Operational Amplifiers

Summing Amplifier

The process of adding and subtracting voltages is performed by a summing amplifier. The figure above shows an arrangement for the summation of three voltages v₁, v₂, and v₃, applied to input resistors R₁, R₂, and R₃ respectively.

The three input currents i₁, i₂, and i₃ may be equated to the current i_f through R_f

The currents are equal to

Since v_A is approximately equal to zero (the virtual ground), the currents which are added can be seen to be

The rearrangement of the equation gives

This equation tells us that each input voltage is multiplied by a gain determined by the value of its own input resistor and the common feedback resistor. In addition, each amplified input voltage is algebraically added to the other amplified input voltages. In the special case, when each resistance ratio is 1, the circuit merely algebraically adds all of the input voltages. Subtraction occur when the signs of some of the input voltages are negative. Note that the total algebraic sum of the input voltages is inverted by the operational amplifier.

Now let’s consider a few examples. Consider the summing amplifier circuit shown in the figure below. Input voltage v₁ (+5 V) will have a gain of 1/2. Input voltage v₂ (+3 V) will have a gain of 1. Input voltages of +5 V and +3 V will produce the following currents: current i₁ = 2.5 μA and i₂ = 3 μA (i.e. v₁/R₁ and v₂/R₂). The output voltage is then -i_fR_f or –5.5 V.

The circuit conditions under slightly different input voltages (v₁ = -10 V, v₂ = +3 V) are considered next. Note that current i₁ flows in the opposite direction when v₁ is negative. Under these conditions, i₁ = -5 μA and i₂ = 3 μA. The current which flows through R_f must be the sum of i₁ and i₂. This sum, -2 μA, flows through the feedback resistor and indicates an output voltage of +2 V.