Summing amplifier configuration

The idea

A summing amplifier uses an operational amplifier with negative feedback to add several input voltages. Each input connects through its own resistor to the inverting input, and a single feedback resistor connects the output back to that same input. The non-inverting input is held at zero volts, so the inverting input is a virtual earth. Because negligible current enters the ideal op-amp input, the sum of the input currents equals the current through the feedback resistor. If all input resistors are equal, the output is the negative sum of the inputs scaled by the ratio of the feedback resistance to the input resistance.

For example: With input resistors of 10 kΩ and a feedback resistor of 20 kΩ, two inputs of 1.0 V and 2.0 V give an output of −6.0 V.

What earns the marks

• Identifies the summing amplifier as an inverting op-amp configuration with several input resistors connected to the inverting input.
• States that the non-inverting input is connected to zero volts, so the inverting input is a virtual earth.
• Applies the ideal op-amp rule that negligible current enters the inverting input, so the sum of the input currents flows through the feedback resistor.
• Writes the current-balance equation in the form V₁/R₁ + V₂/R₂ + ... = −Vout/Rf, preserving the correct signs.
• Rearranges the equation to make the output voltage the subject, for example Vout = −Rf(V₁/R₁ + V₂/R₂ + ...).
• Explains that equal input resistors give an output proportional to the negative sum of the input voltages, scaled by Rf/Rin.
• Describes a practical use, such as mixing audio signals or combining sensor outputs, and notes that the output saturates if the required voltage exceeds the supply rails.
• Explains that changing an input resistor changes the weighting of that input, allowing weighted addition.

Common mistakes and how to put them right

• Omitting the negative sign in the output expression.

  Put it right by remembering that the inputs connect to the inverting terminal, so the output is inverted.

• Adding the input voltages directly without dividing by their resistances.

  Put it right by using each input current, which is the input voltage divided by its own resistor.

• Assuming the virtual earth exists without negative feedback.

  Put it right by checking that the feedback resistor connects the output to the inverting input.

• Mixing units, such as using kilo-ohms for some resistors and ohms for others.

  Put it right by converting all resistances to the same unit before calculating.

Exam tips

• Label each input current with its direction towards the inverting node, then write one current-balance equation.
• If the question gives equal input resistors, state that simplification explicitly before substituting values.
• Keep the feedback resistor symbol distinct from the input resistors so the algebra is unambiguous.
• Check the sign and the order of magnitude of your answer against the supply rails to see whether saturation is likely.