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Hello! I've got this project due for a college course, and the teacher has reviewed my work and said that it is within specification, but he asked me to compute the gain the good old fashioned way with pen and paper and to submit this proof together with my simulations. I tried researching around but I fear that I am not quite up to the task.

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The circuit is a series voltage regulator with temperature(t8, t7) and over-current protection(t9), the amplifier is there to provide negative feedback (through p1, r5, t4)against voltage fluctuations and the like. Input voltage would be 40V, output 20V (DC).

I have also started by computing the bias point on paper so as to make sure that all my components would be within the power dissipation or current specifications. It's just that I don't really understand how I would compute the exact gain for the amplifier.

Here are the simulations for those that are curious: enter image description here

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    \$\begingroup\$ We're not here to replace your teacher. You should use "small signal analysis" to determine the (small signal) gain. This method should have been explained by your teacher but you can also find it explained in many books about analog circuit design. Also it is explained by many on Youtube. So get studying. In my opinion you should not even be allowed to use a simulator before mastering the hand calculation method. The proper way to use a simulator is to confirm your hand calculations. \$\endgroup\$ – Bimpelrekkie Nov 9 '20 at 21:21
  • \$\begingroup\$ Or perhaps use the simulator when you're working with something that's just so nasty and nonlinear that you can't adequately do it by hand. But even there, like with a switching power supply or some such you'd want to do the hand calculations so that you start in the ballpark. \$\endgroup\$ – TimWescott Nov 9 '20 at 21:35
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    \$\begingroup\$ ioan-andrei Why don't you first describe to us many details about how you believe this arrangement works? What does it do? Discussing the details goes a long way in showing us how we can help out. If you can't even discuss how it functions, there is no possible way you can compute anything from it. Which would mean you may be "putting the cart before the horse." And what exactly did you find from your simulations? I'm very curious. \$\endgroup\$ – jonk Nov 10 '20 at 3:02
  • \$\begingroup\$ Did you really try researching? Sedra/Smith which is an ubiquitous book should have the answer, Gray/Hurst/Lewis/Meyer can also work, there are literally tens of books you can read that include that circuit. \$\endgroup\$ – S.s. Nov 10 '20 at 4:41
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    \$\begingroup\$ @IoanAndrei You keep saying you don't know how to calculate the exact gain. Frankly, though I can help there -- I don't care about that, yet. Do you recognize the "long-tailed pair"? Do you recognize the current mirror? If so, how do they interact? What happens at the wire connection between T4, T5, and the base of T1? What does your imagination tell you about all this? Can you break your circuit down into simple sections and talk about them? This is what is really important, right now. The "exact gain" from "pencil and paper" is one thing. But it doesn't matter if you don't follow the rest. \$\endgroup\$ – jonk Nov 10 '20 at 7:51
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Suggestion: these are bipolars, so you need the VEARLY (Early Voltage) in the transistor parameters.

You can examine the SPICE model for the transistor. Probably the VE param is what you need; expect a number between 10 and 100 volts.

The Vearly gives a useful approximation of the Rout of the transistor.

For the two right_hand transistors, The Rout_upper and Rout_lower, in parallel, becomes the current_to_voltage converter portion of this circuit.

The two transistors of the DiffPair are the voltage_to_current converter. Find the transconductance of that diffpair.

Then multiply the Transconductance by the Rout_upper||Rout_lower.

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