In the previous chapter we have seen a general overview of the operational amplifier. In this chapter, we will see that depending on the topology used, the configuration acquires a proper name. Let's look at the topology called operational amplifier in the adder configuration.

In this configuration the non-inverting input is grounded, therefore V₂ = 0. As we have two entrances, V_a and V_b, connected to the node V₁, we can solve this circuit by applying the law of nodes for that node.

In the Figure 44-01, we see the adder circuit. As indicated in the circuit,  i_i = 0, so we can write for the node V₁:

Now, by applying the nodal analysis for this node, we have:

But we know that V₁ = 0. So, isolating V_o we arrive at the desired equation that allows to calculate the output voltage as a function of the input voltages V_a and V_b.

By the equation we see that the output voltage is determined by the ratio between the resistor R_f and the resistor of each input. We can define the quotient of resistances as a weighted factor and represent it as follows:

So we can generalize to "n" entries and we get:

In this item we will analyze the adder in the Non-Inverting configuration. Let's start from a general circuit as shown in the Figure 44-02, initially, with three voltage sources at the non-inverting input.

For the analysis of this circuit we must consider the operational amplifier as ideal and therefore satisfying the following initial conditions:

In addition, by the law of Kirchhoff  for nodes, we have:

This way we can write:

Let's adopt the following equality: Z = R₁ = R₂ = R₃. So we get the relation:

Solving this relationship, we obtain: