The Adder Subtractor, shown in the following schematic, does what its name implies. It adds and subtracts the input voltages from one another to produce an output voltage. You can think of it as a differential amplifier with multiple input resistors or a mash-up of inverting and non-inverting summing amplifiers.
Intuitive Look
The circuit configuration can be intuitively understood by looking at what happens when most of the inputs are removed. The following schematic indicates what happens when all but one of the inputs, in this case Vn1, is an open circuit.
In this case, the circuit becomes a simple inverting amplifier configuration whose gain is set by the ratio of RnF and Rn1. The value of RpF really doesn’t come into play due to the extremely small current into (or out of) the op-amp’s non-inverting input.
In the configuration above the output will have the opposite polarity of the input due to the inverting op-amp configuration. The figure below depicts how the Adder Subtractor is able to operate in a non-inverting configuration. In this case, one of the “Vn” inputs is shown connected to ground. This is a reasonable assumption assuming it is driven by another op-amp or relatively low impedance source.
In the configuration shown above, the Adder Subtractor acts like a non-inverting input whose gain is dictated by the ratio of RnF and Rn1. In this case the non-inverting input is amplifying the voltage divided input (due to Rp1 and RpF) of Vp1. Note that if the values of RnF and Rn1 are the same the amplifier has a gain of 2. If RpF and Rp1 are the same the input at Vp1 is divided in half. The net effect is the output, Vout, has the same value as the input at Vp1.
Messy Math and Interacting Values
Setting the individual gains for this circuit can be messy for a number of reasons, not least of which is the fact that the gain applied to the non-inverting sections is influenced by the resistor values in the inverting sections. Compound this by the number of resistor values and reaching a solution can be a bit tedious. There are design procedures available which are simplified by the addition of a resistor to ground in the “Rn” section. Those procedures are outside of the scope of this article. The most straightforward, and reliable, way to proceed is to make all of the resistor values the same. When all resistor values are the same, the output is given by the sum and difference of the inputs as given in the following equation.
Vout = Vp1 + Vp2 + … + Vpn - Vn1 - Vn2 - … - Vnn