[Workaccount2]

Wikipedia has a nice table of these values that I actually have printed out and hanging above my bench.

https://en.wikipedia.org/wiki/E_series_of_preferred_numbers#...

The fact of the matter is that nowadays, E96 series resistors are readily available and dirt cheap. And if you need more precision than that, you either don't know much about electronics or you know a whole lot about electronics, heh.

[pclmulqdq]

One fun thing to do when designing high-precision analog stuff (audio) was to choose component values that are about 1.5-2% off of a value in the E12 series. You can then go test a whole bunch of resistors and you will find a lot within 0.1% of each other (even within 0.01%). Everything within 1% of E12 is binned as a 1% resistor so those aren't polluting your stock.

Going within 0.1% of an E12 value is a pricey resistor, but resistors that are matched nearly perfectly and are 2-3% off are cheap and easy to find.

[e-khadem]

Raw room temperature value isn't the only reason we use precision resistors. Some parts tend to behave more linearly at higher voltages (especially at the Meg range) and others exhibit much lower tempco's. There is also the problem of long-term stability and value change due to exposure to high temperatures during soldering.

In any case, the above trick is neat, thanks for sharing it.

[amelius]

There are solutions to keep matched resistors at the same temperature.

[klodolph]

Yes—although E96 is cheap, I’m still very fond of E12. You get to keep less stock. I’ll even use two resistors rather than use something outside E12, most of the time. Maybe it’s habit?

Hell, I don’t even think all of E12 is necessary. I’ll stick to E6 most of the time.

[londons_explore]

Being a mostly-digital electronics guy, I think 0.1, 1, 10, 100, 1k, 10k, 100k, 1M and 10M is a perfectly fine series for pretty much any usecase.

Sense resistor? 0.1 ohm.

Resistor for an LED: 100 ohm

Pull up resistor: 10k

Bias resistor for some mosfet gate: 10M

Voltage divider to measure the battery voltage with an ADC: two 100k resistors.

It's super rare I need anything else. I hate fiddling about with switching the reels on the pick'n'place anyway.

[picture]

Have you tried 10 kΩ for LED and FET pull down?

100 Ω sounds like way too much current for modern LEDs. I often end up using 100 kΩ especially for green LEDs. They are very visible under indoor lighting even with 1 MΩ and 3.3 V supply.

For pulling down FETs, you want something in the range of 10 kΩ. 10 MΩ sounds way too high, which makes your circuit sensitive to being touched or affected by moisture, especially if there are near by components connected to the power rail.

My digital electronics grab bag consist of 22 mΩ for sensing, 100 kΩ for battery voltage divider, 22 kΩ for one of the 3.3 V buck converter feedback dividers, 10 kΩ for everything else like I2C pulling.

[hathawsh]

Are you sure all those numbers are in the right ballpark? With a 3.3V supply and a 1 MΩ resistor, the most current you can get from that circuit is in the neighborhood of 3μA, and that's ignoring the LED voltage drop. I would think the LED won't be visible until you're around the mA range. Or are some LEDs visible in the low μA range?

[tuetuopay]

Modern LEDs light up with incredibly low currents. In a RF noisy environment, I've often seen LEDs glow just by touching one side with a wire and the other to ground. Just the parasitic from such a crude antenna was enough.

Of course as stated by another comment, our eyes are also incredible, and can pick up very faint amount of light.

[londons_explore]

human eyes are logarithmic and can easily see microamps.

In fact, just hold an LED between your fingers in a dark enough room and you'll sometimes see them glow from stray magnetic fields inducing enough current in your body to light them.

[zaroth]

Beautiful if true!

[CamperBob2]

Resistor for an LED: 100 ohm

Yeah, that's why I can read a book by the blue LEDs on my alarm clock...

[_carbyau_]

https://www.3m.com/3M/en_US/p/d/b40068069/

Depending on the colour bleed though. It may wipe out all visibility of the clock numbers.

[Liftyee]

And to think a little dimming circuit with LDR/phototransistor (RoHS..) is practically electronics 101...

[klodolph]

I do mostly analog and being off by a factor of 2 or 3 is gonna ruin your day.

[joemi]

How do the tolerances combine when you're using two resistors? I'm pretty sure they'd add together if in series (so two 5%'s become 10%), but I'm having trouble easily intuiting what happens if in parallel. Do they combine in the same way that resistances combine when in parallel?

edit: Actually, I'm not so sure anymore that the tolerances would add up in series... I should probably just look this stuff up, since I'm not awake enough to intuit correctly, I think.

[Brian_K_White]

Values (for resistors) add in series and sort of divide-average in parallel.

In either case though, the tolerance divides.

The combined tolerance becomes more accurate the more resistors there are in total, whether parallel or serial. The highs and lows, and the chances of high or low, cancel each other out and you get a final actual value that is closer to the nominal statistical center of the bell curve the more individual parts there are. (same goes for other components, just resistors are simpler to talk about because their behavior is simple.)

In series, a single 10K might really be 9K or 11K, but if you chain 10 10Ks in series, you don't get a "maybe 90K maybe 110K". That is technically possible but statistics means that what what you actually get is if there was N% chance that a given 10K is 9K or 11K, the there is 1/10th of N% chance (or less, I bet the actual equation is more complicated) that the chain of 10 is 90K or 110K. If the individual 10Ks were 10%, then you get 100K with something like 1% tolerance.

(except also in reality, there is such a thing as batches, where all the parts in a given batch are all high or low the same way, because the process was drifting a little high or low while it was cranking out thousands of them that hour. So Ideally your 10 individuals need to come from 10 different batches or even 10 different manufacturers if that were practical or in a pure math world.)

In parallel, the statistical division is the same though the value centers on the value/N rather than value*N. 10 10% 10Ks in parallel = 1 1% 1k

[klodolph]

> or less, I bet the actual equation is more complicated

https://en.wikipedia.org/wiki/Central_limit_theorem

I’m a bit tired otherwise I’d write something more rigorous. There are different ways the central limit theorem is expressed and proved here—there are more powerful ways to state it that require more complicated proofs, and there are simpler versions that are simple to prove.

A simple version will suffice here. Treat the resistors as iid variables with finite variance σ². When you average them, the variance of the average is σ²/n. More or less… this means that if your resistors are ±10%, and you have 16 of them, you get something with (fuzzy math) ±10%/√16 = ±2.5%.

There’s a lot of unstated assumptions in what I just wrote. But you’ll see the “grows proportional to √n” a lot in stats.

[chongli]

If you have 2 identical resistors that are 5% over nominal and you put them in parallel, you'll get a value 5% over nominal. Example:

Suppose you had a pair of 105 Ohm resistors that are nominally 100 Ohm. In parallel you get:

1/(1/105 + 1/105) = 105/2 = 52.5 Ohm (5% over expected 50 Ohm)

If one is over nominal and the other is under, they'll cancel out for the most part:

1/(1/105 + 1/95) = 49.875 Ohm (0.25% under expected 50 Ohm)

[pavon]

If the resistor values are distributed as a Gaussian where the tolerance is some confidence interval, then the total resistance of resisters in series would be distributed as the sum of those Gaussians whose tolerance would be the root-sum-square of the individual tolerances: sqrt(tol1^2 + tol2^2 + ... tolN^2), or if all the tolerances are the same then sqrt(N)*tol.

[racingmars]

In series they don't add up... doing a quick example, I find that in the worst case (e.g. each resistor out by 5% in the same direction):

22 - 5% = 20.9

47 - 5% = 44.65

Actual resistance in series: 65.55

Nominal resistance in series: 69

69 - 5% = 65.55

So the combination of the components still appears to maintain the 5% tolerance.

[_benj]

There’s also part of, good designs don’t depend on high precision components. I think TAoE emphasized that. For high precision one can use trim potentiometers or maybe even digital potentiometer with an ADC at the other side to measure and get as close as possible, but otherwise depending on resistors for high precision is kinda rough (I’m think like an RC circuit that need a very specific resistance to meet some specific timing requirements)

[picture]

High precision resistors are often necessary for metrology applications like very precise and low drift voltage sources. Often parts like Vishay's same-substrate thin film resistor networks [0] are used, as the temperature of each resistor leg are kept the closely relative to each other, resulting in the ratio between them being stable against temperature changes. Even if you use some adjustable/tunable circuit, you usually still require some sort of precision resistor network as an original standard.

In general, however, it's much better to measure/sense physical phenomenon by first converting it into frequency, because it is much easier to measure frequency precisely. Using something like a TCXO from Seiko Epson with 1 ppm tolerance, and measuring over time, you can easily achieve 0.00001% precision and beyond. I know that strain gauges used in civil engineering often utilize this concept, where a metal string is "plucked" electronically and the frequency is then measured.

[0] https://www.vishay.com/docs/61010/ccc.pdf and https://foilresistors.com/docs/63120/hzseries.pdf

[SAI_Peregrinus]

On the frequency note, the primary standards for voltage are superconducting quantum Josephson junction arrays; basically fancy frequenvy-to-voltage converters.

[contingencies]

Neat. Next time I see resistors in a splayed or star configuration with one leg in shared proximity I will think of this comment.

[segfaultbuserr]

> There’s also part of, good designs don’t depend on high precision components. I think TAoE emphasized that.

If I call correctly, TAoE said engineering calculations should never keep too many significant digits, since no real-world components are that accurate, and all good designs should keep component tolerance in mind - they should not have an unrealistic expectation of precision. It also mentioned that designing a circuit for absolute worst-case tolerance is often a waste of time.

But I don't think TAoE told you to "avoid precision components in your design, use trimmers instead" (Do you have a page number?) when the application calls for it. For example, 0.1% feedback resistors in precision voltage references are often reasonable.

> For high precision one can use trim potentiometers

From what I've read (from other sources), mechanical trimmer used to be extremely popular, but they went out of favor in recent decades because tuning could not be automated and that increased assembly cost. Using a 0.1% resistor is favorable if it allows trim-free production.

> or maybe even digital potentiometer with an ADC at the other side to measure and get as close as possible

Yes, digital trimming and calibrations is today's go-to solution.

[gnramires]

It's not always possible to design avoiding precision components though (although as you mentioned trim components could fit the bill). If you want to precisely measure current with a shunt resistor for example, you need high precision (although you can also calibrate it digitally). More than precision, which can sometimes be calibrated against, there are also various kinds of environmental stabilities that may be more important: temperature stability, pressure stability, etc. -- you'd need other forms of calibration, measurement and compensation.

Also, component-level precision has limits because eventually trace impedance starts to be significant (hence the use of trim components you mentioned!).

Youtuber Marco Reps goes through various high precision equipment that often have precision resistors and such, recommended if interested!

[eternityforest]

I'd say if you need more than E3, you either know a lot of not much, unless you're into analog.

I've done stuff that needs high precision resistors, but usually the specific value isn't that important, just that it's a known repeatable value.

[nick238]

If I want a voltage divider, it's a lot easier to just use some 1% resistors and forward-calculate the expected output (rather than doing a calibration) if you're happy with 1-2% error from the resistors and your ADC or the like. Adding software and testing hardware to do a full on calibration is a lot of work.

But yeah, for digital signals, oft times 1k or 100k make no difference.

[eternityforest]

I definitely agree that 1% or better resistors are easier than calibration, but that doesn't mean you need values outside of E3 most of the time.

I might want want an accurate 1/10 divider or something, but a 1/12 divider would probably be fine too, as long as it's consistent. If it doesn't vary between devices, it's just a line of code to change.

[willis936]

For voltage dividers it's best to use matched networks. Often not much more expensive and orders of magnitude more precise.

[MeteorMarc]

E12 is also great for older users who do not have the keen eyesight anymore to read the 1% codes with certainty without using tools.