I am surprised to see that the ESR of tantalum capacitor for the same package decreases with the capacitances. Here is a series of tantalum capacitor.
If the ESR decreases with the capacitances for the same characteristic, why is it interesting to use low tantalum capacitance?
Thank you and have a nice day.
I will answer your question with a question:
Why wouldn't ESR vary inversely with capacitance?
If we have some method to change the relative cross-sectional area and dielectric thickness -- thus varying capacitance and voltage rating in the same package -- and, assuming ESR depends on the same cross-section, then it should be inverse -- inverse-square, even!
Now, the series shown happens to be fixed voltage, and this is probably where the production method of tantalum comes into play. Among other things. Point being, both assumptions end up broken -- that ESR should vary in any particular direction or not, I mean.
Generally, dry tantalum is manufactured by starting with the granular metal. This packs loosely, with ample space (porosity) between grains. It is (pressed? and) sintered to weld the grains together, producing a metal pellet with high surface area. The surface is oxidized, coated with a solid electrolyte (MnO2), then an electrode (silver).
("Wet" tantalum is generally similar, but the sintered pellet is anodized in sulfuric acid, then impregnated with a sulfuric acid gel; a silver or tantalum casing is hermetically sealed (with fused glass and/or solder) around the pellet. Basically the same thing, but different electrolytes, MnO2 vs. H2SO4.)
Already we see opportunities to adjust the process: grain size, angularity and aspect ratio, pressing force, and sintering time, can all be varied to tweak the pore space. Ideally the pores are evenly sized and spaced, and not pinched off from each other, allowing low and consistent ESR and high capacity from the pellet, but this might be varied to trade ESR for a bit more capacitance, for example.
Grain packing is a stochastic process; pellets might be coated, then sorted by value before packaging. Rejected values might be recycled (coatings stripped off, oxide growth adjusted to reach a new value at another voltage), or it might be that the overall process is consistent enough that tolerances are met with an acceptable reject rate. Such is the domain of industrial production, process optimization, and trade secrets -- who knows what exactly they do; they might not know, themselves, they've just tweaked parameters to give the desired result, damn the theory.
We also don't know how big the pellet is, if the encapsulation mold is mostly filled up or what. That the voltage isn't changing, and the ESR is changing by fairly minor amount, may suggest a combination of effects.
It's also worth mentioning that, tantalum capacitors are generally well derated. It's not clear how much the manufacturer participates in this, themselves, but a rule of thumb is to choose capacitors 2-3 times higher rated than operating voltage, suggesting that manufacturers historically have played a bit loose with ratings for some designers' taste. A partial-failure mechanism involves a self-healing process (with attendant momentary discharge of the capacitor), and there is a catastrophic destruction mechanism (the MnO2 electrolyte is also an oxidizer, which reacts exothermically with Ta metal). Failures are exacerbated by temperature cycling (especially high temperatures, including soldering), and low impedance power sources (tantalum are discouraged for use on unlimited-current power supplies). The manufacturer may choose their voltage rating to have a certain chance or rate of such failures (you'd have to check their quality policy, or ask an FAE), or it may simply be a process defined value (i.e., they grow enough Ta2O5 to meet a nominal X voltage rating) or test value (they were ran up to X voltage during test, for whatever duration and temperature the test takes). Hopefully it is all of these, but only the manufacturer knows for sure.
ESR is a measure how non-ideal the capacitor is. An ideal capacitor would have ESR = 0. So larger capacitors are better, as you might expect.
There are a few circuits (notably things like LDO regulators with output capacitors) that depend, for stability, on the ESR being within a certain range and for those we might want to use a specific type and value of capacitor. Or we could use a better capacitor and add resistance externally.
Larger capacitors than necessary are also generally more expensive than necessary and physically bigger than necessary, so a good designer would probably want to avoid that.
As the capacitance decreases, the DF is constant. So the ESR must decrease to maintain the “Q” factor of the capacitor.
So more than likely it is controlled by design. ESR is actually inversely dependent upon capacitance. So the bulk conductivity of the dielectric or the dielectric constant must be manipulated to reduce ESR as capacitance decreases.
There is a tolerance to that ESR which is very important but, not on the data sheets. A case in point: For a worst case analysis (wca) on a power supply for space the quality engineer from Lockheed insisted that I have to use the standard tables of tolerance of tantulum caps for space quality. That tolerance was listed as +/-50%. The EMI filter using those tantalums had a response outside of any curves within the wca. I took a batch of 20 of the tantalum caps and measured each one of them at 100kHz with a phase-gain analyzer. The ESR range was actually from 20% to 200% of nominal, much greater than the quality standard. . .and these were expensive "space rated" caps. As a side note, that same quality engineer said that we have to use the table tolerances of X7R caps, which was listed as +/-20%. I made it clear that those ceramic caps, at the 24V level they were being used at, was less than 50% of it's 0V value. Nope. He was against using the actual numbers. This gave me a lasting opinion on why old dinosaur organizations like Lockheed Martin and NASA takes 5 times as much money to develop a spacecraft than SpaceX does.
