P 6.4-21 The circuit shown in Figure P 6.4-21 has three inputs: v₁, v₂, and v₃. The output of the circuit is v_o. The output is related to the inputs by

v_o = av₁ + bv₂ + cv₃

where a, b, and c are constants. Determine the values of a, b, and c.

Figure P 6.4-21

Annotating this circuit so we can work through it.

We can see the currents add

From op-amp rules we can see that

Current can be found by first finding

Using the value of , we can write

So we know

Now can be written

Now we find

Now we get by using voltage division. Since the series circuit touching the non-inverting input has two 20 kΩ resistors, we can see

Next find , but first get

Solving for

Then can be found from

Finally can be found from

Multiply by -120 kΩ

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This page last updated on March 16, 2019