The circuit is of a Passive Power Factor Corrector.
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Valley-Fill PFC Circuit
For low power applications, there's a rectifier circuit known as a 'valley-fill' rectifier. It's simple to implement, but is only suitable where a very high effective ripple voltage on the DC output can be tolerated. This limits its usefulness, but it is found in some low-end LED lighting circuits, and is also suitable for some CFLs and similar lighting products where the high ripple voltage is not likely to cause a problem.
The power factor improvement is much greater than one might expect, and a PF of a little over 0.7 is typical. The current waveform is still quite distorted though, and it's unrealistic to expect too much from such a simple circuit. THD measured 82% in the simulation of the circuit shown. While hardly anything to crow about, it's still better than having over 150% distortion or more.
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Essentially, the two capacitors are charged in series, but discharged in parallel. This means that when the peak of the applied AC falls, so too does the output voltage, until it reaches a voltage that's roughly half the AC peak (162V less a few diode voltage drops) and is actually the voltage across the capacitors in parallel. The output 'DC' therefore has half the applied voltage of ripple - 158V peak-peak in the circuit shown. As you can imagine, the applications for any rectifier/filter with this much ripple are limited.
It's interesting to see the current waveform, and it is shown below. The 2.2 ohm resistor helps to reduce the sharp peaks that sit on the top of the waveform. Higher values reduce the peaks more and reduce distortion, but result in higher power dissipation in the resistor, wasted power and less power to the load. While it might seem that adding a small inductor (say 10mH) instead of the resistor would be able to eliminate the spike on top of the waveform, it's not as effective as one would hope. The added cost and bulk isn't worth the small gain obtained.
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If examined closely in a simulation (it's not shown here for clarity), the 'DC' voltage varies from 158 to about 318V - that's a lot of ripple. The mains current waveform looks pretty bad, but it's much, much better than that shown for the standard rectifier and capacitor supply. The power factor is far better than expected, and although there are still some significant harmonics (which result from the distorted waveform), THD is far better than the previous version as well.
As noted though, this type of supply is only suitable where the high ripple is tolerable, and you won't find it used much any more. It's basically an idea that came too late, because cheap PFC ICs that are a great deal better in all respects came along only a short while after this circuit was first used. Until I started working with LED tube lights, I'd never seen it before, and now, only a few years later, I don't see it used in any of the new designs. The latest LED lamps are now using active PFC which is far better than any form of passive PFC can hope to be.