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I have this circuit

enter image description here

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?

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  • \$\begingroup\$ 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. \$\endgroup\$ Jul 8 '16 at 7:18
  • \$\begingroup\$ @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? \$\endgroup\$
    – Tendero
    Jul 8 '16 at 15:47
  • \$\begingroup\$ 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. \$\endgroup\$
    – Whit3rd
    Jul 12 '16 at 20:49
  • \$\begingroup\$ 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.) \$\endgroup\$
    – carloc
    Sep 11 '16 at 9:58
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This is an operational transconductance amplifier (OTA).

The transconductance of the OTA is rather a complex calculation if you want the large-signal model, and takes a few pages to set up... the difference transconductance of the T1-T2 pair is a hyperbolic tangent, with temperature dependence, and that propogates to the output.

See _Analysis and Design of Analog Integrated Circuits by Grey and Meyer for a discussion (chapter 3 section 4).

Common mode input R will depend, I suspect, on the Early voltage of T10. Make a Spice model, with realistic transistor specs, to solve the various parameters.

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  • \$\begingroup\$ Uhm, I am sorry, but just cannot understand what large-signal analysis has to do with small-signal one request by @Tendero \$\endgroup\$
    – carloc
    Sep 11 '16 at 9:59
  • \$\begingroup\$ OTA inputs are truly differential, there is no inference that one should be a signal ground, rather each input can take any value subject to the common-mode and difference ranges. \$\endgroup\$
    – Whit3rd
    Sep 11 '16 at 10:09
  • \$\begingroup\$ Oh yes no matter differential or single ended, we can even drive it into saturation or cut-off, but that's just not what @Tendero asked. He said he's done DC bias analysis and he's now going to study small-signal, i.e. system linearized around bias point found. I just think introducing some (heavy) extras at this point can only mess him up \$\endgroup\$
    – carloc
    Sep 11 '16 at 12:50
  • \$\begingroup\$ If the bias point chosen is with the inputs balanced, and output current near zero, the 'small-signal' model works. If output current is NOT near zero, input voltages are significantly nonequal. His bias point could be anywhere in the large-signal range, and the peak transconductance point is only valid for one differential-input operating point (the one that gives zero output current). \$\endgroup\$
    – Whit3rd
    Sep 11 '16 at 22:30

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