Problem 42-4    Fonte:   Problem elaborated by the author of the site.

For the circuit shown in the Figura 42-04.1, calculate the gain of the circuit when the key S is in the position 1 and in the position 2, considering that R = 1000 Ω , R₁ = 2000 Ω , R₂ = 3000 Ω and R₃ = 6000 Ω.

Solution of the Problem 42-4

Key in position 2

With the switch in position 2, the resistor R₃ is in parallel with the resistor R₂. And this parallel is in series with R₁. By calculating this association we obtain the feedback resistor of the operational amplifier, usually represented as R_f in an inverter circuit. The gain of this configuration is given by eq. 42-01, shown below.

We need to know who the resistors are R_i and R_f in the above equation. From the circuit, it is noted that R = R_i and that:

Substituting the numerical values and performing the calculation, we obtain:

Substituting these values into the eq. 42-01 and by performing the calculation, we get:

Key in position 1

With the key in the position 1, the circuit is similar to the previous problem and the gain is given by eq. 42-3a (discussed in the previous problem, prob. 42-3), shown below.

Thus, by replacing these values in the eq. 42-3a above and by performing the calculation, we get:

Then we conclude that by passing the key from position 2 to position 1, the gain of the circuit is increased by 20 times.