Is it ever a good idea to put lithium ion and NiMH batteries in series?

Not that I actually have a need for something like this, just curious about it.
Let’s say you wanted a 5 volt power source, but you only have lithium ion and NiMH batteries lying around.
The lithium ion is 3.7 volts and the NiMH is 1.2 volts. Anything wrong with putting them in series to get around 5 volts? I guess a consideration is to make sure the watt hours for each battery is the same, which you can achieve by putting the right combination of parallel lithium and parallel NiMH in series. Any other considerations?
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Generally a bad idea. What matters is the internal resistance of each cell. If this isn’t in balance you will end up charging one of the cells instead of discharging it. What makes things harder is that the internal resistance changes with state of charge, and does so in a different manner for different chemistries. So you are pretty much guaranteed to have it wrong at some point.

I don’t think there would be a problem of charging if 1 Li-íon cell and 1 NiMH cell were placed in series - I think they would need to be placed in parallel for the Li-ion to charge the NiMH cell.

Would it potentially be possible to use 1 cell of each chemistry in series for a quick / emergency 5v supply?

If you want 5 volts from a lower voltage (3.7 from a Lithium Ion, or commonly 3.0 volts from a couple of AA batteries or similar), the best way to do it is with a DC-DC step up converter, aka boost converter. There are quite a few ICs out there specifically designed for this task, though they usually require a few additional components like an inductor and a diode and cap or two.

You usually end up with a limited amount of current, but hey, you’re powering this from batteries in the first place, so that’s kinda expected.

Your typical boost converter will run a square wave through an inductor to store up energy in the inductor’s magnetic field. Then the semiconductor will switch off and the inductor’s energy will be shunted through a diode into a capacitor. The capacitor thus gets charged up and provides the higher voltage output to your external loads. Your output can be a bit choppy, but using a high frequency switcher and a decent sized capacitor will reduce the ripple in the output.

Dedicated ICs will do most of the work for you, but the inductor and output cap are generally too large to fit on the IC and are thus required as separate components.

One of them is going to go dead first, and when it does, the other battery will charge it, sometimes with rather disastrous results. The batteries can swell, leak, or possibly explode, which is generally unkind to whatever they are in or on at the time.

You can do it in a pinch for an emergency, as long as you are very careful not to let either battery discharge too far, but I wouldn’t recommend it. Too much of a chance of something going kablooey.

If there is 1 cell NiMH and 1 cell Li-ion in series let’s say the NiMH goes dead first, will the circuit just shut off / voltage drop to zero?
At this stage the positive terminal of one will be connected to the negative terminal of the other cell. For one to charge the other, wouldn’t the positive terminals need to be connected together (and negative terminals)?
Or would the Li-ion try to ‘reverse’ charge the NiMH?

Think of it this way. When the NiMH battery goes dead, you still have a circuit, with current flowing out of the Li-ion battery, through the dead NiMH battery, and through the original circuit load. The circuit will not just shut off.

The NiMH battery will get charged (in the reverse direction) by this current.

If enough current flows, this could be very bad for the NiMH battery (vented hydrogen, the battery overheating and catching fire, an earth-shattering kaboom, that sort of thing).

I thought many applications have batteries in connected in serie. What is the fundamental difference between one pair of batteries in serie vs. an other pair of batteries in serie?

There’s actually a couple different questions here. The first is if the circuit will shut off. The original circuit you want used? Yes, since there won’t be sufficient voltage for the circuit to function. Some circuit involving the batteries? Well, no, which is the problem.

Does the voltage drop to zero? Which voltage? For each battery? To power the circuit? Also, no matter what you are measuring, probably not. It’ll be lower than nominal but probably not absolutely 0V.

It’s important to note that a ‘dead’ battery is probably not completely drained. In an open circuit (unconnected), a 3V drained battery could well measure 2.3V on a DMM but drop closer to 0 when hooked up to something.

This is also why even for matched sets of batteries (say, 4 AA matched dry cells from the same packaging), it’s better to replace all the batteries at the same time. You run into the same problem with internal resistances and depending on the relative discharge states the newer batteries will attempt to charge the older ones.

Many applications do have batteries in series (flashlights, TV remotes, etc). You should always use batteries out of the same package so that they go dead pretty close to simultaneously, and you don’t end up with one charging the other.

People have ruined flashlights and radios by having one good and one nearly dead alkaline battery in there. The dead alkaline gets charged, swells, and leaks goo inside the flashlight, and that goo corrodes the metal contacts inside the flashlight.

In most cases, though, your flashlight gets too dim to be useful or your TV remote stops working, so you change the batteries before one of them really gets a chance to charge the other and cause any damage. So, damage is rare, but it happens.

In this particular case, without knowing the amp-hour ratings of each type of battery, there is a definite potential for danger. Depending on what the load is, the fact that the Li-ion battery has a much higher voltage may make it seem like both batteries still have a fair amount of capacity in them even though the NiMH battery might be flat dead.

What do you mean?

In fact, strictly speaking, batteries are always in series. A “battery” is a set of multiple cells in series to produce a higher voltage (it’s similar to a whole bunch of artillery pieces being a battery of artillery). In this sense, a 9V, a car battery, and a lantern battery are all true “batteries”, but an AA or a D aren’t. But of course, the language has evolved to where they’re all called batteries, even the ones with just a single cell.

The Librarian, when you put two of the same kind of cell in series, they’ll both go dead at the same rate, and so by the time one’s drained completely, the other is as well, or so nearly so that it makes very little difference. But with two completely different kinds, one is likely to die much quicker than other other, when the live one still has enough juice to significantly reverse-charge it.

Yep:

Cells in Series: Simulating a Failed Cell during Discharge.

The Li-Ion battery charges up to 4.2 volts so that’s close to 5 volts. If I want a quick and dirty way to get 5 volts I’d use 2 Li-Ion batteries in series and use diodes in series to drop the voltage from 8.4 volt to 5 volt.

Each diode cause a 0.5 volt drop so to drop 3 volts it’ll take 6 diodes in series.