Electronic Devices - FET Amplifiers - Discussion

From the formula, you can get the value of Vgs:

Id = Idss(1-(Vgs/Vp))^2.

Where;
Id = 6mA and Idss = 8mA.

But solve for Vp first: Given that gmo = 4mS,
gmo = 2(Idss)/Vp,
4mS = 2(8mA)/Vp,
Vp = 4 V.

Then Substituting from the formula Id = Idss(1-(Vgs/Vp))^2 to get Vgs; Vgs then would be 0.536 V.

Note: There would be two values since it is quadratic.

To get gm, use the formula:
Gm = (2(Idss)/Vp)*(1-(Vgs/Vp)).
= (2(8mA)/4)*(1-(0.536/4)).
gm = 3.464 mS.

From the formula, you can get the value of Vgs:
Id = Idss(1-(Vgs/Vp))^2.

Where:
Id = 6mA and Idss = 8mA.

But solve for Vp first: Given that gmo = 4mS,
gmo = 2(Idss)/Vp,
4mS = 2(8mA)/Vp,
Vp = 4 V.

Then Substituting from the above formula to get Vgs; Vgs then would be 7.464 V.

To get gm, use the formula:
Gm = (2(Idss)/Vp)*(1-(Vgs/Vp)).
= (2(8mA)/4)*(1-(7.464/4)).

Gm = -3.464 mS or equal to 3.464 mS neglecting the negative sign.

Let;
X =(1-Vgs/Vp)^2.
Y= Vp.

Id = Idss(X),
6mA = 8mA(X).

Solve for Vp:
gmo = 2(Idss)/Vp.
4mS = 2(8mA)/Y.

Solving gm:
gm= (2(Idss)(1-Vgs/Vp)^2)/Vp.
gm = 2(8mA)(X) /Y.

Please explain the answer.