# Small signal analysis of 2nmos

To introduce myself I am a first year EE student and an exam on AC circuits is comming up. Whilst practising I noticed one question I couldn't solve. No way I tried managed to get me the answer (which I do have) The first question was easy so I got that one. But when trying to solve this I keep getting different values of the gain. I tried multiple ways of connecting the resistor from the backgate effect to solve it but I either get ~-12V/V or ~-14V/V I am not asking for people to do my homework as I really want to understand this course but this one I cant solve. to save some time: gm1 = 4 (20*0.2) gm2 = 10 (8*0.5) ro1 = 25kOhm ro2 = 10kOhm

## 1 Answer

First, solve for DC operation point.

$I_{D1} = \frac{K_{n1}}{2}(V_{GS} - V_t)^2 = 0.4\textrm{mA}$

And for the second NMOS

$I_{D2} = 1\textrm{mA}$ and $V_{GS2} = \sqrt{\frac{I_{D2}}{\frac{K_{n2} }{2}}}+V_T = 1V$

And now the transconductance

$g_{m1} = K_{n1}(V_{GS1} - V_T) = 4\textrm{mS}$

$g_{m2} = K_{n2}(V_{GS2} - V_T) = 4\textrm{mS}$

And finally, the voltage gain of a first stage is:

$Av1 = - g_{m1} \cdot R||ro1$

Where $ro1 \approx \frac{1}{\lambda I_{D1}} \approx 25\textrm{K} \Omega$

Therefore the first stage voltage gain is $Av1 = -9.09\:V/V$

And the voltage gain for a source follower is

$Av2 = \frac{g_{m2} \cdot ro2}{1 + g_{m2} \cdot ro2} = 0.9756 \: V/V$

So the total gain is $-9.09 \cdot 0.9754 = - 8.87 \: V/V$

• I feel so dumb, I made my mistake at the transconductance for Q2. Some times the simplest equations are the hardest to do correctly. I have heard of the term source follower before but never seen that gain equation. Nevertheless my own equations corrected gave the correct output. THANK you – Weird Apr 14 '18 at 21:06