What Is KN in MOSFET? How Do I Find Out?

The transconductance parameter of MOSFET is the product of the mobility of electrons in channel and oxide capacitance and is represented as kn (transconductance parameter)=μn(Mobility of electrons)*Cox(Oxide Capacitance) 

What Is KN in MOSFET

The transconductance parameter (Kn) is a measure of the performance of a bipolar or field-effect transistor (FET). When all other conditions are unchanged, the larger a device’s transconductance figure, the greater the gain (amplification) it is capable of giving.

What Is KN in MOSFET?

To calculate Kn in MOSFET put the values of Gm and current(I) of your MOSFET in the following equation:

Kn = (Gm^2)/(2I)

The most essential parameter of a transistor is its transconductance. It is simply the voltage to current gain. The gain of a voltage amplifier is given by transconductance*load resistance. Additionally, it determines your Gain Bandwidth Product (GBW).

What Is Formula of KN in MOSFET?

The following derivation gives the formula of Kn in MOSFET:

Kn= (gm)^2 / (4*Id)

Here, Id is the drain current.

In saturation, 

I = kn/2 * W/L * (Vgs – Vth)^2 = Kn/2 * (Vgs – Vth)^2  (Vgs is the gate to source voltage and Vth is the threshold voltage of the MOSFET)

If you include W/L in kn, then Gm = Kn * (Vgs – Vth) 

Thus, Kn = (Gm^2)/(2I)

What Does K Mean in MOSFET?

Note that K plays the same role in the MOSFET drain current equation as β plays in the JFET drain. current equation. Some texts define K = k’ (W/L) (1 + λvDS).

Generally, K = Id/(Vgs-Vth)^2

Drain current, Id = k(Vgs-Vth)^2 

Another equation to find ot Id is: Id = k / 2 ( Vgs – Vth ) ^ 2

How Do You Find KN?

To find the Kn of your MOSFET, you need to know the value of Gm (conductance) and current(I). Now put the values in the following equation and you’ll get the value of Kn.

Kn = (Gm^2)/(2I)

How Do You Find the Value of K in a MOSFET?

The following equation will give you the value of K in a MOSFET.

K = Id/(Vgs-Vth)^2

Here, Vgs= Gate to source voltage of the MOSFET.

Vth= Threshold voltage and Id= Drain current.


You can find the approximation of Kn if you fix Vth at an arbitrary value (possibly obtained from a measurement of your device). Then, if you take the value of RDS, Vgs and Vth you can put it in the formula of Id and obtain Kn.

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