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A common technique used in battery charging algorithms is Constant Current / Constant Voltage. That is to say, initially a battery is charged by applying a constant current (which I believe is what is commonly called 'fast-charge'), up to a sensed condition, and then Constant Voltage is applied (which I believe is what is commonly called 'trickle-charging').

I envision this working (at least logically) as having (1) a Constant Current Source circuit set to the fast charge current and (2) a Voltage Regulator set to the fully charged target voltage, and switching the positive terminal of the battery between these two circuits.

What is a useful electrical model (e.g. for simulation) for a discharged rechargable battery? If it matters, I'm most interested in Lithium cell chemistry (Lithium Polymer to be more specific).

UPDATE

In order to get some more concrete feedback on this question (maybe this should be a separate question?), what does a circuit that practically / realizably implements CC/CV charging actually look like? From there, if you were to want to simulate this circuit, in SPICE or CircuitLab.com or whatever, how would you actually model the battery in that circuit?

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It is like a desktop current/voltage limit supply where it applies the maximum of the setting up to the limit, so you start seeing too strong a short for the CV limit to kick in, the CC limit stops you. The voltage finally builds up and you are limited by CV and it slowly trickles the rest of the way. This seems to be what you know, the only serious feedback I have is that this is going to be very different per battery, they mostly all have a specific mode they are looking for. The temperature change sensing for some batteries freaks me out. I know it is safe, and why, but still... –  Kortuk Jan 16 '13 at 20:40
    
Are we talking SPICE here or a mathematical formula? (or both?) –  Oli Glaser Jan 16 '13 at 23:03
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1 Answer

It sounds like you got the charging description of a lead-acid battery. Other battery types need to be charged in different ways.

For the lead-acid case that you describe, all you need is a single power supply that is both voltage and current limited. Initially the battery voltage will be low, so the power supply current limit kicks in. Eventually the voltage reaches the float level, so the power supply starts regulating voltage and the battery draws less current than the limit.

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I think it (CC/CV) applies to Lithium chemistries as well from what I've read... –  vicatcu Jan 16 '13 at 18:53
    
@Olin: Many of the VRLA monoblocks I've used in the past have a lower max voltage under constant current charge, and don't allow going to the higher constant "finish" voltage until the current has tapered below a certain threshold. For these batteries, the voltage- and current-limited supply approach can shorten battery life if the "finish" voltage is used as a limit for the constant current phase. The datasheet is king. –  HikeOnPast Jan 16 '13 at 18:57
    
@Hike: I agree. There are lots of different batteries that need to be treated differently. You can get aways with fixed voltage and current limits for lead-acid most of the time. Even then, for a really low lead-acid battery you want to charge with low current until the voltage builds up to a minimum level, then go to the fixed voltage/current limit regime. –  Olin Lathrop Jan 16 '13 at 19:01
    
It's also important to note that with some battery chemistries, the proper "float" voltage may vary depending upon temperature and other factors; trying to charge a battery pack to a voltage higher than its natural float voltage may severely damage it (likely pushing its natural float voltage even lower!), and trying to charge a battery pack to a voltage lower than its natural float voltage leave much of its capacity unutilized. –  supercat Jan 16 '13 at 21:26
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