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That "operational amplifiers" that could perform operations such as addition, subtraction, integration, were useful for voltage-based analogue computers (that were invented in the 1930s, and the "op amp" invented in 1940s) makes perfect sense to me. But, society has progressed since then. Are "operational amplifiers" still an important tool, or are they more interesting historically just like vacuum tubes are mostly historically interesting although they are still used in very niche cases still?

Context, the term “operational amplifier” itself was coined by John Ragazzini in 1947 for work towards better analogue computers. The device itself was designed for that and optimized for that. Computers use logical operations, and that makes perfect sense. The niche of analogue computers was displaced by digital computers. But the niche of “op amps” was not as it seems. I am interested in why, and asking about what their niche is mostly these days.

The inventor Raggazini was very specific with the use of his device. He wrote in 1947 "it is a simple matter to assemble the particular circuit for any system of equations for which solutions are desired" and "a method for obtaining an engineering solution for integrodifferential equations of physical systems using an electronic system" and "as an amplifier so connected can perform the mathematical operations of arithmetic and calculus on the voltages applied to its input, it is hereafter termed an "operational amplifier". So surely it was invented to calculate the solution to equations. And this makes sense to me. But why they are still so important, is what I am interested in, since they were clearly designed and optimized for something that must have been replaced mostly with digital computation. I was assuming modern uses are either for actual calculations, like their original use was (why they were invented, see Raggazini, 1947), or, that they had a property needed for the calculations that was also ideal for something else. Since this is generally how evolution, incl. technological evolution, works: co-optation.

Reference

J. R. Ragazzini, R. H. Randall and F. A. Russell, "Analysis of Problems in Dynamics by Electronic Circuits," in Proceedings of the IRE, vol. 35, no. 5, pp. 444-452, May 1947, doi: 10.1109/JRPROC.1947.232616.

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    \$\begingroup\$ Operational amplifiers are widely used in analog electronics. I'd consider performing arithmetics with it much less common and rather esoteric application. \$\endgroup\$
    – Eugene Sh.
    Nov 15, 2021 at 21:55
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    \$\begingroup\$ They excel at filters and amplifiers. They work so well because they provide much more ideal parameters than doing something with a few transistors. \$\endgroup\$
    – Aaron
    Nov 15, 2021 at 22:01
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    \$\begingroup\$ An op-amp was literally an amplifier to do operations with. It still is. For example as mundane task as amplifying audio is just using an op-amp to multiply incoming weak signal by a constant. \$\endgroup\$
    – Justme
    Nov 15, 2021 at 22:08
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    \$\begingroup\$ They say there are no bad questions. I think "they" are wrong. What "society progress" has to do with electronic components and how it makes "addition, subtraction, integration" tasks disappear? No amount of wokeness will make hammers obsolete. Zero research effort. \$\endgroup\$
    – Maple
    Nov 15, 2021 at 22:09
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    \$\begingroup\$ "digital computer revolution" was not social progress, it was technological. You seem to have made a lot of effort to justify your question, instead of very tiny effort required to find the uses for operational amplifiers. This is called "trolling", not "curiosity" \$\endgroup\$
    – Maple
    Nov 15, 2021 at 22:19

7 Answers 7

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An alternative view is that analog computers haven't disappeared; they have simply become so ubiquitous we no longer notice them.

If you need a gain of 4 between a sensor and an ADC, you no longer design a transistor circuit to provide a gain of 4; you simply throw in an analog computer "programmed" by external resistors to multiply its input by 4 : job done, with no regrets about using such a powerful machine for such a trivial task.

The same has happened to digital computers : if you want to control a motor or even just blink a light, you may simply throw in a PIC or AVR with a trivial program and think nothing more about it.

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  • \$\begingroup\$ ah good view. Have understood op amps technically now, and a diff amp, and ability to connect output to input, and throw in resistors that differ by 4, is, I guess, necessary to multiply a signal by 4, minimal components needed, and that seems go be what defines ”op amp” at most minimal scale. a diff amp pretty much, plus combined with a different voltage source to output regulated by diff amp output. \$\endgroup\$
    – Doge
    Nov 17, 2021 at 19:40
  • \$\begingroup\$ basically after creating what is needed to multiply signal x times, you have an ”op amp” (no?) but same thing can also do other things. \$\endgroup\$
    – Doge
    Nov 17, 2021 at 19:56
  • \$\begingroup\$ No : after you have given it a gain of X, you have an amplifier with a gain of X. The opamp is the component at the heart of it; a block of pure gain with infinite input impedance (well, approximately!) uncommitted to actual gain, integration, differentiating, filtering, etc. Like a PIC before you program it. \$\endgroup\$
    – user16324
    Nov 17, 2021 at 21:01
  • \$\begingroup\$ yes but making another type of amplifier with gain X, the op amp seems to be the minimal components needed to sense how much to gain input, but I might misunderstand that. seemed to explain why it is so important for that particular use case, that diff amp + output fed back was minimum to "know" that \$\endgroup\$
    – Doge
    Nov 17, 2021 at 21:06
  • \$\begingroup\$ The opamp itself has no feedback (just as the PIC you buy has no program). You add the feedback (usually negative, but positive in an oscillator) as part of the programming that defines its function. The bare chip is the opamp : the circuit with NFB defined by R,C etc is what I would call a (possibly trivial) analog computer. (The autohelm on my boat is a PID controller implemented on an LM324) \$\endgroup\$
    – user16324
    Nov 17, 2021 at 21:11
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Here are some applications I've seen in the past year just off the top of my head:

Current sense amplifiers, A/D input buffering, active filtering, DAC output buffering, transimpedance amplifiers for photodiodes, summing amplifiers, differential amplifiers, level shifters and scaling amplifiers, integrators, differentiators, general purpose signal buffering/amplifying, all kinds of audio amplification or pre-amplification, communications processing, voltage reference or artificial ground buffering, oscillators, and analog servo or control systems.

I'm sure there are some I'm leaving out, but you can see that they're not as niche as vacuum tubes (valves).

What are the alternatives to op-amps in these applications? You could possibly do some of this digitally with a microcontroller/DSP with built-in A/D (which would likely have an internal amplifier for the A/D) but could be 10x the cost of the op-amp. You could also build an amplifier from discrete transistors, at 10X the effort and complexity (and probably worse performance) than using an op-amp.

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    \$\begingroup\$ Anything that requires negative feedback really. They are basically negative-feedback pre-packaged for you. \$\endgroup\$
    – DKNguyen
    Nov 15, 2021 at 22:15
  • \$\begingroup\$ @DKNguyen Good way to look at it. I also like to think of it as a pre-packaged transfer function of Vin(differential) times A/(1+st), where A is large, at least for dominant-pole compensated amplifiers. \$\endgroup\$
    – John D
    Nov 15, 2021 at 22:31
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    \$\begingroup\$ You might be a little too optimistic about emulating an op-amp using discretes. ;-) Accurate temperature compensation is next to impossible without the transistors being right next to each other on the same die, and the offset is also nearly guaranteed to be higher with discretes (without lots of part binning and intricate trimming). \$\endgroup\$
    – TooTea
    Nov 16, 2021 at 8:07
  • \$\begingroup\$ @TooTea Sure, but it’s possible. Philbrick did it for years before monolithic op-amps were available. And depending on the application you may not need tight specs. But my point was it’s not something you normally want to do when you can get a high performance op-amp for very little cost. \$\endgroup\$
    – John D
    Nov 16, 2021 at 12:26
  • \$\begingroup\$ @TooTea For me as a noob, the economic/manufacturing point of view, that it could be done using less functionality but is not really cheaper, is really good explanation. Op amps are a general purpose component, here was another person who found it a bit hard to see just why they were so popular, electronics.stackexchange.com/a/182773. I now looked a bit more at what op amps consist of, and combining a differential amplifier with ability to recursively increase or decrease an input, seems like pretty smart basis for lots of things, if(x<b) x++. \$\endgroup\$
    – Doge
    Nov 16, 2021 at 23:04
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One indication that the premise is incorrect is that the number of individual models of op-amps has proliferated far beyond what was available in (say) 1970. Also, if you look at what is available in inventory as a proxy for sales, some models such as LM324 or OPA363 are available off-the-shelf in quantities well over \$10^6\$ units, even in North America. There are over 10,000 variations (which include packaging and temperature range and grade minor variations) at Digikey, for example.

In 1970 there were likely closer to 1/50 of the variations available, and the performance was not as good as now.

Op-amps are so commonly required in conjunction with MCUs that some include a crude CMOS op-amp or two on the chip. Any kind of precision measurement or control equipment will likely have a number of op-amps.

That said, high-volume consumer and such like applications tend to have mixed signal ASICs developed that absorb the analog circuitry into the chip, for example signal conditioning and ADC chips for weigh scales, temperature sensors, controllers for motion detector lamps and such like. Invariably they have inferior performance in one way or another to what is possible with discrete op-amps but they are good enough for many practical applications, so there is a grain of truth in your premise.

The total market breadth has expanded so much that I suspect there is a large net gain both in units and in dollars, but unfortunately such information is not easily available for free (for ~$4,000 US you can buy a report that is limited to a few well-known suppliers and does not cover all markets). You certainly have an embarrassment of riches when you go looking for an amplifier for a given task.

They are generally not used as analog computers- they are used for signal conditioning (filtering, amplification, anti-alias filtering prior to digitizing, reconstruction filtering post conversion from digital to analog, buffering, and so on). Those functions generally have to be done in the analog domain so there is no way to absorb them into digital processing, even if the latter is practical.

There's a (perhaps weak) analogy with logic chips where small-scale logic chips such as gates and buffers are extremely widely used but more complex functions such as ALUs have limited applications and thus availability because nobody is building processors from MSI logic anymore. But if you want 3.8 million NAND gate chips off the shelf, no problem. There are more logic families available, but unlike op-amps, not so much in the way of variations, because analog is like that.

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    \$\begingroup\$ I guess if I rephrase it a bit: are they popular because of their property to be able to do numerical calculations, as they were originally designed for by John Ragazzini in 1947 who also coined their name in 1947, or, did they have some other property, necessary for but unrelated to the calculation ability, that was "co-opted" to be really useful? Do you understand how I mean? A device that produced exact numerical calculations must have had very different constraints than just a standard amplifier for just amplifying signals. \$\endgroup\$
    – Doge
    Nov 15, 2021 at 23:02
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    \$\begingroup\$ @Doge That property is high but poorly controlled gain combined with negative feedback which reduces the gain to a known and well controlled value dominated by the components in the circuit rather than the gain of the actual opamp itself. Because it's tough to make transistors with well-controlled gains, but it is easy to just make transistors with gains that are a very large but loose number. \$\endgroup\$
    – DKNguyen
    Nov 15, 2021 at 23:03
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    \$\begingroup\$ The property is that they can deal with signals precisely- low DC error, low distortion, low amplification errors and so on. We need to deal with signals precisely fairly often, either for measurement or because distortion affects the signal in unacceptable ways. As DK says, the feedback, precision differential inputs and enormous open-loop gain make all that possible. The low offset is important in many applications- it's part of the reason why Norton amplifiers (eg. LM3900) never really caught on. \$\endgroup\$ Nov 15, 2021 at 23:04
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    \$\begingroup\$ @DKNguyen That sounds like something like what I am looking for. I like to learn using the big picture. And being able to isolate what "operational amplifiers" are used for, vs what they were invented for, seems like easiest way to dissect that concept. \$\endgroup\$
    – Doge
    Nov 15, 2021 at 23:04
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    \$\begingroup\$ Doing calculations is not necessarily easy with op-amps. For example, Vout = V1*V2, cannot be done with just op-amps and resistors. \$\endgroup\$ Nov 15, 2021 at 23:19
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As mentioned in Spehro Pefhany's answer, high volume electronic devices can commonly be simplified to use operational amplifiers. Op amps are still an attractive option because they are extremely cheap. When priced for volume manufacturing, you can get them at 20 to 30 cents apiece.

I designed automotive sensors for a few years, and it is surprising how many small sensors on your car use an op-amp paired with a cheap microcontroller. Typically, low cost automotive grade micros have poor analog performance, and most transducers such as temperature, pressure, and airflow have very low signal levels. For this reason you need to use an op-amp, or even 3 op amps combined in a configuration called an instrumentation amp. This allows you to take a very small signal (say, 0 to 40mV, typical for temperature sensors) and convert it to a range the microcontroller can quantize (usually 0 to 5V).

For automotive sensors, cost optimization usually gives you a substantial competitive edge. To displace an existing vendor for a large automotive manufacturer, you almost always have to come in at a lower price. Using pricey DSPs and fast microcontrollers is not an option. Some products require creative solutions by working in extremely tight cost requirements, where shaving off 10s of cents per unit can make or break the project.

If you were to take apart sensors like your MAF, O2, or exhaust temp sensors, you would definitely find an op amp in there.

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  • \$\begingroup\$ Thanks for answer. Their design with a differential amplifier first and the connecting output back to one input, is pretty smart. I understand why the ”are they more inportant historically” angle upset a few people, but ”calculating on voltages” was not something I could see exactly when or where it is used. Saw another question here from someone who seemed to have similar thoughts, electronics.stackexchange.com/a/182773. \$\endgroup\$
    – Doge
    Nov 16, 2021 at 19:25
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Basically, an opamp is:

  1. an input stage with low offset
  2. followed by a ton of gain
  3. a low impedance output stage to drive loads

This makes it a bit like a Swiss Army Knife, able to implement lots of different functions based on what kind of feedback circuit the user choses. In addition, if the correct opamp is selected for the job, tolerances on the opamp's internal parameters don't influence tolerances on resulting gain and transfer function that much: it mostly depends on feedback components.

The original opamps from 1947 were implemented as discrete circuits, now they are all ICs. For an IC, cost is determined by silicon area and process, plus some fixed costs for packaging, and all logistics from the factory to the finished board. For cheap components, logistics becomes an important part of the price, and that also includes inventory management, the number of reels on the pick and place machine, how many parts it has to place on the board, etc. So if the choice is between a 5-10c opamp like LM358 and a circuit based on a couple BJTs and passives, the opamp could be cheaper even if it's overkill.

For example, to amplify/filter an analog signal, you'd have several choices. You could use an opamp, or an "gain block" IC that really is an opamp with internal feedback resistors, or a different circuit made of one or a few transistors. If you use discretes to implement an opamp, I'd still count that as an opamp.

If you don't want to use an opamp but instead, say, a common emitter BJT, then you lose feature #1: low input offset. Instead the offset becomes 1 Vbe, which is huge and temperature dependent. Not a problem for AC signals, but a big problem for DC signals. So you might want to use a matched monolithic transistor pair. But because everyone is using opamps, there is very low demand on this product, which means that'll cost five bucks. For this price you can get a complete opamp with the same (or better) characteristics. The emitter follower amplifier only makes sense to use at high frequency where opamps lose their edge.

Now if you want tolerances on your transfer function to depend mostly on passive components and not semiconductor tolerances, which are much wider, then you need a lot of gain for feedback and to reduce distortion. This means you're basically reimplementing an opamp with topologies like active load or folded cascode, which require at least 2 transistors in addition to the input and output stages, but most likely 2-5 transistors, plus a lot of passives and 2 current sources. Just the inventory management and pick&place cost for that makes it more expensive than a cheap opamp, not to mention board area, etc.

In addition, it is difficult to make high bandwidth feedback circuits with discretes. If you want say 50-100MHz gain-bandwidth product, then the much smaller parasitic L and C inside an integrated circuit really matter to get low pahase shift and good phase margin, so you'll end up with an opamp again. In addition, with modern processes, manufacturers can put really good/fast transistors on their chips, that would be really hard to beat with discretes.

However, and ironically, DSP has mostly displaced opamps from the "operational" job: when the signal is available in digital form, then it is much cheaper and more convenient to process it in the digital domain. So if you have a signal processing chain, and if there is some digital processing in the middle, you'll still usually get opamps for signal conditioning at the beginning and output filtering at the end, but over the years the DSP block in the middle has been growing and replacing most analog circuits around it.

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op-amps are the basic building block of modern low-frequency analog circuitry. Even when used as basic amplifiers they offer.

  • Customizable, stable and repeatable gains set with only a couple of easily calculated resistors.
  • Easy DC coupling.
  • High input impedance when used in non-inverting configurations.

All of these properties are difficult to achieve with simple amplifiers built around discrete transistors.

Stablity and repeatability are what make the difference between circuits that have to be adjusted before leaving the production line and then adjusted again periodically in service and circuits that do not. Adjustment of analog circuitry is expensive in multiple ways, cost of the components, space taken up by the components and technician time to perform the adjustments. Many precision systems nowadays will do what adjustment they need to do digially, but that only works if the analog side is somewhere in the right ball park.

Op-amps also form the basic building block for more complex amplifier designs. For example the "instrumentation amplifier" built out of 3 op-amps offers a differential amplifier with a high gain, high input impedance and a high common mode rejection.

While no-one builds analog computers anymore we still build simpler analog circuits and we still want to connect our digital computers to the outside world. Generally the inputs of our ADCs and the outputs of our DACs are not suitable for direct connection to the outside world.

And then there are filters. An unfiltered ADC will suffer from aliasing, where multiple input frequencies produce the same result. If an ADC has a sampling frequency of say 1MHz, then a 400kHz sinewave and a 600kHz sinewave will be indistinguisable in the output. On the other side an unfiltered DAC will produce undesirable "staircase" waveforms in it's output.

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There is nothing supernatural about op-amps. They are just very high quality differential amplifiers and nothing else.

Op-amps do not perform mathematical operations; they are performed by the passive elements connected in the negative feedback. Op-amps only help them to be perfect. Here are some examples:

  • In an op-amp summing amplifier, a passive resistor summer sums the input voltages.
  • In an op-amp integrator, an RC circuit integrates the input voltage.
  • In an op-amp log converter, a passive RD log converter does the log conversion.
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  • \$\begingroup\$ Actually, it's the whole circuit configuration, with op-amp and passives that do the calculations. The passives don't really do the calculations themselves either. \$\endgroup\$
    – Justme
    Jan 23, 2023 at 22:13
  • \$\begingroup\$ @Justme, Why not? An RC circuit integrates, CR circuit differentiates, RD circuit logarithmizes, DR circuit antilogarithmizes, etc. \$\endgroup\$ Jan 23, 2023 at 22:29
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    \$\begingroup\$ An inverting op-amp circuit does not invert without the op-amp. And you get no amplitude gain (inverting or non-inverting) either. The external components define what the whole circuit with the amplifier then performs. \$\endgroup\$
    – Justme
    Jan 23, 2023 at 22:42
  • \$\begingroup\$ @Justme, Exactly... The almighty op-amp serves the humble passive circuit:-) \$\endgroup\$ Jan 23, 2023 at 22:47

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