Summing, Difference and Real Amplifiers

Several input resistors can join the same virtual-earth node. Each supplies a current proportional to its input voltage and inversely proportional to its resistance. With negligible op-amp input current, their sum flows through the feedback resistor.

Equal input resistances give equal weights. A smaller input resistance gives that signal a larger contribution. Sum signed values before applying the overall negative sign, and check output headroom. This can combine sensor signals or mix analogue audio.

A suitably matched resistor network gives an output proportional to the difference between two inputs. This is useful when the desired measurement is a small difference riding on a larger voltage common to both leads.

The simple expression assumes the resistor ratios on the two sides are correctly matched. Common-mode rejection is imperfect if they are mismatched or the real op-amp is non-ideal. Identify the sign convention from the circuit: swapping the two signal inputs reverses the useful output.

A real op-amp has finite open-loop gain and finite input resistance, and it cannot output beyond its supply range. Its useful closed-loop gain also falls at high frequency. For a device in the usual single-dominant-pole regime, gain times bandwidth is approximately constant.

A larger required gain therefore leaves a smaller useful bandwidth. Read whether a graph shows gain as a ratio or in dB; do not multiply a dB value by frequency as though it were a linear gain. A high-frequency signal can be attenuated or distorted even if its low-frequency output prediction fits within the rails.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.