Problem 47-5    Source:   Problem 5.79 - page 186 -    ALEXANDER, Charles K., SADIKU, Matthew N. O. -    Book: Fundamentos de Circuitos Elétricos - 5ª Edição - Ed. McGraw Hill - 2013.

In the circuit shown in the Figura 47-05.1, determine the value of V_o knowing the values of the input voltages, or V₁ = 5 V and V₂ = 1 V.

Attention -    The answer to this problem in the book is slightly different (8 mv less) from the answer found here. This is because the book used the PSPICE program to solve it and this program does not consider the operating amplifier as IDEAL.

Solution of the Problem 47-5   

Note that the non-inverting input of OP 1 has been made the Thévenin equivalent resulting in voltage V_th= 5 x 10 / (10 + 20) = 5/3 V. The resistance of Thévenin is the parallel of the two resistors, or R_th= 20 x 10 / (10 + 20) = 6.67 kΩ. In the figure above the transformation performed is shown. From the circuit it can be concluded that OP 2 is connected in the inverter configuration. So:

Putting V_o in terms of V₄ we have:

Now using the nodal method for the 3 point we get:

After some algebraic manipulation in the above equation we arrive at the following relation:

Recalling that, virtually V₃ = V_th = 5/3 V and that V₂ = 1 V, replacing in the above equation:

Substituting this value into eq. 47-05.1, we found the value of V_o, or: