For safety, most people should be using protected cells. These have a built in circuit to prevent both overcharging and excessive discharge. Most of these circuits cut off the battery when it drops to 3.2 volts. If you do what I do and use cells pulled out of some device, these are unprotected cells. The device itself (the laptop pack) contained a circuit board that performed the protection function. If you use unprotected cells, you are taking a risk. If you use a good charger, you are protected on that end (but should still charge in some fire-proof location). Monitoring discharge is entirely up to you, and good advice is to recharge often and not take chances.
The problem with over-discharging unprotected cells is not when they are discharged, but when they get charged again. In other words, if a cell is discharged below a certain voltage (2.5 volts is commonly cited) internal changes take place which make it unsafe to charge again. This becomes a "russian roulette" situation, since there is no way to know what has taken place inside the battery. You may find a cell that measures 1.9 volts and charge it without problems. Or it may go into thermal runaway while charging and start a fire. Or it may work just fine for ever and ever. Or it may short out internally some impossible to predict time later and start a fire. So avoid over-discharging your cells and discard any you find that have been over-discharged. Or gamble -- it is up to you.
I have a link above to "testers". I was thinking of building one myself, but I see a variety of these for low prices on "Banggood", and have ordered two different ones. More when these arrive.
You can go nuts and buy a "hobby charger" like the RC model people use and become a total battery nerd. I am tempted, but they are pricey. But you can buy them cheap from China. The IMAX B3 and IMAX B6 are examples. Another to look at (some say it is better) is the Accucel-6. These expect to be driven by a separate power supply, so beware low priced units without one and/or look for a giant wall wart as part of the deal. I have seen rumors that the IMAX B3 source code is open.
These things are dangerous. You absolutely should get a high quality charger designed explicitly for lithiums and learn about the hazards. Lithium batteries can catch fire, explode, and cause fires, particularly if abused. Abuse can be either overcharging or discharging below a safe level. Most people should use only protected cells.
A solid rule is that no lithium cell should ever be discharged below 3.0 volts. 3.5 volts is a recommendable point to take a battery out of service and recharge it. Batteries should not be stored fully charged. It is recommended to charge a battery to 3.8 volts and store them in that state.
People say that at 3.3 volts, from 92 to 98 percent of the battery capacity has been used. It is also said that at 3.6 volts (at rest) is pretty much empty. Under load, a battery may drop as low as 2.5 volts when discharged.
Keep this table in mind:
4.2 volts 100% 4.1 about 90% 4.0 about 80% 3.9 about 60% 3.8 about 40% 3.7 about 20% 3.6 empty for practical purposes <3.5 = over-dischargedStoring batteries not in use in a refrigerator at about 40 percent charge level is probably a great idea. High temperatures are definitely not good.
You will hear claims that lithium polymer batteries offer higher energy density, and/or can deliver more current. Certainly they save weight by not having metallic casings. They must be enclosed in some kind of protective package to be used safely. Unless you need an unusual thin battery shape, these are probably not what you want. Certain lithium polymer batteries can deliver extremely large currents, which may be important to some applications (such as the RC model community). This needs to be evaluated on a cell by cell basis. Maximum current ratings vary widely among different 18650 cells, and almost certainly among different soft pack lithium polymers also.
One nice thing is that these have a (possibly) safe charging circuit in them. So if you are using questionable cells, and something goes wrong during charging, you haven't ruined your fancy expensive XTAR unit. On the other hand if something goes wrong while using one of these things to power your phone, you have to quickly toss the whole thing out the window.
My units have served me well, and I have yet to install truly doubtful batteries in them. Mine have a TP4221 chip inside and are the exact units described in the following article. They hold 4 cells. Checking with my meter shows that the unit charges nicely to 4.2 volts. I had some other cheap units that charged to significantly over the specification.
I have another power bank with a 8 pin FM9833E chip. You can find the data sheet (in Chinese) for this online. This unit holds two 18650 cells and I have yet to check charge levels.
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