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**1. Homework Statement**

Design an op-amp that uses a variable 50k ohm resistor. when this variable resistor is at one extreme, the gain is 13, and at the other extreme, the gain is 3. you may use up to 2 op-amps, and up to 7 resistors (including the variable resistor)

**3. The Attempt at a Solution**

here is the circuit i came up with:

I made it so all I would have to find is Rf to satisfy the design.

here is how I solved for Rf

first extreme:

[tex] (1 + \frac{R_f}{60k-ohms}) = 13 [/tex]

next extreme:

[tex](1 + \frac{R_f}{110k-ohms}) = 3 [/tex]

combine the two equations:

[tex]11 + \frac{R_f}{110k-ohms} = 1 + \frac{R_f}{60k-ohms}[/tex]

[tex] 10 = R_f (\frac{1}{60k-ohms} - \frac{1}{110k-ohms})[/tex]

[tex] R_f = 1.32M-ohms[/tex]

this answer gives a gain of 13 on one extreme of the variable resistor and 23 on the other. whoops. any help?

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