Summing amplifier

A summing amplifier combines several input voltages to produce one output voltage. It uses an inverting operational-amplifier circuit: each input voltage is connected to the inverting input through its own resistor, while a feedback resistor connects the output to the inverting input.

The non-inverting input is held at zero potential. Negative feedback keeps the inverting input approximately at zero potential too. This point is called a virtual earth: it is at approximately zero potential, although it is not directly connected to earth.

Combining the input currents

Because the inverting input is at approximately zero potential, the current supplied by input $$$V_i$$$ through its resistor $$$R_i$$$ is approximately $$$V_i/R_i$$$ . For an ideal amplifier, negligible current enters the amplifier input. The input currents therefore combine and flow through the feedback resistor $R_{\mathrm{f}}$ .

The resulting output voltage is:

V_{\mathrm{out}}=-R_{\mathrm{f}}\left(\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}+\ldots\right)

Each input contributes $-R_{\mathrm{f}}V_i/R_i$ to the output. Its contribution is therefore weighted by the ratio of the feedback resistance to its own input resistance: for the same input voltage, a smaller input resistance produces a larger contribution. The minus sign indicates inversion of the weighted sum.

If all the input resistances equal the feedback resistance, each input has the same weight and the output is the negative of the sum of the input voltages.

Difference amplifier

A difference amplifier produces an output determined by how far apart two input voltages are. It uses an operational amplifier and a matched network of resistors: one signal is applied through the inverting side and the other through the non-inverting side.

The resistor network is matched when the ratio of feedback resistance to input resistance on the inverting side equals the corresponding resistor ratio on the non-inverting side. This matching allows the circuit to amplify the difference between the signals rather than their shared voltage.

Here, $$$V_+$$$ and $$$V_-$$$ are the signals applied to the non-inverting and inverting sides respectively. They represent the external input signals, not necessarily the voltages directly at the operational amplifier’s input terminals. The resistance $R_{\mathrm{f}}$ is the feedback resistance and $$$R_l$$$ is the input resistance.

The ratio $R_{\mathrm{f}}/R_l$ is the gain for the voltage difference. For example, if the ratio is 2, the output is twice the difference between the input signals.

If the signals are equal, their difference is zero, so the ideal output is zero. If $$$V_+$$$ is larger than $$$V_-$$$ , the output is positive; if $$$V_-$$$ is larger, the output is negative. Reversing which signal is larger therefore reverses the output polarity.