In the previous installments of Cursed Circuits, we looked at two switched capacitor circuits: the voltage halver and the capacitor lowpass filter.
In today’s episode, I’d like to talk about the use of operational amplifiers to do something other than amplification: to solve analog math. Analog computing at a scale is wildly impractical because errors tend to accumulate every step along the way; nevertheless, individual techniques find a number of specialized uses, perhaps most prominently in analog-to-digital converters. Let’s have a look at how it’s done.
The following assumes familiarity with core concepts in electronic circuits and with the fundamentals of signal amplification. If you need a refresher, start with the two linked articles first.
Op-amps at a glance
Before we get to less obvious circuits, let’s start with a brief recap: operational amplifiers are to analog electronics what logic gates are to digital logic. They are simple but remarkably versatile building blocks that let you accomplish far more than appears possible at first blush.
Unfortunately, in introductory texts, their operation is often explained in confusing ways. All that an op-amp does is taking two input voltages — V in- (“inverting input”) and V in+ (“non-inverting input”) — and then outputting a voltage that’s equal to the difference between the two, amplified by a huge factor (A OL , often 100,000 or more) and then referenced to the midpoint of the supply (V mid ). You can write it the following way:
\(V_{out} = V_{mid} + (V_{in+} - V_{in-}) \cdot A_{OL}\)
That’s all the chip does. Because the gain is massive, there is a very narrow linear region near V in- = V in+ ; a difference greater than a couple of microvolts will send the output toward one of the supply rails. The chip doesn’t care about the V in- or V in+ it can’t “see” any external components you connect to it, and its internal gain can’t be changed.
To show the versatility of the component, we can have a quick look at the following circuit that you might be already familiar with — a non-inverting amplifier:
The basic non-inverting voltage amplifier.
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