Can someone explain the last paragraph? The author gives the example of trying to find a 70 Ohm resistor and how the 68 Ohm and 75 Ohm are a little off. They conclude by saying you should just use 33 and 47 Ohm resistors, but wouldn't that give an resistance of 80, not 70?
This part is the thing that made me understand the numbering series:
[…] Continuing this trend, rounding as needed, and we end up with the series 10, 15, 22, 33, 47, and 68. Components built to the E6 standard have a 20% relative error tolerance, and if we look at the values again we’ll see a trend. Starting with 10 again and adding 20% error we end up with 12. Moving to 15 and subtracting 20% we get… wait for it… 12. Moving up from 15 we get 15 + 20% = 18 and 22 – 20% = 17.6. This trend repeats no matter what range of powers of 10 you use, as long as they are consecutive. So 47kΩ + 20% = 56400, while 68kΩ – 20% = 54400.
Look again at the values 47 and 68. The max/min values overlap right about 56, don’t they? That sounds familiar. The E12 standard uses all of the same values as E6, but with 6 more values mixed in. These 6 additional values are roughly where the E6 values overlap, and now in order to cover the entire range our %-error is reduced to 10%. Starting again at 10, we have 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, and 82. The math holds true here as well, with the error values just slightly overlapping.
It's the 'tolerance overlap' concept that makes the numbers work, but I don't think I've ever seen it explained so clearly before.
I feel like the author conflates tolerance in component value choice and fabrication tolerance. The E-series were chosen so that if you have perfect resistors (no fabrication tolerance) of only their values available, you can replace any resistor value you need with one from the series, and you'll never be more off than a fixed error (e.g. 20% for the E6 series).
This only works with perfect resistors, though. If your actual resistors have a fabrication tolerance, you might be more off. For example, if you need a 41 Ohm resistor, you can use a perfect 47 Ohm resistor from the E6-series, and you'll be within 20% error. However, if that 47 Ohm resistor has a 10% fabrication tolerance, in reality it might be 51 Ohm, and that's more than 20% off from the 41 Ohm you needed.
To take the example from the author's last paragraph, if you need a 70 Ohm resistor, the idea is not that you could be lucky and find an exact 70 Ohm in your E24 resistor set, but that you change the design to use a 68 Ohm instead, and don't introduce more than 5% off by doing so (regardless of the resistor value you needed).
In 2024, if your resistor vendor has even 5% tolerance, you need to find another vendor.
Thin-film resistor design engineer here! It's dependent on value and geometry -- if you order a 0.5 ohm resistor the meters on our trimming lasers only go down to 20 mΩ and you're getting a 5% part at best.
And that's why the really precise resistors are so damn expensive. E.g. VPG makes a 10k 1/5W 0.001% tolerance ±0.2ppm/°C, but they're $116 each with a minimum order quantity of 25 on DigiKey (so $2900 minimum purchase). They've got a really expensive meter for their trimming setup!
I see. I guess that's why high-end audio is so expensive
As both a sound and electrical engineer I think most high end audio electronics is bullshit.
If you know what you're doing a 50 cent opamp will give you results that are beyond what a human could identify in a double-randomized blind test. Same goes for comparing two rusty pieces of wire against highly pure copper speaker cables.
For some reason audiophiles will use darn massive gold (or silver) RCA connectors instead of something like a balanced connection that would actually make sense.
For audio applications 1% resistors are fine. You can use still affordable 0.1% in places where you truly care. Below that it is getting ridiculous, as the influence of harder to match things will take over. Things like speakers or the room they are placed in. How about the speed of sound changing with air temperature and humidity? You better have a room that has uniform and stabilized air temperature and humidity.
A big part of the audiophile game is about psychological impact and the joy of personalized optimization. I spent a lot of money on audio equipment and a lot of time on researching it myself. It is an interesting thing. But in the end it is also physics that are interpreted by your brain and I can't help but feel bad for people who need to (incoming hyperbole) turn every part of their setup into gold in order to be able to enjoy listening to their equipment as music passes through it.
For some reason audiophiles will use darn massive gold (or silver) RCA connectors instead of something like a balanced connection that would actually make sense.
It's hard to find XLR (or even TRS) balanced connectors on most non-professional (=TV studios, expensive conference room setups, DJs/clubs/similar venues) equipment.
We're talking audiophiles, it's not like they're trying to cheap out.
Even a 80 Euro Berhinger USB audio interface has balanced outs nowadays.
I think this is more of a cultural divide than anything, with tradition being a big part of it. In the olden days balanced I/O had to be done using specialized transformers. Unless you got really expensive well wound ones these could degrade your signal significantly — that might've contributed to a bad rep in audiophile circles. But today you can balance or unbalance electronically with indistinguishable fidelity and... ironically a lot of the analog "warmth" people love in old recordings came from the transformer on the inputs of old mixing desks.
There is really no reason to use unbalanced today other than being really pressed for money or running so short cables that it won't matter - and even then you could do better than RCA connectors.
It's on all music studio equipment except the cheapest or small form factors.
Yeah, but I wonder why? Sure, a Extron DMP with 128 bit DSp processing and 8 channels of balanced in and 12 channels of balanced out would qualify as professional conference equipment. But at a cost of approx 2.8 grand it is cheaper per channel than most audiophile equipment you can find.
The truth is that we sound engineers who use that stuff for work often do not have the luxury of caring for things that don't matter to the process or the outcome.
Professional AV equipment is expensive because it needs to be reliable on top of sounding as if it wasn't there, one of those units described above was running without fault for 15 years 24/7 in a room that was 30°C each summer (and it still works). Meanwhile my brother bought a silver RCA connector that broke off after a year of use — tip stuck in the amp, guess who had to fix it..
For some reason audiophiles will use darn massive gold (or silver) RCA connectors instead of something like a balanced connection that would actually make sense.
Is there a reason why they don't just use digital audio everywhere and convert to analog as late as possible? Inside the speakers for example? I mean, digital audio is pretty much perfect. Why are analog audio signals still a thing? People actually pay thousands of dollars for magical analog audio cables and it boggles my mind.
Good question, this is what most modern studio engineers would do, especially given that more and more speakers (like the Neumann KH120 II) feature internal FIR filters so you can calibrate them using measurement microphones.
Many modern Studios run some form of digital audio network as well (Dante, Ravenna, etc) so you can go digital as early and close to the source as possible and do all the routing using network switches and some sort of managment software (e.g. Dante Domain Manager). So if you do that it makes sense to go digital all the way to the speakers and convert directly to analog there after running through a DSP that allows you to correct for the speakers position in the room.
Cables can matter. But more for mechanical reliability, good shielding and perfect handling after years of use than any other magical properties. If you want to run balanced audio signals at miniscule loss for a few thousand meters it turns out that you can just use CAT6 for that. These cable are made for far more challenging (speak: higher frequency) signals and they have a track record of working.
That makes perfect sense. Thanks for clarifying.
My speakers convert digital to analog. They have ethernet jacks in the back. Maybe you bought the wrong speakers?
Stepping back for a moment… you see digital interconnects in high-end pro audio gear, using systems like Dante. These systems are NOT simple. When you have multiple digital audio systems connected together, you have to worry about whether they are all running from the same clock, or whether you can convert from one clock to another. Systems like AES solved this by having “word clock” running on separate coax cables with BNC connectors.
If you look at consumer digital audio stuff, like Bluetooth speakers, you find all sorts of weird problems. It turns out that for cheap consumer gear, you get better quality audio from simple analog connections anyway.
If you want speakers with digital inputs, you also need to power those speakers. That uses up more power outlets.
I'm not as familiar with foil resistors, but if you apply the same rules as thin film I would expect that you could trim this with a normal meter (the ± is 0.1 ohms) and the major cost driver is laser trim time and the space cost of some extra geometry on the resistor to support the tight tolerance (i.e. more fine trim features than standard).
I believe Vishay's ±0.2ppm/°C TCR is a materials science process specific to one of the companies they own, so that is also a reason they can charge quite high prices.
If you don't need that kind of TCR (i.e. your part is not going to space) the price should go down considerably for a thin film NiCr resistor (5 ppm - 25 ppm). There is actually a lot more direct sales and custom design volume than I would have expected when I started in this industry, so what you see on Digi-Key is not the entire market.
What about shunt resistors? I can pretty easily get a 1% 5mΩ resistor, but they don't look to me like they are constructed in the same way as a generic resistor.
They're made in a bunch of ways but the general principle is "the stuff inside is much lower resistance than what's normally used."
AFAIK, it used to be that parts binning was used to sort parts by tolerance. So the 5% bin wouldn't include <1% parts because those were already selected into the 1% bin in the factory and so on. Is it still like this?
Mostly, no. Nobody except for expensive precision resistor companies are actually measuring resistors more than statistically.
The resistors are manufactured so that they are "guaranteed by manufacturing" such that the outliers are 1%, 5%, 10%, etc. And they do statistical checks on batches, but not really looking for the 10% outlier (which is stupendously rare and very difficult to catch) but looking for slight drifts off nominal (which are much easier to spot) which would result in more outliers than expected.
As such, if you measure resistors, you tend to find that you get really close to nominal--much closer than you would expect for 10%, say. Resistors are so cheap that binning simply doesn't make economic sense.
They should still bin, so that each individual resistor gets the highest price possible by the virtue of its classification, even if the binning is costly.
Not if the additional cost is more than the additional revenue.
Let's assume that without binning you get 20% over cost of manufacturing. If it costs 5% more to bin-check all resistors, and you wind up selling 1% of them for an additional 100% mark-up:
No bin Bin
Cost to mfg: $ 1.00 $ 1.00
Cost to bin: .05
------ ------
Total cost $ 1.00 $ 1.05
Base price $ 1.20 $ 1.188 (99% sold at base)
Premium price 0.00 $ 0.022 (1% sold at un-binned cost x 2.2)
------ ------
Total revenue $ 1.20 $ 1.21
====== ======
Profit $ 0.20 $ 0.16Is this how LEDs are binned as well, or are they powering each node on the wafer before packaging? They're orders of magnitude more expensive than resistors, so I figure they might...
There are all kinds of crazy parameter variations in optoelectronics. I understand that resistors are really close to nominal because the manufacturer's ability to tune the process controls are so much better than the standard 5% and 10% bins, but it seems that LED manufacturing is way more difficult and they can't always tune the process to get exactly what they want.
I saw a video from the WS2812 factory and from what I remember all of the LEDs were tested individually on the die before assembly. I don’t know if that’s typical but those are pretty cheap for what they are.
It depends on the component and the company/process. Laser trim time for thin film is a significant cost-driver, so if possible you want to aim for a specific value and reject or bin-sort the rest out. My company only makes 1% tolerance resistors by laser trimming.
you can't always bin a ±5% resistor as a ±1% resistor if its value tests within ±1%, because, as i understand it, a ±1% resistor often needs to be ±1% over its temperature range, working voltage range, and lifetime, so it has to be made differently than a ±5% resistor
if your temperature range is -40° to 85° and your resistance is +0.9% off nominal when measured at 22°, your temperature coefficient of resistance would need to be under +16 ppm/° to ensure that it was still below 1% even at 85°. a more typical tcr for ±5% thick-film resistors is +250ppm/° (see, e.g., https://www.vishay.com/docs/51058/d2to35.pdf) and so there is no hope of binning such a resistor as a 1% one
aging is another source of component value error that can prevent binning (the component value drifts over time, usually proportional to the square root of its age), and some kinds of resistors also have a significant voltage coefficient of resistance (mostly semiconductor types like carbon-film and the antediluvian carbon composition)
these phenomena sometimes lead designers to use expensive tight-tolerance resistors (±0.01% nowadays, 50¢–250¢ each) even in circuits that can easily be calibrated to handle component value error, just to keep the calibration from going off due to temperature or aging and to improve linearity
disclaimer: i'm not an electrical engineer, i just play one in ngspice
I didn't understand the Renard Numbers tangent until realizing it's the same principle of exploiting "usage tolerance": He replaced the 400 different cable lengths with 17 "standard" cables that can be stretched to any of the desired actual lengths. The choice of numbers ensures that the "stretch", i.e. error never exceeds a certain factor.
These things all made sense before laser trim resistors. At even a modest volume you can get any value you want at better than 1% for basically no money.
Usually the minimum order is something like 10K parts (a.k.a. one reel) and you might pay something like $75 for it. $0.0075 per resistor.
https://www.ppisystems.com/ppi-systems-designs-and-manufactu...
And before digital circuits. All I see now is 10k, 1k and 100 Ohm resistors.
Most resistor in power supplies would be different values. For digital stuff and low current applications (along with designated FET drivers) you dont need too much.
'Laser-trimmed resistors' will be the next selling point on a boutique guitar FX company's 57th clone of a Tubescreamer.
Factored into the tolerance is the temperature coefficient, because the tolerance is specified over the operating range. There are also 3 basic temperature ranges: Industrial, automotive, and military. I've used this to my advantage by spec'ing automotive capacitors when I needed tighter tolerances for my normally room temperature applications.
They also laser-trim IC's.
Seems easier to me to say they are logarithmically distributed, rounded to 2 digits.
Like yes, this means that if your manufacturing tolerances are typically some percentage of the amount (more natural than an additive error) then the overlaps are nicely spaced. But a log scale means that's true for any relative allowance (manufacturing or otherwise), which is the much more natural sort. It doesn't matter if your 100-foot house is off by 1mm, but it does matter if your 1mm-thickness fork is.
Seems easier to me to say they are logarithmically distributed, rounded to 2 digits.
Except that it is the tolerance overlap that allows for that specific distribution to work.
I can’t tell what you mean.
I still don't really get the overlapping tolerances, though, because each resistor is not a range, it's a single value that's somewhere in that tolerance.
He says about the cables:
Each size of cable had a max/min rating that just overlapped it’s neighbor above and below, so every required value was covered by one or more cable.
So that means if you needed a "size 12" cable you could pick a size 10 OR a size 15, and they would both work.
But if you need a 12ohm resistor, it's possible that neither the 10 nor the 15 might work, because the 10 could be a 9 and the 15 could be a 17. So I don't really see how it connects.
To put it another way, what if we had 1000% error tolerances? Could we then get away with just a 1ohm. 1000ohm and 1Mohm resistors, because their tolerances overlap? Obviously not, so I don't see how it relates.
Each resistor in the design is a range. The designer picks the tolerance to use, some resistors will be fine with a 10% tolerance, others only with a 2% or 1% tolerance.
Also each resistor is a range, not a single value, since each resistor changes value with temperature & other environmental factors (though temperature is the biggest). That variation is (for normal resistors) less than the tolerance range.
The image it what made it clear to me.
https://digilent.com/blog/wp-content/uploads/2015/01/E12_ser...
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.
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.
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.
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.
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?
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.
Beautiful if true!
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.
Resistor for an LED: 100 ohm
Yeah, that's why I can read a book by the blue LEDs on my alarm clock...
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.
And to think a little dimming circuit with LDR/phototransistor (RoHS..) is practically electronics 101...
I do mostly analog and being off by a factor of 2 or 3 is gonna ruin your day.
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.
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
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.
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.
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.
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)
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.
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.
For voltage dividers it's best to use matched networks. Often not much more expensive and orders of magnitude more precise.
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.
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)
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
Neat. Next time I see resistors in a splayed or star configuration with one leg in shared proximity I will think of this comment.
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.
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.
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.
There are solutions to keep matched resistors at the same temperature.
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.
Why don't resistors show their power rating on the package, always? Or at least more often.
Because there's basically no design downside to having a higher power rating than needed, aside from BOM cost. If you're ordering a bunch to have on hand, you should just order the highest power rating you're likely to need in that size.
For me, that means that my 0402s are all 1/16W, 0805 are 1/8W, 1206 1/4W, etc. And all of my through-hole resistors are 1/4, because the wire stock plays well with breadboards better.
There are probably 1/4W 0402s out there, but that's definitely a specialty piece. I'm seeing 16 cents a resistor/each for a 1 MOhm 1/4W 0402, which is about 4 times what I'd expect to pay for a 1/16W of the same resistance and package.
I'd be surprised to find a 1/4W 0402, you'd just about melt the solder off. Yageo claims this one is good to 3W, do you think it glows cherry red? What trace width and pad geometry do you need to push 3W into a 0.0025 ohm resistor?
https://www.digikey.com/en/products/detail/yageo/PA0402CRF5P...
But to your point, Digikey has >70,000 0402s in 1/16W. There are 900 rated for 0.05W, and they're all exotic high-frequency/low temp coefficient/high-precision specialty parts.
It probably has the cutest little heat sink.
I'd be surprised to find a 1/4W 0402
Something close to this is pretty common these days; for example Vishay's CRCW-HP series are good to 1/5W in 0402 size: https://www.mouser.co.uk/ProductDetail/Vishay-Dale/CRCW04021...
The package is the power rating ;)
That could be an internet game: given a picture of a resistor, guess its power rating.
Probably because only you and I have a problem with it ;)
Can be inferred from the size usually.
Insightful article. Not something I had considered before, but also...isn't this just a fancy way of defining a geometric sequence thats convenient for values in base-10?
do geometric sequences care about the base?
The ones mentioned in the article return to powers of 10.
In contrast, musical notes don't, their frequencies return to powers of 2.
It's not just a geometric sequence that's convenient for base 10, it's the standard set of geometric sequences (that was chosen because they're convenient for base 10).
The caption on the graph (and the paragraph before the graph) directly addresses this: "This graph shows how any value between 1 and 10 is within ±10% of an E12 series value, and its difference from the ideal value in a geometric sequence."
It's a more accessible way of explaining it that doesn't require understanding geometric sequences first.
Yes, the values are produced by a geometric series. For E6, the series has a ratio of R, where R^6 = 10, and the values are further rounded to two significant figures.
The thing that's blowing my mind here is that this standard was adopted as ISO 3. It reminds me of the Simpsons joke that Mr. Burns' social security number is 000-00-0002.
I think a lot of people are surprised to learn just how old the field of electronics is. It's an easy mistake to make with the relative novelty of digital electronics, but the science has been around for a good long time
It's less about the field of electronics being old and more about being surprised that ISO apparently just started counting with number 1 and that the preferred numbers would be so early relative to other things you might want to standardize.
At my local hackerspace we got a donation of a _huge_ 3D printer (~1m³ IIRC), after a while we realized that the number "3" printed on it is actually the serial number
Slight sidetrack:
We have to go back a few years to 1877 France. The French military used balloons for various purposes and of various sizes, and they had to be anchored using cables. Over time, they ended up with 425 different sizes of mooring cables that had to be individually ordered and inventoried. Talk about a nightmare. > > Enter Charles Renard. He was tasked with improving the balloons, but discovered this rat’s nest of cables in the inventory closet instead. He spent some time thinking about it and came up with a series of 17 cable sizes that would allow for every type of balloon to be properly moored.
I'm astonished that 425 distinct mooring-cable sizes were ever allowed to happen, and I'm also slightly astonished that even the cleaned-up version used 17. Anyone have more info about that? What were they doing with all those different-sized ropes? How many different balloon models could there have been?
Think about tethering a zeppelin with a curved body shape, where you need to attach in multiple places. Combine that with needing to tether at different elevations and it will get out of hand pretty quick.
You're thinking that shorter lines can be thicker without tearing under their own weight, so the optimal mix is a few heavy lines supported by a larger number of light ones? And/or heavy lines for safety, many light lines for stability?
I suppose that makes sense, though it still seems weird that they needed that many types.
These sometimes end up being useful in UI/graphics work too. And the math/code is dead simple! https://gist.github.com/tshddx/8341d1bdbe2f83ed4e2c26bc48faf...
I like the 5-smooth numbers and related sequences, because they include a lot of numbers that are very common in engineering
Related: https://www.veith.net/e12calc.htm
It quickly calculates pairs of resistors from E12 (and other) resistor series to meet a target.
I worked at a company with a technician who clearly did not understand this. When I asked him to order an assortment of resistors with a range of values, he came back to me and said that Digikey did not have most of them. Turns out he had submitted a request for quote, listing desired values in a linear progression: 1 ohm, 2 ohm, 3 ohm, 4 ohm, etc.
Having been around electronic components since before I could read: these aren't odd values. They're normal expected values.
I'd always wondered why 47 ohm resistors were so common!
Yellow and Purple striped critters inside of HeathKits.
I also thought that was interesting. Also, wouldn't the tolerance be doubled when you add them in series? Or does it still average out to +/- 5%?
tolerance should actually go down since the errors help cancel each other out.
reference: https://people.umass.edu/phys286/Propagating_uncertainty.pdf
disclaimer: it will be a relatively small effect for just two resitors
aleph's comment is also correct. the bounds they quote are a "wost-case" bound that is useful enough for real world applications. typically, you won't be connecting a sufficiently large number of resistors in series for this technicality to be useful enough for the additional work it causes.
Complete nonsense. The tolerance doesn't go down, it's now +/- 2x, because component tolerance is the allowed variability, by definition, worst case, not some distribution you have to rely on luck for.
Why do they use allowed variability? Because determinism is the whole point of engineering, and no EE will rely on luck for their design to work or not. They'll understand that, during a production run, they will see the combinations of the worst case value, and they will make sure their design can tolerate it, regardless.
Statistically you're correct, but statistics don't come into play for individual devices, which need to work, or they cost more to debug than produce.
If you're going to say "Complete nonsense." you shouldn't get the calculation wrong in your next sentence.
Very true, I was writing as absolute value, not % (magnitude is where my day job is). My point still stands: it is complete nonsense that tolerance goes down.
They said it "should" go down, but that another comment saying the worst case is the same is "also correct".
I do not see any "complete nonsense" here. I suppose they should have used a different word from "tolerance" for the expected value, but that's pretty nitpicky!
I'm sorry, but it's incorrect, as stated. It's a false statement that has no relation to reality, with the context provided.
Staying the same, as a percentage, is not "going down". If you add two things with error together, the absolute tolerance adds. The relative tolerance (percentage) may stay the same, or even reduce if you mix in a better tolerance part, but, as stated, it's incorrect.
It's a common misunderstanding, and misapplication of statistics, as some of the other comments show. You can't use population statistics for low sample sizes with any meaning, which is why tolerance exists: the statistics are not useful, only the absolutes are, when selecting components in a deterministic application. In my career, I’ve seen this exact misunderstanding cause many millions of dollars in loss, in single production runs.
It only stays the same if you have the worst luck.
Yes you can. I can say a die roll should not be 2, but at the same time I had better not depend on that. Or more practically, I can make plans that depend on a dry day as long as I properly consider the chance of rain.
Sounds like they calculated the probabilities incorrectly. Especially because more precise electrical components are cheap. Pretending probability doesn't exist is one way to avoid that mistake, but it's not more correct like you seem to think.
I've repeatedly used a certain words in what I wrote, since it has incredible meaning in the manufacturing and engineering world, which is the context we're seeking within. It's a word that determines the feasibility of a design in mass production, and a metric for if an engineer is competent or not: determinism. That is the goal of a good design.
And, you will get that "worst luck" thousands of times in production, so you must accommodate it. Worst off, as others have said, the distributions are not normal. Most of the << 5% devices are removed from the population, and sold at a premium. There's a good chance your components will be close to +5% or -5%
No you cannot. Not in the context we're discussing. If you make an intentional decision to rely on luck, you're intentionally deciding to burn some money by scrapping a certain percentage of your product. Which is why nobody makes that decision. It would be ridiculous because you know the worst case, so you can accommodate it in your design. You don't build something within the failure point (population statistics). You don't build something at the failure point (tolerance), you make the result of the tolerance negligible in your design.
Or, you could look at it as being a poorly engineered system that couldn't accommodate the components they selected, where changing the values of some same-priced periphery components would have eliminated it completed.
Relying on luck for a device to operate is almost never a compromise made. If that is a concern, then there's IQC or early testing to filter out those parts/modules, to make sure the final device is working with a known tolerance that the design was intentionally made around.
Your perspective is very foreign to the engineering/manufacturing world, where determinism is the goal, since non-determinism is so expensive.
The Central Limit Theorem (which says if we add a bunch of random numbers together they'll converge on a bell curve) only guarantees that you'll get a normal distribution. It doesn't say where the mean of the distribution will be.
Correct me if I'm wrong, but if your resistor factory has a constant skew making all the resistances higher than their nominal value, a bunch of 6.8K + 6.8K resistors will not on average approximate a 13.6K resistor. It will start converging on something much higher than that.
Tolerances don't guarantee any properties of the statistical distribution of parts. As others have said, oftentimes it can even be a bimodal distribution because of product binning; one production line can be made to make different tolerances of resistors. An exactly 6.8K resistor gets sold as 1% tolerance while a 7K gets sold as 5%.
That's kind of overstating and understating the issue at the same time. If you have a skewed distribution you might not be able to use the central limit theorem at all.
>If you have a skewed distribution you might not be able to use the central limit theorem at all.
The CLT only requires finite variance. Skew can be infinite and you still get convergence to normality ... eventually. Finite skew gives you 1/sqrt(N) convergence.
That's incorrect. They, by definition, guarantee the maximum deviation from nominal. That is a property of the distribution. Zero "good" parts will be outside of the tolerance.
Yes' and that's why tolerance is used, and manufacturer distributions are ignored. Nobody designs circuits around a distribution, which requires luck. You guarantee functionality by a tolerance, worst case, not a part distribution.
The total tolerance is not +/- 2x, because the denominator of the calculation also increases. You can add as many 5% resistors in series as you want and the worst case tolerance will remain 5%. (Though the likely result will improve due to errors canceling.)
For example, say you're adding two 10k resistors in series to get 20k, and both are in fact 5% over, so 10,500 each. The sum is then 21000, which is 5% over 20k.
If values are normally distributed, random errors accumulate with the square root of the number of components. Four components in series have 2x the uncertainty over all, etc, but if you divide that double uncertainty by four times the resistance, it's half the percentage uncertainty as before. (I avoid using the word "tolerance" because someone will argue whether it really works this way)
In reality, some manufacturers may measure some components, and the ones within 1% get labeled as 1%, then it may be that when you're buying 5% components that all of them are at least 1% off, and the math goes out the window since it isn't a normal distribution.
I wonder about the effect of different wiring patterns. For example you can can combine N^2 resistors in N parallel strips of N resistors in serie.
I expect that in this case the uncertainty would decrease
In the article's example, I'd prefer 2 resistors in parallel. That way result is less dramatic if 1 resistor were to be knocked off the board / fail.
Eg. 1 resistor slightly above desired value, and a much higher value in parallel to fine-tune the combination. Or ~210% and ~190% of desired value in parallel.
That said: it's been a long time since I used a 10% tolerance resistor. Or where a 1% tolerance part didn't suffice. And 1% tolerance SMT resistors cost almost nothing these days.
This might be why pretty much all LED lightbulbs/fixtures have two resistors in parallel. Used for the driver chip control pin, that sets the current to deliver via some specific resistance value.
It's always a small and a large resistor. The higher this control resistance, and the lower the driving current.
Cut off the high value resistor to increase the resistance a bit. In my experience this often almost halves the driving current, and up to 30% of the light output (yes, I measured).
Not only most modern lights are too brights to start with anyways, this fixes the intentional overdriving of the LEDs for planned obsolescence. The light will last pretty much forever now.
Iterating either of
f(x) = 3/(1/x + 1/110 + 1/90)
g(x) = 1/(1/(3x) + 1/(3110) + 1/(3*90))
Seems to show that 100 is a stable attractor.
So I will postulate without much evidence that if you link N^2 resistors with average resistance h in a way that would theoretically give you a resistor with resistance h you get an error that is O(1/N)
Note that tolerance and uncertainty are different. Tolerance is a contract provided by the seller that a given resistor is within a specific range. Uncertainty is due to your imprecise measuring device (as they all are in practice).
You could take a 33k Ohm resister with 5% tolerance, and measure it at 33,100 +/- 200 Ohm. At that point, the tolerance provides no further value to you.
It’s not nearly that simple:) Component values change with environmental factors like temperature and humidity. Resistors that have a 1% rating don’t change as much over a range of temperatures as 5% or 10% components do. This is typically accomplished by making the 1% resistors using different materials and construction techniques than the lower tolerance parts. Just taking a single measurement is not enough.
Fun fact is that afaik component values are often distributed in a bi-modal way because actually +-5% often means that they sorted out already the +-1% to sell as a different more expensive batch. At least it used to be that way. Wonder if it is still worth doing this in production. So I guess one could also measure to average things out otherwise the errors will stay the same relatively.
If you can measure them with that precision, would it make sense to sell them with that accuracy too? So if you tried to manufacture a resistor at 68kΩ +/- 20%, and it actually ended up at 66kΩ +/- 1%, couldn't you now sell it as an E192 product which according to TFA are more expensive?
Selling with different tolerances only makes sense to me if the product can't be reliably measured to have a tighter tolerance, perhaps if the low- quality ones are expected to vary over their life or if it's too expensive to test each one individually and you have to rely on sampling the manufacturing process to guess what the tolerances in each batch should be.
Resistors with worse tolerances may be made out of cheaper, less refined wire, which will vary resistance more by temperature. The tolerance and resistance is good over a temperature range. For more reading looking up "constantan".
Most resistors don't use wire, but some film of carbon (cheaper, usually the E12 / 5% tolerance parts) or metal (E24, or 1% and tighter tolerances) onto a non-conducting body. Wires mean winding into a coil, which means increased inductance.
I suspect in most cases the tolerances are a direct result from the fabrication process. That is: process X, within such & such parameters, produces parts with Y tolerance. But there could be some trimming involved (like a laser burning off material until component has correct value). Or the parts are measured & then binned / marked accordingly.
Actual wire is used for power resistors, like rated for 5W+ dissipation. Inductance rarely matters for their applications.
Accuracy depends on the technology used. Carbon comp tends have less accuracy then carbon film. And it's not true that higher accuracy is always better.
Some accurate resisters are essentially wound coils and have high inductance and will also induce and pick up magnetic interference. Stuff like that matters often a lot.
Thanks, always good to remember that the tolerance of a resistor is not just a manufacturing number but also defined over the specified temperature range.
The issue is probably volume. Very few applications need a resistor that's exactly 66kΩ, but a lot of applications need resistors that are in the ballpark of 68kΩ (but nobody would really notice if some 56kΩ resistors slipped in there).
For every finely tuned resonance circuit there are a thousand status LEDs where nobody cares if one product ships with a brighter or dimmer LED.
Depends on where in the production line they are being tested. If they are tested after they've had their color bands applied, then you wouldn't be able to sell it as a 66kH since the markings would for a 68kH
Unless the components are expensive, that proposition seems dubious. It's much more economical to take a process that produces everything within 12% centered on the desired value and sell it as ±20%. 100% inspection is generally to be avoided in mass production, except in cases where the process cannot reach that capability, chip manufacturing being the classic example. For parts that cost a fraction of a penny, nobody is inspecting to find the jewels in the rough.
Actually it seems to be really the case that multimodal distribution are rather the result of batches not having a mean. So it is rather the effect of systematic error [1]. I guess it is really a myth (we did low cost RF designs back in 2005 and had some real issues with frequencies not aligning die to component spread and I really remember that bi modality problem, but I guess okhams razor should have told me that it makes no economical sense)
[1] https://www.eevblog.com/2011/11/14/eevblog-216-gaussian-resi...
Yup, forever the reason for the trim pot.
I'm not sure where the line is, but at some point things like temperature a matter and so a low % resister cannot be high % that passes tests.
Nope, still averages to +/- 5%.
To give an example, let's say you've got two resistors of 100 Ohm +/- 5%. That means each is actually 95-105 Ohm. Two of them is 190-210 Ohm. Still only a 5% variance from 200 Ohm.
Can you assume that +/-5% isn't linearly distributed? If so, the tolerance in practice may likely end up even smaller.
There's a fundamental misunderstanding here.
Tolerance is a specification/contractual value - it's the "maximum allowable error". It's not the error of a specific part, it's the "good enough" value. If you need 100 +/- 5%, any value between 95 and 105 is good enough.
Using two components to maybe cancel out the error as you describe. On average, most of the widgets you make by using 2 resistors instead of one may be closer to nominal, but any total value between 95 and 105 would still be acceptable, since the tolerance is specified at 5%.
To change the tolerance you need to have the engineer(s) change the spec.
Neither.
Let R_{1, ideal}, R_{2, ideal} be the "ideal" resistances; both with the same tolerance t (in your example t = 0.05).
This means that the real resistances R_{1, real}, R_{2, real} satisfy
(1-t) R_{1, ideal} ≤ R_{1, real} ≤ (1+t) R_{1, ideal}
(1-t) R_{2, ideal} ≤ R_{2, real} ≤ (1+t) R_{2, ideal}
Adding these inequalities yields
(1-t) (R_{1, ideal} + R_{2, ideal}) ≤ R_{1, real} + R_{2, real} ≤ (1+t) (R_{1, ideal} + R_{2, ideal})
So connecting two resistors with identical tolerance in series simply keeps the tolerance identical.
But 80 is within 20% of 70 so we're fine ;)
So are the 68 Ohm and 75 Ohm.
I think the author maybe doesn’t know how to order 1% resistors from Digi-Key??
My intro circuit analysis prof gave these wise words to live by: “If you need more than one significant digit, it isn’t electrical engineering, its physics”
Even ordering from China the 1% are perfectly fine. E96 resistors are ubiquitous and cheap.
You are correct. Two of the comments on the article itself also mention this error.
Brilliant, informative writing, and yet people will jump to nit-pick the arithmetic.
I'd better spell-check this comment before clicking reply...
I think that was a typo and they meant 22 + 47, which equals ~70 Ohms