Question

An op-amp adder sums voltages using

• A. Voltage divider
• B. Series connection of resistors
• C. Inverting configuration
• D. Differential pair

Hint:

The presence of a virtual ground in the inverting configuration isolates each input channel from the others. This ensures that changing the voltage or resistance of one branch has absolutely no cross-talk impact on the currents flowing through the other input branches.

Answer 1

The Correct Option is C

Concept: An operational amplifier summing amplifier (or adder) is designed to take multiple separate input voltages, scale each individual input according to its corresponding resistor value, and produce an output voltage proportional to the algebraic sum of those inputs. The circuit is constructed directly on an inverting configuration framework. In this arrangement:
• The non-inverting terminal (\(+\)) is tied directly to the circuit ground (\(0\text{ V}\)).
• Due to the operational amplifier's extremely high open-loop gain, a property known as a virtual ground is established at the inverting input terminal (\(-\)). Therefore, the potential at the node joining all input resistors is kept nearly equal to \(0\text{ V}\). Let multiple input voltages \(V_1, V_2, \dots, V_n\) be connected via independent input resistors \(R_1, R_2, \dots, R_n\) to this virtual ground node. According to Kirchhoff's Current Law (KCL) applied at the inverting node: \[ I_1 + I_2 + \dots + I_n + I_f = 0 \] Since the input impedance of an ideal operational amplifier is infinite, no signal current enters the inverting terminal itself. Thus, all currents combined must exit through the feedback path resistor \(R_f\): \[ \frac{V_1 - 0}{R_1} + \frac{V_2 - 0}{R_2} + \dots + \frac{V_n - 0}{R_n} + \frac{V_{\text{out}} - 0}{R_f} = 0 \] Isolating the output voltage \(V_{\text{out}}\) mathematically: \[ V_{\text{out}} = -R_f \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \dots + \frac{V_n}{R_n} \right) \] If all resistor values are set identically such that \(R_1 = R_2 = \dots = R_n = R_f\), the expression simplifies perfectly to: \[ V_{\text{out}} = -(V_1 + V_2 + \dots + V_n) \] This expression is the explicit inversion of the sum of inputs, proving that the adder relies explicitly on the properties of the inverting configuration.