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What is the difference between a switch mode power supply and a transformer power supply?

Comparison: transformer power supply vs. switched-mode power supply

Unlike conventional power supplies with 50- or 60-Hz transformers, less magnetic volume is required for the same power due to the conversion to higher frequencies.
In the switching power supply, the transistor is always completely blocked or completely open and is therefore hardly heated. Thus, high efficiencies above 90% can be achieved. The disadvantage is that the circuit must be well shielded because of the internally used powerful AC frequency to ensure good electromagnetic compatibility, and that at the output is always a small proportion of this AC voltage measurable. This disturbs less digital circuits or chargers, but very much sensitive amplifiers e.g. in radios, hi-fi systems or EEGs.

Switching power supply Linear transformer power supply
More complex circuitry - high frequency Simpler design - low frequency
Shielding required to provide electromagnetic compatibility Scarcely any interference suppression measures necessary
Smaller and lighter design for same energy due to smaller magnetic volume of transformer Relatively large and heavy, due to large transformer
Higher efficiencies up to over 90%, economical in consumption, more favorable to the environment and customers Lower efficiencies, high energy consumption