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A
hall sensor operates by detecting the deflection of a current within a semicondustir material by an ambient magnetic field. The external DC supply is used to create the sense current through the sensor. The sensor will then output a voltage in response to the external magnetic field.
Therefore a Hall sensor will output DC voltage for a constant magnetic field and AC voltage for an alternating magnetic field or a mixed voltage (DC+AC) if the magnetic field has both a ststic and an alternating component.
A typical application is the contact-free measurement of an electric current by measuring the magnetic field produced by this current. This is what the sensors you use were designed for.Contrary to current transformers, Hall sensors are able to measure DC current, too (current transformes, as any wire-wound transformer, can measure AC current only.
A pure Hall sensor will not, however, output a DC voltage for an AC magnetic field. This will require rectification (and possibly filtering and amplification). I don't see where the datasheet states that the sensor delivers DC voltage from an AC magnetic field. What it
does state is that the output is ratiometric, meaning that the output voltage depends on both the magnitude of the magnetic field as well as the supply voltage. The consequence thereof is that you should use a well stabilized supply voltage to get consistent measurements of the current, or use the supply voltage (or a voltage derived from it by ratiometric division - resistive divider) as reference for an ADC (if you're going to digitize the sensor output).
Cheers,
Harald