# small signal analysis solve

I have found this small signal analysis circuit in my exercise.

simulate this circuit – Schematic created using CircuitLab

I tried both $\pi$-model and T-model but can't go anywhere. When trying to figure out $V_o$ can't decide whether take only $R_L$ or $R_L$ || $(R_1 +R_2)$ as DC current also flow through $R_1$ and $R_2$ . For other parameters like $V_{in} , R_{in} , R_{out}$ can't even make any idea.

How can I solve this and please,explain in detail so that in future I can solve this kind of circuits by myself. Thanks in advance.

• Look up Common Gate (common base for BJT) . people.seas.harvard.edu/~jones/es154/lectures/lecture_6/pdfs/… Even though your grounds are different, the Common gate might lend understanding Jun 7, 2014 at 14:23
• I know about common gate.Here main problem is $R_1$ and $R_2$ . If only $R_1$ or $R_2$ exist then it will not draw any current and can be solved.As both exist at same time, It draws a sufficient amount of current and again for equivalent circuit , make confusing whether to use $\pi$-model or T-model. Jun 7, 2014 at 15:22

It's easy to see that the small-signal drain voltage is given by

$$v_d = -i_d R_L||(R_1 + R_2)$$

so that's all there is to that.

If this were a true common-gate circuit, the small-signal gate-source voltage would be

$$v_{gs} = v_g - v_s = 0 - v_{sig} = - v_{sig}$$

but, in this circuit, the gate is not at signal common so we have

$$v_{gs} = v_g - v_s = v_d \frac{R_1}{R_1 + R_2} - v_{sig}$$

And, recalling that

$$i_d = g_mv_{gs}$$

you should have all you need to finish the problem.

• when I tried to solve this problem, I manage to find $V_d$ though I was confused about the result. thnx for ensuring. I mainly having trouble to find voltage gain $A_v$ and $R_{in}$ Jun 7, 2014 at 18:22
• @Anklon, if you have $v_d$, you have all you need for the voltage gain. Jun 7, 2014 at 23:59
• What about $V_{in}$ ?? when I looked through any equivalent model either $\pi$ or T , It become confusing to say which part I'll consider as $V_{in}$. Again other things also need to found like $R_{in}$ , $G_v$ Jun 8, 2014 at 4:00
• @Anklon, isn't $v_{in}$ just $v_{sig}$? Jun 8, 2014 at 19:47
• ops... due to exam's pressure I can't notice that.sorry But what about $R_{in}$,$R_{out}$ & $G_v$?? Jun 9, 2014 at 15:51