Single OpAmp Window Comparators

A recent question on the Electrical Engineering Stack Exchange site got me thinking about some interesting window comparator circuits. Here’s how to detect three different input voltage levels with just one op-amp!

References and additional reading:

Description Reference
Simplified window comparators Applications of Operational Amplifiers, Third-Generation Techniques, Jerald G. Graeme, Chapter 4.1.2
Tri Level Voltage Detector LVM821 Datasheet, Texas Instruments, Section 8.2.3

The RC Filter Transfer Function

Most people are familiar with the simple first-order RC low pass filter:

RC Low Pass Filter

Also well known is the equation for calculating the -3dB (aka, half-power) cutoff frequency of the RC low pass filter:

\(
\begin{equation}
\mathbf{f}_{c} = \frac{1}{2 \pi RC}\\
\end{equation}
\)

It’s an easy equation to memorize, but if you’re interested in where this equation comes from, read on; if you’re familiar with resistor voltage dividers, this will be a piece of cake!

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