The Difference Amplifier (or Differential Amplifier)
Difference 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 difference amplifier, as the name suggests, amplifies the difference between two inputs with the gain being set by the two resistor pairs. 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:
Simulation:
Gain Derivation
The derivation of the gain equation for this amplifier involves applying Kirchoff’s Current Law (KCL) to each node. Since we assume the inputs to be at the same potential and that no current enters them, we will first solve the simplified circuit at the non-inverting input and then substitute that value into the simplified circuit at the inverting input.
Simplified Schematic
Gain Derivation
Using KCL in the direction indicated by the arrow on the bottom portion (the non-inverting input) V+ can be solved for according to the following derivation.
Solving the top portion of the circuit for Vout is shown in the following derivation.
Now, remembering the assumption that V+ and V- (the two inputs to the op-amp) are at the same potential, V+ can be substituted in to the last equation for V-. This substitution and some reorganization are the final steps in the derivation.
For the simulation, I chose to make R1=R2 and Rf=Rg. With Rf=10*R1, the gain is 10*(V2-V1). I set V2=0.5V and varied V1 from 0 to 1V, giving a difference ranging from -0.5V to 0.5V and the output ranging from -5V to 5V.