Problem 42-2    Source:   Problem 4-21 - page 211 - THOMAS, Roland E. , ROSA, Albert J. , THOUSSAINT, Gregory J. -   Book: The Analysis & Design of Linear Circuits - 6ª ed. - Ed. John Willey & Sons, Inc. - 2009.

In the circuit shown in the Figura 42-02.1 determine V_o in function of V_a.

Solution of the Problem 42-2

Since this is an inverter circuit, the equation for calculating the voltage gain is:

In this problem we have to    R_f = 330 kΩ and R_i = 33 kΩ. With these values we can calculate the value of K.

Note that there is a voltage divider in the input circuit. Therefore, we must calculate the value of V_i in function of V_a. Note that the 33 kΩ resistor end that is connected to the inverter input of the amplifier is virtually connected to ground. In an ideal operational amplifier the potential difference between the inputs is null. Thus, to find the value of V_i, we calculate the parallel of 33 kΩ and 56 kΩ.

To calculate V_i, note the figure above. The parallel of the two resistors results in one of 20.764 kΩ. In this way, the voltage will be:

Knowing the relationship between V_o e V_i, given by K, simply substitute its values in the equation below.

An alternative solution is to calculate the Thévenin equivalent for the input circuit. The same result should be obtained. Make and check !!!!