ECE101 – Basic Electrical and Computer Engineering

Inverting 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 inverting amplifier consists only of an op-amp and two resistors.  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 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 arrow and treating Vgnd as zero volts results in the following derivation.

Gain Derivation

As you can see in my simulation, I chose Rf=1Meg and Ri=100k (Mega must be entered as Meg) giving me a gain of 10.  My simulation sweeps the input from 0 to 100mV and the output is shown to go from 0 to -1V as would be expected.