# How to calculate the transconductance of this circuit?

I have this circuit where the "FES" blocks are simple current mirrors and the block "PD" is a differential pair. All the transistors in those blocks are BJT, NPN or PNP, respectively.

I found all the dc values but when trying to analyze the circuit with small-signal, I get lost. I want to find the transconductance with differential mode and common mode, i.e. $G_{md} = \frac{i_l}{v_{id}}$ and $G_{mc} = \frac{i_l}{v_{ic}}$, both when $v_o=0$ (namely, RL is taken away). I'm also having problems finding the input resistances, i.e. $R_{ic}$ and $R_{id}$. I believe $R_{id}=2r_{\pi}$ and $R_{ic}=r_{\pi}+2\beta r_{o_{10}}$ but I'm not sure.

How should I start?

• Maybe this will help: The circuit looks like a textbook operational transductance amplifier like the CA3080 with a fixed bias current generated by T11. So the same Gm calculations that apply to OTAs should apply here as well. Jul 8 '16 at 7:18
• @NilsPipenbrinck That's a nice tip, thanks. Unfortunately, I haven't found anything on the Internet that helps me out with this. Could you provide a link or something? Jul 8 '16 at 15:47
• T1 is shown with some wrong connection; it's a source follower, gate grounded, feeding a mirror input that is diode-clamped to Vdd. It has no current-limiting function. Jul 12 '16 at 20:49
• I belive you should just draw the two basic building blocks, FES and PD, each alone and study them for $g_\text{md}$ , $g_\text{mc}$ , $r_\text{id}$ and so on. This must be pretty simple, it's just a couple of BJT in kwown configuration. The you can use these results in your full amplifier. (P.S. differential, small signal quantities must be written small, not capital symbols.) Sep 11 '16 at 9:58