Question

Please help me with this problem i really can't complete it

Answer 1

• VX = V1·R2/(R2 +R1(1 +AVOL))
• VX ≈ -99.0001 μV
• Vout = -V1·R2·AVOL/(R2 +R1(1 +AVOL))
• Vout ≈ 0.990001 V

Step-by-step explanation:

It is useful to consider the voltage at X to be the superposition of two voltages divided by the R1/R2 voltage divider. It is also helpful to remember that OUT = -VX·AVOL.

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a)

`V_X=(V_1\cdot R_2+V_(out)\cdot R_1)/(R_1+R_2)=(V_1\cdot R_2-V_X\cdot A_(VOL)\cdot R_1)/(R_1+R_2)\\\\V_X(R_1(1+A_(VOL))+R_2)=V_1\cdot R_2\\\\\boxed{V_X=V_1(R_2)/(R_2+R_1(1+A_(VOL)))}`

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b)

Filling in the given numbers, we find VX to be ...

`V_X=-0.01V\cdot(400000)/(400000+4000(1+10000))=-0.01V\cdot(100)/(10101)\\\\\boxed{V_X=(-1)/(10101)V\approx-99.0001\mu V}`

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c)

As we said at the beginning, OUT = -VX·AVOL. Multiplying the expression for VX by -AVOL, we get ...

`\boxed{V_(out)=-V_1\cdot(A_(VOL)\cdot R_2)/(R_2+R_1(1+A_(VOL)))}`

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d)

As with the expression, the output voltage is found by multiplying VX by -AVOL:

`V_(out)=((-1)(-10000))/(10101)V\\\\\boxed{V_(out)=(10000)/(10101)V\approx 0.990001V}`