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.

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."

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.

[delayed]

> Even a 80 Euro Berhinger USB audio interface has balanced outs nowadays.

Yeah but who outside of people already interested in DJing buys that kind of stuff. It just looks ugly, unlike your classic home theater setup.

Out of "looks decent (=passes the Spouse Acceptance Factor test)", "reasonably affordable" and "has decent quality", choose two... unless you got a partner accepting you literally putting up a 2m truss with lasers, movingheads and a strobe in your living room that could compete with a mid-range disco, and a 1.200W fogger on the ground. I'm lucky enough to have such a partner, but I'd say about 99% of people don't.

There's something to it that the equipment should look beautiful in your living room, Bang and Olofssen -style. Music is beautiful, equipment playing it should be too. Or at least it enhances the experience.

Yeah, no issue with that. But the connectors are rarely front-facing and thus not really of aesthetical concern.

It is perfectly possible to build beautiful balanced equipment.

Yeah it is a cheap mobile usb interface. Beauty is not the name of the game there — which is why I used it to argue against balanced being a feature of expensive equipment.

Balanced outputs have nothing to do with the aesthetics of the object. And I choose option 4 — build it yourself — then it can be done cheap and look however decent, massive, invisible, ridiculous or whatever the aesthetical ven diagram between your second half and you looks like. And it can have balanced I/O if needed ; )

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.

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.

Right and isn't it the case that good quality D/A-converters still cost much money. So if you want every speaker to have them, and you want many speakers to get an immersive sound then "digital loudspeakers" can become expensive?

Eh, not so fast.

There are a lot of different parts involved—D/A converters, crossover networks, and amplifiers. Back in the day, good D/A converters were expensive, but they have gotten really cheap. If you have amplifiers that are cheap enough, you can put them after the crossover network and save money on the crossover network. If you have D/A converters that are cheap enough, you can eliminate the crossover network entirely and do it in DSP.

At that point you are comparing the cost of one more channel of D/A against the cost of an electronic crossover. It’s super easy to just buy a D/A with more channels. If you get to completely eliminate an analog crossover network, maybe that’s a win in terms of BOM cost.

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.

> digital audio is pretty much perfect.

It can be. But standard Bluetooth connections for audio can be terrible. Streaming from the internet, that is digital, and there can be delays and gaps in the sound.

Not much reason to use aggressive compression when wires have many orders of magnitude more bandwidth than bluetooth. And inconsistent latency is also not an issue when you control the whole network & don't need to share it with anyone else.

By "perfect" I just meant that digital audio perfectly reproduces the recorded analog signals. https://youtu.be/cIQ9IXSUzuM

I didn't mean to indirectly praise Bluetooth in my post. Bluetooth anything pretty much sucks. Bluetooth audio in particular is pretty bad and full of usability issues. It doesn't seem to have the bandwidth required since the audio gets transcoded to some lossy format.

I once set up an mpd music server on my local network and audio quality was perfect. However I encountered significant latency issues. Play and pause had a latency of one second which made it unusable. That was true even for uncompressed audio streams over the network.

I got bored before I was able to resolve the problem. Maybe the problem was my network. I should try it again now that I have a much higher performance router running OpenWRT which is capable of traffic shaping.

Ha! No, they're not using metrology resistors, just ripping people off.

High-end audio is a status-symbol. It shows that not only you are rich, but that you are also sophisticated.

But what happens if you don't like the music coming out of your stereo? No gold-plated connectors can cure that.

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.

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?

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.

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.

Is 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.

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       $ 0.16

SMT resistors in bulk are a fraction of a penny.

Tester time FAR outweighs any gain you could get by binning.

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)

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...