Differences between single-section and two-section filters

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I am referring to the choke being used in power supply. Some circuit connects the choke to the rectifier without a cap and some has a cap. There is a voltage output difference but other than this, is there any particular reason to use each of them?
 
Forward converters as well as half/full bridge and push pull must not have a capacitor on the rectifier side of the inductor as the inductor is part of the voltage regulation circuit.
Flyback converters, however, must have a capacitor on the rectifier side. The LC filter afterwards is used to reduce noise. In an application that does not mind much noise (such as charging batteries or running motors), the extra filter can be omitted.
 
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