you can se Cox - cap), yours transconductance reffers to JFET if I'm right. Same transconductance applies for MOSFET except "K" is defined differently (look to my question). \$\endgroup\$
    – MucaGinger
    Mar 24, 2017 at 20:37

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