Let's look at a random case.
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I have some capacitors identified as TPSE107K016R0. I know that they're a 100uF 16V 10% low ESR capacitor. What else can I find...
Going to Digikey and sticking in the part number tells me that the part number is incomplete. It should have a few more digits on it e.g. TPSE107K016R0125. From Didgikey's catalogue I can see that they come in 125, 100, and 55 milliohm ESR and that they are manufactured by AVX.
Clicking on one at random I see that they are TPS series and that there is a link to the series datasheet. Searching through that I note that they're all in an E case and they have significantly different ripple current ratings. But it doesn't tell me what part markings I should see, and whether that will identify the ESR.
However it does say "For part marking see page 132". This document goes from page 33 to page 43, so clearly this is part of a much larger document. Digikey also has links to a photograph and technical drawings, but these are totally generic, the photo having no markings shown at all). So it's off to AVX...
The obvious site is
http://www.avx.com, and that turns out to be correct. Looking at "technical Papers" and "Tantalum Capacitors" yields a document called "AVX TPS Series III..." which after a brief synopsis leads you to a very technical paper describing these capacitors and includes a subset of the specs we've already seen. Possibly of interest if you need some construction details, but not what I'm looking for...
After some searching around, I again search for TPSE107K016R0 on the AVX site and look at the "Master Catalog". Sure enough pages 33 to 43 correspond to the other document, and page 132 tells you what you'll see on the devices themselves.
According to the manual, you cannot tell the ESR value from the case (only capacitance, voltage, and lot code).
So how do I tell if I should use the 55, 100, or 125 milliohm version as a replacement?
For a single capacitor you're looking at between $US8.50 and $US13.75, so they're not cheap.
Let's try another example...
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An electrolytic capacitor, surface mount, with the markings 47 / 35A / P25 over 3 lines. It's a small aluminium cylinder. There is no manufacturers logo. The only other marling is a dark segment painted on the top to indicate polarity.
A good guess is that it's 47uF 35V, but it could also be 25V. Can we find any specs?
I happen to know the part number of this capacitor, but going on what I have here, I would have extreme trouble unambiguously identifying it if it were on a board.
Third example
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Some through-hole electrolytic capacitors in a power supply labelled Suntan / CD286 / 105 degC / 25V / 470uF.
It's pretty unambiguous what the capacitance and voltage rating are. In addition, this being a 105C part amongst other 85C parts tells me that it's not rated 105C because of elevated ambient temperature -- so it's probably a low ESR capacitor.
I go to digikey and quickly look up 470uF 25V, and after I tell it that I'm looking for aluminium electrolytic capacitors I note that "Suntan" is not a brand that is listed.
http://www.suntan.com/ clearly isn't the right place to go. A quick Google tells me that I want
http://www.suntan.com.hk/. A couple of clicks gets me a datasheet on CD293 capacitors, which isn't overly helpful, but does tell me that CD286 is the series code.
Back to Google and a quick search for CD286 yields a page on the suntan site with a PDF. This has the capacitor in question with height and diameter of the package (for confirmation), and it's low ESR. It has ESR at 2 temperatures and max ripple current.