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:
The inputs of the op amp don’t connect to anything internally.
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.
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.
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:
The inputs of the op amp don’t connect to anything internally.
The output mysteriously will do what it can to make the inputs equal, as far as it is physically possible.
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.
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 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.
We are all used to the op-amp, as a little black box from which we can derive an astonishingly useful range of circuit functions. But of course within it lurks a transistor circuit on a chip, and understanding the operation of that circuit can give us insights into the op-amp itself. It’s a subject [IMSAI Guy] has tackled during the lockdown, recording a set of videos explaining a simple discrete-component op-amp.
The op-amp circuit in question.
He starts with the current source, a simple circuit of two diodes, a resistor, and a transistor that sets the bias for the two-transistor differential amplifier. This is followed by a look at the output driver, and we would expect that shortly to come will be a video on the output itself. Start the series with the first episode, which we’ve placed below the break.
His style is laid-back, making it a restful watch as he builds each circuit on a breadboard and explains its operation with the aid of a multimeter. If this whets your appetite for more on simple op-amps, we looked at the first integrated circuit op-amp back in 2018.
Hardly a person hasn’t experienced the sudden, sharp discharge of static electricity, especially on a crisp winter’s day. It usually requires a touch, though, the classic example being a spark from finger to doorknob after scuffing across the carpet. But how would one measure the electrostatic charge of an object without touching it? Something like this field mill, which is capable of measuring electrostatic charge over a range of several meters, will do the trick.
We confess to not having heard of field mills before, and found [Leo Fernekes]’ video documenting his build to be very instructive. Field mills have applications in meteorology, being used to measure the electrostatic state of the atmosphere from the ground. They’ve also played a role in many a scrubbing of rocket launches, to prevent the missile from getting zapped during launch.
[Leo]’s mill works much like the commercial units: a grounded shutter rotates in front of two disc-shaped electrodes, modulating the capacitance of the system relative to the outside world. The two electrodes are fed into a series of transimpedance amplifiers, which boost the AC signal coming from them. A Hall sensor on the shutter allows sampling of the signal to be synchronized to the rotation of the shutter; this not only generates the interrupts needed to sample the sine wave output of the amplifier at its peaks and troughs, but it also measures whether the electrostatic field is positive or negative. Check out the video below for a great explanation and a good looking build with a junk-bin vibe to it.
Meteorological uses aside, we’d love to see this turned toward any of the dozens of Tesla coil builds we’ve seen. From the tiny to the absurd, this field mill should be able to easily measure any Tesla coil’s output with ease.
If you’ve got the hankering to own a lab full of high-end gear but your budget is groaning in protest, rolling your own test equipment can be a great option. Not everything the complete shop needs is appropriate for a DIY version, of course, but a programmable DC load like this one is certainly within reach of most hackers.
This build comes to us courtesy of [Scott M. Baker], who does his usual top-notch job of documenting everything. There’s a longish video below that covers everything from design to testing, while the link above is a more succinct version of events. Either way, you’ll get treated to a good description of the design basics, which is essentially an op-amp controlling the gate of a MOSFET in proportion to the voltage across a current sense resistor. The final circuit adds bells and whistles, primarily in the form of triple MOSFETS and a small DAC to control the set-point. The DAC is driven by a Raspberry Pi, which also supports either an LCD or VFD display, an ADC for reading the voltage across the sense resistor, and a web interface for controlling the load remotely. [Scott]’s testing revealed a few problems, like a small discrepancy in the actual amperage reading caused by the offset voltage of the op-amp. The MOSFETs also got a bit toasty under a full load of 100 W; a larger heatsink allows him to push the load to 200 W without releasing the smoke.
When you think of simple synths, what components come to mind? All you really need to make one is an oscillator, an amplifier, and some kind of input such that you can play different notes. Our favorite go-to for churning out square waves is probably the 40106 IC, which has six inverting Schmitt triggers, and then usually a 386 to amplify the output.
[Jule] says those momentary switches are sub-par, and will add a vibrato effect if properly wiggled while pressed. To us, the buttons looks pretty nice, and much easier to jam out with than the ones with 1/8″ diameter actuators. Plus, whenever you press multiple buttons, the additive resistance unlocks the synth’s inner R2D2 voice. We really see no downsides here.
By default, this is an eight-button synth tuned to C major. But there’s a surprise — you can plug different capacitors into a piece of header and change the octave on the fly. Check it out after the break.
Today, most of what we think of as a computer uses digital technology. But that wasn’t always the case. From slide rules to mechanical fire solution computers to electronic analog computers, there have been plenty of computers that don’t work on 1s and 0s, but on analog quantities such as angle or voltage. [Ken Shirriff] is working to restore an analog computer from around 1969 provided by [CuriousMarc]. He’ll probably write a few posts, but this month’s one focuses on the op-amps.
For an electronic analog computer, the op-amp was the main processing element. You could feed multiple voltages in to do addition, and gain works for multiplication. If you add a capacitor, you can do integration. But there’s a problem.
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.
