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I have a Peltier module rated 12V 12A. I want to regulate voltage on it continuously from -12V to 12V, i.e. make an adjusted heater or cooler from the module.

There are some industrial solutions, but they are extremely expensive for me.

1) Is a switching regulator my only choice?

There is an alternative circuit here for 6A. Is it better or cheaper than just a switching regulator?

To reverse polarity I will need an H-bridge.

2) Is an electromechanical relay simplest and optimal solution here?

I do not need to switch it often, so limited cycle count is not an issue. Building H-bridge based on FETs seems to me very complex and expensive solution in this case.

Do you have any advices in solving this problem?

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You do really want a switching regulator, whether it's a commercially bought 'switching regulator', or the 6A 'alternative circuit' that you link to, which is PWM with output filtering.

As explained in the article around your alternative circuit, straight PWM, though efficient for the supply, is not efficient for the Peltier. As the cooling power depends on the current, but the resistive losses depend on current squared, it will generate more heat, that is run at lower overall efficiency, if there is any fluctuation in its supply. The ripple of a switch mode regulator is just fine. Slamming the power between 0% and 100% with PWM is not.

To look at some other PWM/switcher applications for comparison ...

a) you can PWM a filament lamp, as the heat output is what you want
b) you can PWM a brushed DC motor, stepper motor or solenoid, as its intrinsic inductance smooths the current out
c) you shouldn't PWM a Peltier, or a charging battery, because you want the current, and the excess \$I^2R\$ heat that you get during the 100% on phase is unwanted. You need more or less smooth DC for these applications.

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It sounds like you don't need to modulate the Peltier voltage very quickly. Think of a H bridge with each bottom leg being a switching power supply. That probably sounds a lot more complicated than it is. It's actually quite easy to control. You switch on one of the top switches depending on what polarity you want, then you PWM the opposite bottom switche for the drive level you want. Something slow like a Peltier isn't going to care if you take a whole millisecond or more to switch things at the polarity crossover.

Here is a snippet from the schematic of a real commercial product where I had to do something similar:

In this case I needed to control the voltage across two electrodes in electrolyte. The electrode specs were up ±24 V at up to 500 mA, but the concept is the same.

Q16 and Q17 are the high side switches of the H bridge. These are switched infrequently, and the current is arranged to be off during that time. In this case it was acceptable to take a few 100 ms to switch, so there was absolutely no need to try to switch the gates quickly. In fact, C58 and C59 deliberately slow down the switching to roughly constant current drive. This allowed for filtering the voltage to the electrodes with C60 and C61, but avoiding large current spikes when the polarity changed.

One side of the electrodes is always held at the supply voltage. The other side is then variably pulled down according to the PWM duty cycle applied to the opposite low side switch. These are Q20 and Q21. L12 and L13 filter the current pulses. Another way to think of this is that the low side switches are really switching power supplies. For the left leg, Q20 is the switch, L12 the inductor, D16 the diode, and C60 the output capacitor.

One advantage of using switching is that the result is efficient and therefore there is little heat to deal with. Q20 and Q21 are in small SOT-23 packages. You'll need something more beefy for your 12 A, but the concept is the same.

The two lines going off to the right near the bottom connect directly to the two electrodes, which would be the Peltier connections in your case.

The stuff at top is part of a high side current sensor. R49 is the sense resistor, and IC14 converts the differential voltage across R49 to a ground-referenced signal that eventually goes into the A/D of the microcontroller that produces the PWM pulses. Note that the flyback current of the inductors that goes thru the diodes D16 and D17 go all the way back to the top supply above the current sensor. Since the flyback current is also experienced by the load, it needs to flow thru the current sensor to get a reading of the true load current. The high side gate drive current does not go thru the load, so it's power is taken from above the current sensor.

The H bridge control signals HIGH1, HIGH2, PWM1, and PWM2 are directly from the microcontroller. In your case you probably can't get away with that for the low side switches since you need much higher current capability. FETs with that capability will need higher gate drive voltage, so you'll probably end up with a FET driver in front of each low side gate.

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Analog Devices makes a thermoelectric cooler control chip (ADN8831). There is an eval module available that works very well. If the eval module is in your budget it would be an easy solution. Linear tech may make an equal product.

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Peltier controllers up to 20 A start at 130 €. I doubt that you can beat this with your own solution considering parts and pcb price and also your time invested. Still, if you want to go that way, you have 3 alternatives:

  1. H-bridge with discrete transistors -- see Olins answer.

  2. Commercial H-bridge. Not many are available for 6 A and more. A DRV8432 would work but the Evaluation board is also around 120 €. You can also use PWM to control the current but do not forget to filter the output - non-filtered PWM reduces your peltier lifetime drastically.

  3. Use a linear regulation. An OPA549 would be suited, there are alternatives. Additionally, you need something to set the current, a DAC or programmable resistor. This solution is good for peltier performance and lifetime but is also the worst solution in terms of efficiency.

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