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The circuit in question

I need to calculate the gain of this amplifier. However, when I do this, I get the value two times bigger than the simulation of this circuit, which I run in Multisim, suggests.

My line of thought is this: The gain should be equal to $$R_1/((r_{e1}+R_2)+(R_4 \parallel (R_3+r_{e2}))$$ where \$r_{e1}\$ and \$r_{e2}\$ are the thermal resistances of the corresponding transistors.

Calculating gives me the value of approximately 6.2, when the simulation suggests that the gain is 3.3. I have double-checked and the simulation circuit has no errors in it.

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  • \$\begingroup\$ hFE only 20? try 200. did U choose f so Zc1=~0 \$\endgroup\$ Commented Oct 17, 2016 at 22:54
  • \$\begingroup\$ @Tony Stewart. EE since '75 My source frequency is 1GHz, it's in the range where resistncae in negligible. I can't change the hFE values, as the task I'm given specifically states I should use 20. Even if I do, the change is just a small fraction of the result. \$\endgroup\$
    – Mu3
    Commented Oct 17, 2016 at 23:06
  • \$\begingroup\$ ok I never expected 1GHz with 1uF due to ESL \$\endgroup\$ Commented Oct 17, 2016 at 23:34
  • \$\begingroup\$ With R4=1K it works for me at low f with a gain of 4. But you never specified R4 \$\endgroup\$ Commented Oct 18, 2016 at 0:19
  • \$\begingroup\$ R4 is 129 Ohms. Frankly, the frequency is not given either. I just assumed 1GHz to eliminate the capacitive resistances. \$\endgroup\$
    – Mu3
    Commented Oct 18, 2016 at 13:49

1 Answer 1

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Obviously, since the hFE of the transistor is 20, you cannot expect a large gain. You wrongly deduced that the gain is R1/((re1+R2)+(R4||(R3+re2)). The gain, in fact, is R1/((re1+R4)+(R2||(R3+re2)). Look at it from the right side of the base.

The next point is your comment: ' I just assumed 1 GHz to eliminate the capacitive resistances.'. Just 'assuming' and wildly guessing a number because you heard somewhere that high frequencies eliminate 'capacitive resistances' (which are capacitive reactances) is no way to model a system.

Picking 517.3 MHz will give you much better results. As for why - I will leave that to you to figure out. This brings us to the final conclusion - implement the aforementioned changes and you will see a gain of 6.2.

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    \$\begingroup\$ Answers on this site are expected to be generally useful to readers, not just the OP. While it may be fun for you to include snide remarks such as "painfully obvious", leave readers guessing with the value of 517.3 MHz, and criticize "begging for homework answers", they don't actually make this a helpful answer to the community at large. If you instead explained your rationale and derivation, this would be a much more useful answer. With that said, the question is also from 2016, so you're >4 years late on calling the OP out for their mistake and terminology. \$\endgroup\$
    – nanofarad
    Commented Jan 5, 2021 at 20:05

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