原创 Questioning assumptions

Is it true that men become curmudgeons as they get older?

Anecdotal evidence suggests this is so. I see bits of it in myself, my friends, and the previous generation (though I have observed that after 75 or 80 a lot of men mellow greatly). For instance, for some time I've gotten increasingly impatient or worse with the behaviour of our elected officials. As one who writes it's hard not to express outrage in this or other forums about these issues.

But this is not the place for political rants. It is, however, a reasonable place to express frustration with some approaches to engineering.

A recent article I read about ultra-low power design contains this gem about CR2032 batteries: "A part of the coin cell's energy is exhausted through self-discharge; another part is not viable due to the increased source impedance near end-of-life. Both are assumed to take 20% of the capacity away."

Huh? Who assumes that? Why would an engineer base anything important on an assumption? If some critical parameter is an assumption, at the least cite chapter and verse so the thoughtful engineer can examine the evidence himself.

The best engineers are pessimists. They assume one thing: everything will go wrong. That network of 5% resistors will all come in clustered at the worst possible end of the tolerance band. The transistor's beta will be just exactly at the datasheet's min value. The op amp's gain-bandwidth product will be lower than the rated min due to PCB parasitics.

Datasheets in many cases are getting worse. Far too many list typical specs in lieu of min or max. If worst case is listed that's often just for extreme cases, like at some greatly elevated temperature. While that's important data, we need to understand how components will work over the range of conditions our systems will experience in the field.

Firmware people should share the same curmudgeon-ness. The C language's sqrt() can't take a negative value, so it makes sense to check or guarantee the argument is legal. Weird stuff happens so we liberally salt the code with asserts(). We should use C's built-in macros to insure floating point numbers are, well, floating point numbers and not NaNs or some other uncomputable value.

As for that assumption that "source impedance" and self-discharge account for 20% of the capacity, that's simply wrong. For almost a year I've been discharging CR2032s and have gobs of data points, which, are still being turned into meaningful information. In these ultra-low power applications coin cells don't behave like anything I have seen published.

Everyone uses "internal resistance," rather than impedance, to describe their reduced ability to supply current as they discharge, but that's merely a proxy for some complex chemistry, since a load on the battery causes the voltage to continue to drop the longer the load is applied.

The following chart in the figure shows experimental results on nine Panasonic CR2032s. All are from the same batch; all are from a very reputable, high-volume distributor (Digikey). The data—real, experimental results, not assumptions—are interesting and puzzling.

Figure: Experimental results on nine Panasonic CR2032s.

What the heck is going on with battery five? It dies at half the rated capacity, mirroring the behaviour of a CR2025. But it is visually identical to the other eight, has the same markings, and is the same size. Is this just a dud or is it something we can expect?

The batteries are being discharged at a 0.5 mAh rate so should die (vendors rate "dead" at 2.0V) at about 440 hours, though they do not specify what this means. Is it measured under any load? The charted data is the battery voltage about a millisecond after connecting a 10 mA load, which is probably a light load for an MCU which has woken up and is doing work. If there's any comm involved (think the "Internet of things") expect much higher current levels, even if for just a very short period of time.

Consider the internal resistances (IR). At the 300 hour point, well short of the 440 we expect, the average battery is at 2.5V with an IR of about 40Ω. Ultra-low current embedded systems can easily take tens of mA for a few ms when awake; if the system pulls just 25 mA (15 more than the 10 being pulled in the charted data) the voltage will drop below 2.0 at 300 hours. The battery is effectively dead long before its rated capacity is used.

Systems are getting extraordinarily complex. If we don't question our assumptions that gadget may be built on quicksand, sure to fail if our guesses prove to be incorrect. In this era of crowdsourcing it's easy to rely on hearsay—or Internet-say. But a question lobbed onto the net usually elicits a dozen conflicting answers, each of which is claimed to be authoritative.

As Joe Friday didn't say: "Just the facts, ma'am."