For a Coursera test I need to analyze a common source amplifier: CS Mosfet Amplifier

I need to calculate the

  • DC gate voltage - easy: -2.3077
  • drain current Id - should be easy but the results are wrong. I use this formula from the course or from here: $$ I_d=(\frac{\sqrt{1+4*K*V_1*R_{SS}}-1}{2*\sqrt{K}*R_{SS}})^2 \\ V_1=V_G-V_{TO}-V_{SS} $$
  • the drain voltage Vd=Vdd-Id*Rd which gives me -3.7719 V with the "wrong" current ??
  • the amplification which gives me -24.8174 (which is wrong!) $$ \frac {V_{out}}{V_{in}}=-\frac {R_D ||R_L}{r_s+R_S||R_3}\\ r_s=\frac{1}{g_m}\\ g_m=2*\sqrt{K*I_D} $$


Here are my calculations from Matlab:

Vdd=15; Vss=-15;K=1.1*1e-3;Vto=2;R1=150000;R2=110000;Rd=10000;Rs=5000;
R3=200; Rl=10000;

Vg = -2.3077


Vd = -3.7719

gac=-R_parallel(Rd, Rl)/(rs+R_parallel(Rs, R3))
gac = -24.8174

No I wonder am I too dumb to be true or is there a flaw in the automatic grader?

In case I am too dumb, please, tell, where my error is. Thanks.


1 Answer 1


If I use your equations

$$ I_d=(\frac{\sqrt{1+4*K*V_1*R_{SS}}-1}{2*\sqrt{K}*R_{SS}})^2 \\ V_1= (V_G -V_{SS})-V_{TO} $$

And if I substitute the resistors in kiloohms and all the voltage in volts and all current in milliamps I get this:

$$ I_d=( \frac{\sqrt{1+4*1.1*((-2.3077) - (-15) - 2)*5}-1}{2*\sqrt{1.1}*5} )^2 = 1.87719 $$


And this result is also in milliamps.

\$I_D = 1.87719\textrm{mA}\$

The drain voltage is \$V_D = -3.77V \$

and \$g_m =2*\sqrt{K*I_D} = 2.87396\:\textrm{mS}\$

\$r_s = \frac{1}{g_m} = 0.347952 \textrm{k}\Omega = 347.952 \Omega \$

And the voltage gain is

$$ \frac {V_{out}}{V_{in}}=-\frac {R_D ||R_L}{r_s+R_S||R_3} = \frac{5\textrm{k}\Omega}{0.347952\textrm{k}\Omega + \frac{1}{\frac{1}{0.2\textrm{k}\Omega}+\frac{1}{5\textrm{k}\Omega}}}=-9.25481 V/V $$

Do you have any additional questions? And next time you should track your units with more care.

  • \$\begingroup\$ Thanks for calculating all this. It's not my unit that don't match but the accuracy of Matlab. When I increase it with function called vpa() wrapped around the expression. And my second error was, thanks to you, the calculation of gm: I used K+Id NOT K*Id. Thanks a lot!! \$\endgroup\$
    – Andreas K.
    Sep 18, 2018 at 15:54

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