# Need help for pointing out, source follower circuit with current source, designing NMOS

I'm not sure did I solve this problem right.

I made $$\ r_{o2} \$$ , which is resistance looking at Q2 drain. So I can get $$g_{m,Q3} = 1.8m(A/V)$$ from $$A_v = \frac{r_{o2} || r_{o3}}{1/g_m + (r_{o2} || r_{o3})}$$

and I could get W/L by

$$g_{m,Q3} = \sqrt{2I_D \mu C_{ox}(W/L)}$$ then $$(W/L)_{Q3} = 16.2$$

And I can find out $$\ V_{GS} = 0.8V , V_{GS} = V_{DS}\$$ at Q1

so

$$I_{REF} = 1/2 \mu C_{ox}(W/L)_{Q1}(V_{GS}-V_T)^2(1+ \lambda V_{DS})$$

then I get $$(W/L)_{Q1} = 20.576$$ and I can guess (W/L){Q2} = (W/L){Q1} because their $$\V_{GS}, V_{DS}\$$ is same.

I know in Q2 $$g_m = \frac{2I_D}{V_{GS}-V_T} = \mu C_{ox}(W/L)(V_{GS}-V_T)$$

But this equation is not true when I substitute my values. What's the problem?

• While I think this could be a "good" homework question because it shows your work and allows someone to help point out where you went wrong, I think the title desperately needs to be revised. – JYelton Jun 15 at 18:14
• @JYelton Do you have some idea about that?? – Pare Kanes Jun 15 at 18:43
• You need to treat the current mirror Q1, Q2 separately from Q3. Determine W/L of Q1 and Q2 such that $I_{REF}$ is flowing. Now you can determine the output resistance $r_{o}$ of Q2. Then we know that small signal equivalent of the current mirror: an ideal current source with value $I_{REF}$ and a resistor $r_{o2}$ in parallel with it. Now draw the small signal equivalent circuit of Q3 and use the model of the mirror connected to its source. – Bimpelrekkie Jun 15 at 18:56
• if the gain is 0.9 you need to have ro2||ro3 = 9*gm3 – G36 Jun 15 at 18:57
• The gain of 0.9 V/V is the result of the output impedance of the source follower (roughly 1/gm) and $r_{o2}$, these make a voltage divider. From $r_{o2}$ determine what the output impedance of the source follower needs to be. Then you know what the gm of Q3 needs to be, from that determine W/L (you know the biasing current already). – Bimpelrekkie Jun 15 at 18:58