The Summing Amplifier
Summing Amplifier
Note: For this and future circuits topics I’ll be using LTSpice, which is provided free from Linear Technology here. I also recommend viewing my LTSpice Tutorial. Also, unless otherwise stated, any future discussions involving op-amps will assume an ideal op-amp. This will assume that the voltages at both inputs are at the same voltage and that no current enters either input.
The Basics
The summing amplifier is similar to the inverting amplifier, but has multiple inputs each with their own input resistor. Only three inputs are shown here, but there can be two or more (having only one input would be an inverting amplifier) and my gain equation and derivation are shown with the standard “n” inputs. The schematic and gain equation are below as well as a simple simulation. Continue reading below for more information on the derivation of the gain equation.
Schematic:
Gain Equation:
Simulations:
Sweeping V1
Sweeping V2
Sweeping V3
Gain Derivation
The derivation of the gain equation for this amplifier is very simple using Kirchoff’s Current Law (KCL). First, remember that we are considering the op-amp to be ideal, meaning that the inputs are at the same potential. With the non-inverting input grounded, this creates a virtual ground on the inverting input. Also, we assume no current enters the inputs of the op-amp. With these two assumptions, the circuit can be simplified as shown below.
Simplified Schematic
Using Kirchoff’s Current Law in the direction indicated by the arrows and treating Vgnd as zero volts results in the following derivation.
Gain Derivation
For my simulation, I selected varying values for the input resistors, resulting in a weighted sum and swept each source from 0 to 0.5 volts. The effect of the difference in resistor values is shown by how much the output varies depending on the source being swept. Since V3 is weighted more than V2, which in turn is weighted more than V1, the output varies most when V3 is swept and least when V1 is swept.