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.

  • \$\begingroup\$ 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 \$\endgroup\$
    – Marla
    Jun 7, 2014 at 14:23
  • \$\begingroup\$ 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. \$\endgroup\$
    – Anklon
    Jun 7, 2014 at 15:22

1 Answer 1


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.

  • \$\begingroup\$ 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}\$ \$\endgroup\$
    – Anklon
    Jun 7, 2014 at 18:22
  • \$\begingroup\$ @Anklon, if you have \$v_d\$, you have all you need for the voltage gain. \$\endgroup\$ Jun 7, 2014 at 23:59
  • \$\begingroup\$ 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\$ \$\endgroup\$
    – Anklon
    Jun 8, 2014 at 4:00
  • \$\begingroup\$ @Anklon, isn't \$v_{in}\$ just \$v_{sig}\$? \$\endgroup\$ Jun 8, 2014 at 19:47
  • \$\begingroup\$ ops... due to exam's pressure I can't notice that.sorry But what about \$R_{in}\$,\$R_{out}\$ & \$G_v\$?? \$\endgroup\$
    – Anklon
    Jun 9, 2014 at 15:51

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