Problem 47-1    Source:  2ª question of 1º test - Electric Circuits - Ufrgs - 2017.

For the circuit shown in the Figura 47-01.1, calculate I_o in function of V_i.

Solution of the Problem 47-1   

This circuit is composed of an operational amplifier (OP2) connected in the non-inverting configuration and another in the buffer configuration that feedback the output signal to the non-inverter input of the OP2 . It is known that a buffer copies the signal on its input to the output without changing its phase and magnitude (gain = 1). Of the circuit, virtually V_a = V_b and, through a voltage divider can be written as:

Now using the nodal method for point a, we get:

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

Substituting in this equation the value of V_a found in eq. 47-01.1, we have:

However, from the circuit we can find a relation between V_o and V_x.

Therefore, replacing this relation in the previous equation and after some algebraic manipulation, we get:

Note that if R₁ = R₂, the current I_o will only depend on the value of R_o (independent of the load). Therefore, this circuit behaves like a controlled current source by the input voltage V_i, that is: