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By definition, the diode clipper, also known as a diode limiter, is a wave shaping circuit that limits positive or negative amplitude, or both. A circuit which removes the peak of a waveform is known as a clipper. While a half wave rectifier is a type of rectifier which allows one half-cycle of an AC voltage waveform to pass, blocking the other. They have same functions, however, they are different. So what is the difference between clippers and half-wave rectifiers?
They both are wave form shaping... but not in the same way. However you can turn a clipper into a half wave rectifier by clipping all of the negative signal but none of the positive. See below: