There comes a time in every electronic designer’s life when, whether they know it or not, they need an analog filter in their design. If you’re coming from a digital background, where everything is nice and numeric, the harsh reality of continuous voltages can be a bit of a shock. But if you’re taking input from, or sending output to the big analog world out there, it pays to at least think about the frequency-domain properties of the signal, and maybe even do something about them.
Designing an analog filter to fit your needs can be a bit of a daunting task: there are many factors that you’re going to need to consider, and they all interact. It’s easy to get lost. We’re going to simplify this as much as possible by instead focusing on a few common applications and building up the simplest possible filters that work well for them.
Today, we’re going to consider the lowpass filter, and specifically a Sallen-Key filter with Butterworth characteristics and a second-order rolloff. Sound like word salad? We’ll fix that up right away, because this is probably the single most important filter to have in your analog toolbox for two very common use cases: pulse-width modulated (PWM) output and analog-to-digital conversion (ADC) input.
There is an old saying: “In theory, theory and practice are the same. In practice, they are not.” We spend our time drawing on paper or a computer screen, perfect wires, ideal resistors, and flawless waveforms. Alas, the real world is not so kind. Components have all kinds of nasty parasitic effects and no signal looks like it does in the pages of a text book.
Consider the following problem. You have a sine wave input coming in that varies between 0 V and 5 V. You want to convert it to a square wave that is high when the sine wave is over 2.5 V. Simple, right? You could use a CMOS logic gate or a comparator. In theory…
The problem is, the sine wave isn’t perfect. And the other components will have little issues. If you’ve ever tried this in real life, you’ll find that when the sine wave is right at the 2.5 V mark the output will probably swing back and forth before it settles down. This is exacerbated by any noise or stretching in the sine wave. You will wind up with something like this:
Notice how the edges of the square wave are a bit fat? That’s the output switching rapidly back and forth right at the comparator’s threshold.
Hysteresis
The answer is to not set the threshold at 2.5 V, or any other single value. Instead, impose a range outside of which it will switch, switching low when it leaves the low end of the range, and high when it exceeds the high end. That is, you want to introduce hysteresis. For example, if the 0 to 1 shift occurs at, say, 1.9 V and the 1 to 0 switch is at 0.5 V, you’ll get a clean signal because once a 0 to 1 transition happens at 1.9 V, it’ll take a lot of noise to flip it all the way back below 0.5 V.
You see the same effect in temperature controllers, for example. If you have a heater and a thermal probe, you can’t easily set a 100 degree set point by turning the heater off right away when you reach 100 and then back on again at 99.9999. You will usually use hysteresis in this case, too (if not something more sophisticated like a PID). You might turn the heater off at 99 degrees and back on again at 95 degrees, for example. Indeed, your thermostat at home is a prime example of a system with hysteresis — it has a dead-band of a few degrees so that it’s not constantly turning itself on and off.
Schmitt Triggers and How to Get One
A Schmitt Trigger is basically a comparator with hysteresis. Instead of comparing the incoming voltage with VCC / 2, as a simple comparator would, it incorporates a dead band to ensure that logic-level transitions occur only once even in the presence of a noisy input signal.
Assuming you want a Schmitt trigger in a circuit, you have plenty of options. There are ICs like the 74HC14 that include six (inverting) Schmitt triggers. On a schematic, each gate is represented by one of the symbols to the right; the little mark in the box is the hysteresis curve, and the little bubble on the output indicates logical negation when it’s an inverter.
You can also make them yourself out of transistors or even a 555 chip. But the easiest way by far is to introduce some feedback into a plain op amp comparator circuit.
Below are two op amps, one with some positive feedback to make it act like a Schmitt trigger. The other is just a plain comparator. You can simulate the design online.
If you haven’t analyzed many op amp circuits, this is a good one to try. First, imagine an op amp has the following characteristics:
The inputs are totally open.
The output will do whatever it takes to make the inputs voltages the same, up to the power supply rails.
Neither of these are totally true (theory vs. practice, again), but they are close enough.
The comparator on the right doesn’t load the inputs at all, because the input pins are open circuit, and the output swings to either 0 V or 5 V to try, unsuccessfully, to make the inputs match. It can’t change the inputs because there is no feedback, but it does make a fine comparator. The voltage divider on the + pin provides a reference voltage. Anything under that voltage will swing the output one way. Over the voltage will swing it the other way. If the voltages are exactly the same? That’s one reason you need hysteresis.
The comparator’s voltage divider sets the + pin to 1/2 the supply voltage (2.5 V). Look at the Schmitt trigger (on top). If the output goes between 0 V and 5 V, then the voltage divider winds up with either the top or bottom resistor in parallel with the 10K feedback resistor. That is, the feedback resistor will either be connected to 5 V or ground.
Of course, two 10K resistors in parallel will effectively be 5K. So the voltage divider will be either 5000/15000 (1/3) or 10000/15000 (2/3) depending on the state of the output. Given the 5 V input to the divider, the threshold will be 5/3 V (1.67 V) or 10/3 V (3.33 V). You can, of course, alter the thresholds by changing the resistor values appropriately.
Practical Applications
Schmitt triggers are used in many applications where a noisy signal requires squaring up. Noisy sensors, like an IR sensor for example, can benefit from a Schmitt trigger. In addition, the defined output for all voltage ranges makes it handy when you are trying to “read” a capacitor being charged and discharged. You can use that principle to make a Schmitt trigger into an oscillator or use it to debounce switches.
If you want to see a practical project that uses a 555-based Schmitt, check out this light sensor. The Schmitt trigger is just one tool used to fight the imprecision of the real world and real components. Indeed, they’re nearly essential any time you want to directly convert an analog signal into a one-bit, on-off digital representation.
DC to DC conversion has come a long way. What was once took an electromechanical vibrator and transformer has been reduced to a PC board the size of a largish postage stamp that can be had for a couple of bucks on eBay. So why roll your own buck-boost converter for the ground up? Maybe because sometimes the best way to learn is by doing.
Hearing aids are probably more high-tech than you think. They are tiny. They have to go through a lot of trouble to prevent feedback. They need a long battery life. The good ones match their amplification to the inverse of your hearing loss (amplifying only the bands where you don’t hear as well).
[NotionSunday] put together a hearing amplifier project that probably doesn’t hit many of those design criteria. However, thanks to a 3D printed case, it looks pretty good. The device uses a dual opamp to boost the output from two microphones and feeds it to a conventional headphone.
When a job can be handled with a microcontroller, [devttys0] likes to buck the trend and build a circuit that requires no coding. Such was the case with this “Clapper”-inspired faux-AI light controller, which ends up being a great lesson in analog design.
The goal was to create a poor man’s JARVIS – something to turn the workshop lights on with a free-form vocal command. Or, at least to make it look that way. This is an all-analog circuit with a couple of op amps and a pair of comparators, so it can’t actually process what’s being said. “Aziz! Light!” will work just as well as any other phrase since the circuit triggers on the amplitude and duration of the spoken command. The AI-lite effect comes from the clever use of the comparators, RC networks to control delays, and what amounts to an AND gate built of discrete MOSFETs. The end result is a circuit that waits until you finish talking to trigger the lights, making it seems like it’s actually analyzing what you say.
We always enjoy [devttys0]’s videos because they’re great lessons in circuit design. From block diagram to finished prototype, everything is presented in logical steps, and there’s always something to learn. His analog circuits that demonstrate math concepts was a real eye-opener for us. And if you want some background on the height of 1980s AI tech that inspired this build, check out the guts of the original “Clapper”.
In order to help his friend prepare for a talk at DEFCON this weekend, [Craig] built an IR photodiode amplifier circuit. The circuit extended the detection range of the hack from a few inches to a few feet. We’re suckers for some well-designed analog circuitry, and if you are too, be sure to check out the video embedded below.
In the first article about measurement systems we looked at sensors as a way to bring data into a measurement system. I explained that a sensor measures physical quantities which are turned into a voltage with a variable conversion element such as a resistor bridge. There will always be noise in any system, and an operational amplifier (op-amp) can be used to remove some of that noise. The example we considered used an op-amp in a differential configuration that removes any disturbance signal that is common to both inputs of the op-amp.
But that single application of an op-amp is just skimming the surface of the process of bringing a real-world measurement of a physical quantity into a digital system. Often, you’ll need to do more work on the signal before it’s ready for sampling with a digital-to-analog converter. Signal conditioning with amplifiers is a deep and rich topic, so let me make it clear that that this article will not cover every aspect of designing and implementing a measurement system. Instead, I’m aiming to get you started without getting too technical and math-y. Let’s just relax and ponder amplifiers without getting lost in detail. Doesn’t that sound nice?
