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Analog Addition

Linear equations are not always limited to a single input variable. In fact, most real-world equations involve a number of variables operating independently of each other. Fortunately, the operational amplifier is not limited to a single input signal.

Remember that the junction of Rf and Rin, which is also the input to the op amp, is a virtual ground. Therefore, we can add a second input resistor (or more) without causing any interference between input signals. The current through Rf will match the composite of all of the input currents, forcing the output voltage to reflect the combination of all input voltages and their individual coefficients. As a result, the common junction of all resistors is known as the summing junction, and the whole circuit becomes a summing amplifier.

A summing amplifier to solve Z = 2X - Y

The circuit shown to the right is designed to solve the equation Z = 2X - Y. Note that the two input resistors are not the same value; therefore each input signal has its own separate coefficient. Since Rf is necessarily common to both inputs, the coefficients must be set by selecting different input resistors for the input signals, according to the desired coefficients. Each input signal uses its own input resistor, Rin, and its own separate value of Rf/Rin to determine its coefficient. There is no interaction between input signals or resistors.

It is also possible to use multiple inputs to obtain coefficients that cannot be produced with the standard resistance values used in analog computers. For example, there is no 40k resistor (there is a 50k resistor, however). But to obtain 4X, we cannot use a single Rf and Rin to obtain this resistance ratio. What we can do, however, is to use a 20k feedback resistor and two 10k input resistors, and then apply the X signal to both inputs. The op amp will multiply X by 2 separately for each input, and then add the two signals together. This will produce a total of 4X.

There is no theoretical limit to the number of input signals that may be applied to an operational amplifier. However, as with many real-world situations, it is generally undesirable to apply more than four to six signals to a single amplifier. This is partly because too many signals can more easily cause the op amp to exceed its output voltage range, and partly because the more input resistors there are, the longer the internal wiring becomes, and longer wires can more easily pick up stray signals and electromagnetic fields. Any such stray signals will introduce errors into your results.

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