[tasty_freeze]

I learned this in a circuits class I took back in college, around 1984. Specifically, it was about amplifier circuits an op-amp design. Such designs are a puzzle of tradeoffs, and the teacher emphasized that often the "optimal" design is an inferior design in the light of real world constraints.

The globally optimal point on whatever thing we were optimizing might indeed be the highest peak of the graph, but if it is a sharp peak, any deviation in the voltage, temperature, or the real world values of the components would put the operating point far down the slope of that peak.

It was much better to find a reasonable operating point that had low sensitivity to voltage/temperature/component values but had acceptable behavior (gain, noise, whatever was important).

The surprising thing I learned from that class is that even though resistor and capacitor values and the gain of individual transistors of IC op-amps is an order of magnitude worse than for discrete designs, the matching of those terrible components was an order of magnitude better than for discrete components. Designers came up with many clever ways to take advantage of that to wring terrific performance from terrible components.

For example, say the nominal value of a given resistor in the design might be 4K ohms, and in the discrete design they might be 2%, or 1%, or 0.5% off (the ones with tighter tolerance get ever more expensive), while in the monolithic design the tolerance might be +/- 20%. But all the resistors would be off by the same amount and would match each other to a fraction of a percent, even across temperature and voltage variations.

The other funny effect is that when you buy a discrete 2% tolerance resistor, the distribution isn't gaussian around the mean. That is because the manufacturers have measured all of them and the ones within 0.5% get marked up and put in the 0.5% bin, and the remaining ones within 1% tolerance get marked up less and get put in the 1% bin. As a result, the distribution is bimodal on either side of the "hole" in the middle.

[stefanpie]

This brings flashbacks of standing next to part bins in circuit labs with a multimeter in hand, trying to match components. Unfortunately, the TAs and course instructors did not emphasize your point, and the measured part values and thus the measured filter cutoffs had to be close to perfect to be checked off.

In the past, I have looked at using optimizers to solve for component values of complex analog circuits. I only looked at optimizing accuracy at one corner, but it would be interesting to see what people have done to optimize multiple variables, like including noise, for multiple corners. I think I've seen some Monte Carlo simulation mentioned once to suggest fuzzy solutions within some specification. I would be curious to see if others know more about this.

[kwhitefoot]

Surely anyone doing analogue design for serial or mass production would do a sensitivity analysis, even in 1984. Now it should be much easier to repeatedly randomise the values of every part within their tolerance and run a simulation to check that the end product remains in spec.

You might even do this in order to find out if wider tolerance parts would be good enough and save a little money.

[nonrandomstring]

> measured all of them and the ones within 0.5% get marked up and put in the 0.5% bin, and the remaining ones within 1% tolerance get marked up less and get put in the 1% bin. As a result, the distribution is bimodal on either side of the "hole" in the middle.

That's a great explanation of how iterative tolerance filtering works and why that happens!

[rcxdude]

That last part is a bit of a myth, or at least it's something that doesn't consistently happen, at least nowadays. Binning parts is expensive, and for something like a resistor it's rarely worth it, so it's much more likely it's just a well dialed-in manufacturing process and design which stays within that tolerance.