So the absolute resistance depends on the doping, which is tricky enough to control (furnaces, impurities, voltages, sputtering, etc.) that even with good control, the final resistance is within 20-30% of the target.
The relative resistance comes from the shapes themselves: it's the same material for both resistors, with the same properties from the same doping. And photolithography is great at matching shapes and patterns, so you get fantastic relative tolerancing.
There are, of course, still plenty of other sources of error.
It very much is a basic technique you learn in analog circuit design (or at least it was 30 years ago when I was in school). Similarly, there are circuits (like that current mirror) which rely on the nonlinear behaviors of diodes or transistors varying in sync — you can build them on the same chip, or you can carefully select matched sets from one manufacturing run.
An example with resistors is a voltage divider. The output voltage depends on the ratio of resistances not on the absolute values (within reason). The resistors in a long-tailed-pair also need to be matched but their precise value is less important. Or you might have a bias current that's temperature-dependent but in a way that matches the temperature-dependent needs of some other bit of circuitry on the output.
There's a famous early integrated opamp which has a four-way-symmetrical die layout to compensate not only for temperature variations across the die but also process variations.
It is well known. "Matched components" are common in analog design. (No two things are ever identical, but things fabricated next to each other are more likely to be much closer, and you can get better tolerances if you're going for a specific ratio.)
As a simple example, a voltage divider has the output voltage depend only on the input voltage and ratios of the resistance values. Vout = R1/(R1+R2)*Vin https://en.m.wikipedia.org/wiki/Voltage_divider
> Default LaTeX fonts give me a nasty uncomfortable feeling
> in the stomach by reminding me of Math and CS tests
Me too. The formulas look so dark. Do you know of any typefaces where the mathematics and physics formulas look lighter, and, at least to some of us, less imposing?
I wonder if the author realizes the Jehovah's Witnesses refuse to be drafted. In World War II Germany, they paid dearly for this refusal. Belief in a flat earth seems like a minor failing compared to the moral strength the Witnesses have shown in resisting one of the demands of "civilization" on its members.
Not to me. I was so happy when I tried MacWrite on my new (early 1984) Macintosh. I enjoy "fighting myself" because I am very unwilling to separate content and appearance. InDesign provides me with some succor but nowhere near what I would like. It is not visual enough. Why can't I align text by dragging a vertical line onto the text and request alignment to that? After all, this can be done with figures in InDesign, and unlike tabs, you get an immediate sense of what the result of the alignment will look like.
(A sad setback in word processing is Apple's Pages. It has two modes "word processing" and "page layout". I hope Larry Tesler never encountered it.)
I don't know how you're laying out text in InDesign, but in the workflow I was speaking about above, you draw a set of "text boxes", link them into a sequence, and then drop an RTF file onto one of the boxes to create a live link between the boxes and the RTF document's content. You then align text to things like guides/rulers by snapping the boundaries of the text boxes to those guides/rulers.
Changing the text layout automatically re-flows the text across the text boxes. That means: adding/removing a text box; editing the properties of a text box; changing the content in the linked RTF; or moving another element to partially overlap a text box, when the box is set to make the text dodge intrusive elements. You don't have to worry about resizing a text box to make room for something; that text just appears in the next box and pushes everything down.
And changing the visual layout does absolutely nothing to the text. That is: moving any of the text boxes, or moving/creating/destroying any element other than a text box, as long as this doesn't affect overlap; editing text boxes of a different linked document, or static text boxes (e.g. a masthead); etc. So, visual design tweaks are guaranteed not to wreck a finished typography pass, even if that means you're sliding the margins around.
For the sake of anyone who hasn't tried a system like this: picture creating an HTML CSS layout, with your composition embedded in a <div> with `overflow: scroll;`... but then picture a magical new <viewport> element, that provides distinct viewports onto a single scrolling container's render-context at different (contiguous, non-overlapping) scroll offsets. You could use such an element to implement CSS columns—but also any number of other arbitrary layouts.
I do understand the workflow you outlined, but I don't follow it, because I don't like it. In InDesign, I just open up a text box and start typing. Once I am within a text box, however, my irritation begins. I don't want to use tabs to align text. I suggested an alternative in my first post.
I think Xiki might help me escape the editing environment of the shell and REPLs provided via the shell (specifically the bash shell of Mac OS X Terminal, and various Scheme REPLs.) I want to work just as I can in TextEdit, or for that matter in the humble HTML textarea: put the cursor anywhere and start typing or deleting. The Mac OS X program Eddie permits some of this.
I want to agree with po from an entirely different point of view--a non-programmer often trying to figure out how a particular program (in a language I don't know) works.
If I spot the "my" or "my-" prefix, I take it that the corresponding token (e.g. "mypref", "my-limit") is not a reserved term of the language, but one the programmer is defining or assigning. So the "my" prefix can be helpful (at least to some non-programmers) and I don't want it co-opted to become a reserved word.
Just for complete clairty, my-* does in fact indicate a token that the author/programmer is defining (a custom property), in the same way that data-* properties do in HTML, which is why my-* was used. But I understand that you dislike it and I can appreciate why. As I mentioned to Po, the draft is open on github, and you are free to make better suggestions here as well... I don't think anyone is particularly married to my- we do know that var- and data- have caused what we think was unnecessary confusion. Set- was proposed and denied. What are your thoughts - that's what this is all about. Let's not wind up with something that people find unintuitive if as a community we can make it better.
"Thus, analog ICs are designed so only the ratio of resistors matters, not the absolute values, since the ratios remain nearly constant"
If it well known, a reference would be helpful.
(K. Shirriff, your posts offer a lot, even to those of us who do not have a technical background. Thank you.)