Problem 47-6    Source:   Problem 4.69 - page 218 - THOMAS, Roland E. , ROSA, Albert J. , THOUSSAINT, Gregory J. -    Book: The Analysis & Design of Linear Circuits - 6ª Edição - Ed. John Willey & Sons, Inc. - 2009.

In the circuit shown in the Figura 47-06.1, determine the value of V_o in terms of V₁ and V₂.

Solution of the Problem 47-6   

From the circuit, we easily find a relation between V_o and V₄ through a voltage divider. Like this:

Now using the nodal method for the OP 1:

After some algebraic manipulation in the above equation, and recalling that virtually V₃ = V₄, we obtain the following relation:

Clearly OP 2 is connected in an adder configuration. In this case, we can extract the following relation:

Replacing the value of V_x, found previously, in this equation:

But, it is known from the first equation that V₄ = V_o / 3. So, replacing this value in the above equation:

Then, passing -V_o to the first member and simplifying the desired relationship is found, or:

That is, this circuit behaves like a subtractor.