0
\$\begingroup\$

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!) $$ \frac {V_{out}}{V_{in}}=-\frac {R_D ||R_L}{r_s+R_S||R_3}\\ r_s=\frac{1}{g_m}\\ g_m=2*\sqrt{K*I_D} $$

OK.

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=(Vdd*R2+Vss*R1)/(R1+R2)
Vg = -2.3077

V1=Vg-Vss-Vto
Id=((sqrt(1+4*K*V1*Rs)-1)/(2*Rs*sqrt(K)))^2
Id=0.0019

Vd=Vdd-Id*Rd
Vd = -3.7719

gm=2*sqrt(K+Id)
rs=1/gm
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.

\$\endgroup\$
0
1
\$\begingroup\$

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:

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

http://www.wolframalpha.com/input/?i=((Sqrt%5B1+%2B+4*1.1*((-2.3077)+-+(-15)+-+2)*5%5D+-+1)%2F(2+Sqrt%5B1.1%5D*5))%5E2

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.

\$\endgroup\$
1
  • \$\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 '18 at 15:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.