MOSFET Amplifier Configuration

[francisg3]

A Common-Source amplifier utilizes a MOSFET with µnCox = 400µA/V2, W/L = 10, and VA = 10V. It is biased at ID = 0.2 mA and uses RD = 6 kΩ. Find Rin, Avo and Ro. Also, if a load resistance of 10kΩ is connected to the output, what overall voltage gain Gv is realized? Now, what if a 0.2V peak sine-wave signal is required at the output, what must the peak amplitude of vsig be?


Below I have included the general model of the MOSFET along with what I believe is the equivalent pi-model.

I have found Ro to be RD//ro = (50*6)/(56) = 5.35kΩ (that part is correct according to the answer key.
where ro= VA/ID = 10/0.2 = 50kΩ

What I am having trouble with is the Avo and Gv.

I have the following:

ID = 0.5*Kn*(W/L)*(Vov^2)
subsituting values I get:
200 = 0.5*(400)*(10)*Vov^2
therefore Vov = 0.3162 Volts

gm = Kn*Vov
=(0.4)*(10)*(0.3162)

therefore Avo = -gm*(RD//ro)
= -(0.3162)*(5.3535kΩ)
= -6.76 (the answer is -2.14 V/V


Where did I go wrong? Any help would be appreciated!

 

[KataKoniK]

Hello,

Thank you for your detailed response. It seems like you have the correct values for Ro and Vov. However, I believe your calculation for Avo is incorrect.

To find Avo, we need to use the small-signal equivalent circuit of the MOSFET, which includes the transconductance parameter (gm) and the output resistance (ro). The formula for Avo is Avo = -gm*ro.

In your calculation, you used the parallel combination of RD and ro, which is correct for finding Ro, but not for Avo. To find Avo, we need to use the value of ro, which is 50kΩ in this case.

Therefore, the correct calculation for Avo would be:
Avo = -gm*ro
= -(0.3162)*(50kΩ)
= -15.81 V/V

As for Gv, we need to take into account the load resistance of 10kΩ. Therefore, the overall voltage gain would be:
Gv = Avo/(1 + Avo*RL)
= (-15.81)/(1 + (-15.81)*(10kΩ))
= -0.940 V/V

To find the peak amplitude of vsig, we can use the formula:
vsig = Vpeak/Gv
= (0.2)/(0.940)
= 0.213 V

I hope this helps clarify the calculations for Avo and Gv. Let me know if you have any further questions. Keep up the good work!