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I have a device with 4 series 1.5V D cells batteries (About 8000maHour).

The batteries last 40 hours, making the average draw around 200mA. The problem however is that the duty is about 2% at 1/3Hz, so it seems to deliver bursts of about 10A, and I don't really want to put in a 10A 60W supply for something that is only about 1.2W average. And unless my math has failed me, the bursts are 1000J so I would need about a 55F capacitor, which is out of the question.

Any one know of any other tricks I could use?

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And unless my math has failed me, the bursts are 1000J so I would need about a 55F capacitor, which is out of the question.

Your math has failed you. :-)

You mention that the duty cycle is 2% at 1/3 Hz. The period is therefore 3 seconds, and only during 2% of those 3 seconds does your device deliver 10 A. 2% of 3 seconds is 0.06 seconds.

While your device may consume 60 W while delivering 10 A, it does so for only 0.06 seconds, then "rests" for 2.94 seconds. This means that the energy delivered per pulse is only 3.6 J, not 1000 J:

$$60\text{ W}\times0.06\text{ s} = 3.6\text{ W}\cdot\text{s} = 3.6\text{ J}$$

This amount of energy can definitely be stored in a relatively non-exotic capacitor.

You may not even require a huge power supply. If the device was designed by someone competent, it would already have its own specialized power supply to deliver those 10 A pulses 2% of the time, so while the device can deliver 10 A pulses, it doesn't consume anywhere near 10 A.

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Find a suitable rechargeable battery capable of 10A peak current. Some quick research points to NiCd as having the lowest internal resistance. Once you have assembled a suitable pack, you only need to supply a little more than the required 200mA to keep them charged. As is often the case, batteries are a more practical choice than very large capacitors.

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