Electronic – Calculating power requirements

Your post deals with several different aspects, which I'll clarify:

1) The power necessary to charge the battery can be almost anything. You can charge a battery with 1W or with 5W. The voltage must always be the same. If you use less watts, the resulting lower current means less charge and therefore longer chargning time. There is a maximum current at which a battery can be charged. Ususally this is 1C, where the C is the capacity of the battery which is 1650mAh. So, battery max current is 1650mA. In reality, it can be C/2 or other values depending on the battery chemistry. Chargers must remain below this

2) CNET must be wrong about 55W. At 3.7V you're talking about 14.86A which is very high and a battery of 1650mAh would likely get destroyed. I've worked with Cell Phones and although the peaks are high, they are never this high. Given a 1650mAh battery, you can draw 1650mA in one hour, or double in half an hour. In reality, the rate of discharge ends up changing the nominal capacity, so this isn't linear but an approximation.

As you calculated, the wattage is about 0.76W at 3G.

To answer in your question about the “PC power supply”. Briefly the switching mode ps does not have a good transient response in load changes and also they are generates lot of EMI. So you can not use in ,lets say, inductance dominated loads or in high end audio applications. It is common practice to banking (parallelize) capacitors, since this allows to sum their capacity as well as reduce their series resistance. So we can handle bigger currents with less dissipation and heating, since ripple current per microfarad is often increased by reducing capacitor sizes. Regarding max ripple current, do not forget to include the "ripple current multiplier" given at the operating temperature, an d also keep in mind that temperature of the capacitor core is hotter 3~5 oC /watt of ripple power compared with the case temperature. Usual heat dissipation factor is 0,00093W/oC/cm^2. So in a 4700μF/35V capacitor, a 10oC temperature rise limits the current to 2A In case of capacitors banking, main task is to keep them in low temperature (i.e do not place close to high heat generated or dissipated components, or use forced cooling methods) Bonding each cap even with hot glue to a cooler base helps allot. Also protect capacitors from high frequencies (i.e using of very fast and exceptionally soft recovery power diodes, or RC snubers) since elcap does not respond well in hf and ESR decrease more than twice at resonance. The type of capacitors that you have (temperature rating as well as geometrical size) plays important role to the dissipation factor (or tanδ) stated in data sheets (there is also a temperature and frequency derating). For banking we often use large diameter and short length capacitors. My experience limits to 20x1000μF/35V bank, but your is 50x4700μF.... Assume that your capacitors are uniform, or if you mix them keep in mind that each capacitor have a different discharging time. As already stated above, rectifier bridge plus heatsink sizing should carefully design because on this VA rates, the equivalent series resistance of transformer it is very low and now comparable to the total capacitor ESR. So it is very possible to need an external power resistor.

Regarding the comparison cost of the two: do you have price of a good torroidal transformer 2500VA that you need?