Differential amplifier common mode gain

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SUMMARY

The discussion focuses on the derivation of equations 10-8 and 10-9 related to the common mode gain of differential amplifiers. It emphasizes that for a differential amplifier to function correctly, the ratio R2'/R1' must equal R2/R1, resulting in a difference mode gain of R2/R1 and a common mode gain of 0. Additionally, the sensitivity analysis involves introducing an error term to a resistor, such as R2 → R2 + ΔR, to observe discrepancies in the common mode gain calculations.

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paulmdrdo
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Summary:: Differential amplifier common mode gain derivation of forumlas

I'm having a hard time deriving for equations 10-8 -10-9.
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I tried adding equation's 18-6 and 18-7 but cannot proceed with the derivation. I need help on this. Thank you!
 
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It's kind of a confusing section, much appears to be left out.

For this to be a differential amp, you would have to set R2'/R1' = R2/R1. Then the difference mode gain is R2/R1 and the common mode gain is 0. If you don't do this, I don't think the premise makes sense.

Then for the sensitivity analysis, I would pick any single resistor and add in an error term eg. R2 → R2 + ΔR. Then recalculate the common mode gain. You may find some discrepancies from their result because of how you introduce the component value error term.
 

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