The gains of an OP-AMP are listed below:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]G_d = (R_1*R_4+R_2*R_3+2*R_2*R_4)/(2*R_1*(R_3+R_4))[/tex]

[tex]G_s = (R_1*R_4-R_2*R_3)/(R_1*(R_3+R_4))[/tex]

[tex]\frac {\partial G_d} {\partial R_1} = -R_2*(R_3+2*R_4)/(2*R_1^2*(R_3+R_4))[/tex]

My questions is...

Is there a mathematical perform the following:

Differential gain equal to 1 (Gd=1)

Summing gain equal to 1 (Gs=0)

Minimize partial derivatives (This would reduce the sensitivity to the Gains to Resistor Tolerances)

Idea is that if I can minimize the Partial Derivatives then the tolerance of the resistors could be larger and get the same desired results (Gains are 1 and 0 respectively). This isn't about this one specific example. This could be done for most systems that have tolerance stickups that have to be accounted for.

I am looking for a mathematical process to perform the above. Lagrangian doesn't seem to work or I don't truly understand its fully use it for this process.

Thanks

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# I Optimization of an Amplifer Circuit

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