Low-power applications such as e-meters (electricity or energy meters) often require a simple ac line-powered supply where a 3.3-V rail powers a microcontroller and charges a lithium-ion battery to 4.2 V. You can implement this with a mains-frequency power transformer or with a more complicated ac-dc (offline) power supply. Both approaches have well-known disadvantages related to a combination of weight, size, and complexity. Two simpler options are a full-wave capacitor-drop circuit with the bridge rectifier (Fig. 1) and similar half-wave circuit...
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