Op-Amp as summing amplifier

Op-amp as a summing amplifier

An op-amp summing amplifier produces an output equal to the sum of several input voltages. Because the op-amp is operated in the inverting mode, the output appears as the negative sum of the inputs, with each input scaled by its own gain factor. It is one of the most frequently tested linear op-amp circuits in the Karnataka 2nd PUC Electronics board exam.

In the circuit of figure 5.5.1, three input voltages $V_1$, $V_2$ and $V_3$ are applied to the inverting terminal (node A) through resistors $R_1$, $R_2$ and $R_3$. A feedback resistor $R_f$ connects the output back to node A, and the non-inverting terminal (node B) is grounded.

Treating the op-amp as ideal (open-loop gain $A = \infty$, input impedance $Z_i = \infty$), two facts follow: the bias current into the op-amp is zero ($i_b = 0$), and by the virtual-ground concept $V_B = V_A = 0$. Applying Kirchhoff's current law at node A, the total input current equals the feedback current, $i_i = i_f$, i.e.

Putting $V_A = 0$ gives the summing-amplifier output

If all resistors are equal, $R_1 = R_2 = R_3 = R_f = R$, this reduces to $V_O = -(V_1 + V_2 + V_3)$ — the output is simply the negative sum of the inputs, so the circuit is also called an op-amp inverting adder. By choosing the input resistors relative to $R_f$, each input can be given a different weight, which lets the same circuit realise a weighted sum such as $V_O = 3V_1 - 2V_2 + V_3$.

Op-amp as a subtractor (difference amplifier)

A difference amplifier, or subtractor, gives an output proportional to the difference of two input voltages. In figure 5.5.2, $V_1$ is applied through $R_1$ to the inverting terminal (node A) and $V_2$ through $R_2$ to the non-inverting terminal (node B); $R_3$ connects node B to ground and $R_f$ is the feedback resistor.

The output is found using the superposition theorem:

• With $V_1$ alone ($V_2$ grounded) the circuit behaves as an inverting amplifier, giving $V_{O1} = -\dfrac{R_f}{R_i}V_1$. …