Circuit VR: Even More Op Amps

In the last Circuit VR we looked at some basic op amp circuits in a simulator, including the non-inverting amplifier. Sometimes you want an amplifier that inverts the signal. That is a 5V input results in a -5V output (or -10V if the amplifier has a gain of 2). This corresponds to a 180 degree phase shift which can be useful in amplifiers, filters, and other circuits. Let’s take a look at an example circuit simulated with falstad.

Remember the Rules

Last time I mentioned two made up rules that are good shortcuts for analyzing op amp circuits:

  1. The inputs of the op amp don’t connect to anything internally.
  2. The output mysteriously will do what it can to make the inputs equal, as far as it is physically possible.

As a corollary to the second rule, you can easily analyze the circuit shown here by thinking of the negative (inverting) terminal as a virtual ground. It isn’t connected to ground, yet in a properly configured op amp circuit it might as well be at ground potential. Why? Because the + terminal is grounded and rule #2 says the op amp will change conditions to make sure the two terminals are the same. Since it can’t influence the + terminal, it will drive the voltage through the resistor network to ensure the – terminal is at 0V.

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Remoticon Video: Basics Of RF Emissions Debugging Workshop

These days we’re surrounded by high-speed electronics and it’s no small feat that they can all play nicely in near proximity to each other. We have RF emissions standards to thank, which ensure new products don’t spew forth errant signals that would interfere with the data signals traveling through the ether. It’s long been the stuff of uber-expensive emissions testing labs, and failure to pass can leave you scratching your head. But as Alex Whittimore shows in this workshop from the 2020 Hackaday Remoticon, you can do a lot of RF emissions debugging with simple and inexpensive tools.

Professionally-made probes in several sizes
Build your own probes from magnet wire
You can get a surprisingly clear picture of what kind of RF might be coming off of a product by probing it on your own workbench. Considering the cost of the labs performing FCC and other certifications, this is a necessary skill for anyone who is designing a product headed to market — and still damn interesting for everyone else. Here you can see two examples of the probes used in the process. Although one is a pack of professional tools and other is a bit of enameled wire (magnet wire), both are essentially the same: a loop of wire on which a magnetic field will induce a very small current. Add a Low-Noise Amplifier (LNA) and you’ll be up and measuring in no-time.
I really enjoyed how Alex started his demo with “The Right WayTM” of doing things — using a proper spectrum analyzer to visualize data from the probes. But the real interesting part is “The Hacker WayTM” which leverages an RTL-SDR dongle and some open-source software to get the same job done. Primarily that means using SDRAngel and QSpectrumAnalyzer which are both included in the DragonOS_LTS which can be run inside of a virtual machine.

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Circuit VR: Some Op Amps

Circuit simulations are great because you can experiment with circuits and make changes with almost no effort. In Circuit VR, we look at circuits using a simulator to do experiments without having to heat up a soldering iron or turn on a bench supply. This time, we are going to take a bite of a big topic: op amps.

The op amp — short for operational amplifier — is a packaged differential amplifier. The ideal op amp — which we can’t get — has infinite gain and infinite input impedance. While we can’t get that in real life, modern devices are good enough that we can pretend like it is true most of the time.

Op-amp schematic symbol
a very simple op amp circuit with some detail omitted

If you open this circuit in the Falstad simulator, you’ll see two sliders to the right where you can tweak the input voltage. If you make the voltages the same, the output will be zero volts. You might think that a difference amplifier would take inputs of 1.6V and 2.4V and either produce 0.8V or -0.8V, but that’s not true. Try it. Depending on which input you set to 2.4V, you’ll get either 15V or -15V on the output. That’s the infinite gain. Any positive or negative output voltage will quickly “hit the rail” or the supply voltage which, in this case, is +/-15V.

Practical Concerns

The biggest omitted detail in the schematic symbol above is that there’s no power supply here, but you can guess that it is +/- 15V. Op amps usually have two supplies, a positive and a negative and while they don’t have to be the same magnitude, they often are. Some op amps are specifically made to work with a single-ended supply so their negative supply can connect to ground. Of course, that presupposes that you don’t need a negative voltage output.

The amount of time it takes the output to switch is the slew rate and you’ll usually find this number on the device datasheet. Obviously, for high-speed applications, a fast slew rate is important, particularly if you want to use the circuit as a comparator as we are here.

Other practical problems arise because the op amp isn’t really perfect. A real op amp would not hit the 15V rail exactly. It will get close depending on how much current you draw from the output. The higher the current, the further away from the rails you get. Op amps will also have some offset that will prevent it from hitting zero when the inputs are equal, although on modern devices that can be very low. Some older devices or those used in high-precision designs will have a terminal to allow you to trim the zero point exactly using an external resistor.

Op Amps Can Provide Steady Voltage Under Variable Load

Rather than dig through a lot of math, you can deal with nearly all op amp circuits if you remember two simple rules:

  1. The inputs of the op amp don’t connect to anything internally.
  2. The output mysteriously will do what it can to make the inputs equal, as far as it is physically possible.
Op amp with inverting input connected to output
1x amplifier

That second rule will make more sense in a minute, but we already see it in action. Set the simulator so the – input (the inverting input) is at 0V and the noninverting input (+) is at 4V. The output should be 15V. The output is trying to make the inverting input match the noninverting one, but it can’t because there is no connection. The output would like to provide an infinite amount of voltage, but it can only go up to the rail which is 15V.

We can exploit this to make a pretty good x1 amplifier by simply shorting the output to the – terminal. Remember, our rules say the input terminals appear to not connect to anything, so it can’t hurt. Now the amplifier will output whatever voltage we put into it:

You might wonder why this would be interesting. Well, we will learn how to increase the gain, but you actually see this circuit often enough because the input impedance is very high (infinite in theory, but not practice). And the output impedance is very low which means you can draw more current without disturbing the output voltage much.

Voltage divider with and without 1x amplifier
Comparing voltage divider performance with and without a 1x amplifier

This circuit demonstrates the power of a 1x amplifier. Both voltage dividers produce 2.5V with no load. However, with a 100 ohm load at the output, the voltage divider can only provide around 400mV. You’d have to account for the loading in the voltage divider design and if the load was variable, it wouldn’t be possible to pick a single resistor that worked in all cases. However, the top divider feeds the high impedance input of the op amp which then provides a “stiff” 2.5V to whatever load you provide. As an example, try changing the load resistors from 100 ohms to different values. The bottom load voltage will swing wildly, but the top one will stay at 2.5V.

Don’t forget there are practical limits that won’t hold up in real life. For example, you could set the load resistance to 0.1 ohms. The simulator will dutifully show the op amp sourcing 25A of current through the load. Your garden-variety op amp won’t be able to do that, nor are you likely to have the power supply to support it if it did.

What’s Being Amplified?

This is an amplifier even though the voltage stayed the same. You are amplifying current and, thus, power. Disconnect the bottom voltage divider (just delete the long wire) and you’ll see that the 5V supply is providing 12.5 mW of power. The output power is 62.5 mW and, of course, varies with the load resistor.

Notice how this circuit fits the second rule, though. When the input changes, the op amp makes its output equal because that’s what makes the + and – terminals stay at the same voltage.

Of course, we usually want a higher voltage when we amplify. We can do that by building a voltage divider in the feedback loop. If we put a 1:2 voltage divider in the loop, the output will have to double to match the input and, as long as that’s physically possible, that’s what it will do. Obviously, if you put in 12V it won’t be able to produce 24V on a 15V supply, so be reasonable.

Non-inverting opamp circuit
Non-inverting amplifier example

This type of configuration is called a non-inverting amplifier because, unlike an inverting amplifier, an increase in the input voltage causes an increase in the output voltage and a decrease in input causes the output to follow.

Note that the feedback voltage divider isn’t drawn like a divider, but that’s just moving symbols on paper. It is still a voltage divider just like in the earlier example. Can you figure the voltage gain of the stage? The voltage divider ratio is 1:3 and, sure enough, a 5V peak on input turns into a 15V peak on the output, so the gain is 3. Try changing the divider to different ratios.

What’s Next?

While it isn’t mathematically rigorous, thinking of the op amp as a machine that makes its inputs equal is surprisingly effective. It certainly made the analysis of these simple circuits, the comparator, the buffer amplifier, and a general non-inverting amplifier simple.

There are, of course, many other types of amplifiers, as well as other reasons to use op amps such as oscillators, filters, and other even more exotic circuits. We’ll talk about some of them next time and the idea of a virtual ground, which is another helpful analysis rule of thumb.

Remoticon Video: How To Reverse Engineer A PCB

You hold in your hand a circuit board from a product you didn’t make. How does the thing work? What a daunting question, but it’s both solvable and approachable if you know what you’re doing. The good news is that Eric Schlaepfer knows exactly what he’s doing and boiled down the process of reverse engineering printed circuit boards into this excellent workshop. It was presented live during the 2020 Hackaday Remoticon, and the edited video, which you’ll find below, was just published. Slides for the talk have been published on the workshop project page.

Need proof that he has skills that we all want? Last year Eric successfully reverse-engineered the legendary Sound Blaster audio card and produced his own fully-functional drop-in replacement called the Snark Barker. And then re-engineered it to work with the ancient MCA bus architecture. Whoa.

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DSP Spreadsheet: The Goertzel Algorithm Is Fourier’s Simpler Cousin

You probably have at least a nodding familiarity with the Fourier transform, a mathematical process for transforming a time-domain signal into a frequency domain signal. In particular, for computers, we don’t really have a nice equation so we use the discrete version of the transform which takes a series of measurements at regular intervals. If you need to understand the entire frequency spectrum of a signal or you want to filter portions of the signal, this is definitely the tool for the job. However, sometimes it is more than you need.

For example, consider tuning a guitar string. You only need to know if one frequency is present or if it isn’t. If you are decoding TouchTones, you only need to know if two of eight frequencies are present. You don’t care about anything else.

A Fourier transform can do either of those jobs. But if you go that route you are going to do a lot of math to compute things you don’t care about just so you can pick out the one or two pieces you do care about. That’s the idea behind the Goertzel. It is essentially a fast Fourier transform algorithm stripped down to compute just one frequency band of interest.  The math is much easier and you can usually implement it faster and smaller than a full transform, even on small CPUs.

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Local And Remote Debugging With GDB

As a debugger, GDB is a veritable Swiss Army knife. And just like exploring all of the non-obvious uses of a those knives, your initial response to the scope of GDB’s feature set is likely to be one of bewilderment, subsequent confusion, and occasional laughter. This is an understandable reaction in the case of the Swiss Army knife as one is unlikely to be in the midst of an army campaign or trapped in the wilderness. Similarly, it takes a tricky debugging session to really learn to appreciate GDB’s feature set.

If you have already used GDB to debug some code, it was likely wrapped in the comfort blanket of an IDE. This is of course one way to use GDB, but limits the available features to what the IDE exposes. Fortunately, the command line interface (CLI) of GDB has no such limitations. Learning the CLI GDB commands also has the advantage that one can perform that critical remote debug session even in the field via an SSH session over the 9600 baud satellite modem inside your Swiss Army knife, Cyber Edition.

Have I carried this analogy too far? Probably. But learning the full potential of GDB is well worth your time so today, let’s dive in to sharpen our digital toolsets.

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Axe Hacks: Spinning Knobs And Flipping Switches

From a guitar hacking point of view, the two major parts that are interesting to us are the pickups and the volume/tone control circuit that lets you adjust the sound while playing. Today, I’ll get into the latter part and take a close look at the components involved — potentiometers, switches, and a few other passive components — and show how they function, what alternative options we have, and how we can re-purpose them altogether.

In that sense, it’s time to heat up the soldering iron, get out the screwdriver, and take off that pick guard / open up that back cover and continue our quest for new electric guitar sounds. And if the thought of that sounds uncomfortable, skip the soldering iron and grab some alligator clips and a breadboard. It may not be the ideal environment, but it’ll work.

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