Assume magnetic field oscillating at *f*_{M} = 5 Hz with rms amplitude *B*_{0}, and a Hall sensor measuring the magnetic field at *f*_{H} = 23 Hz with a rms current *I*_{0}. Both current *I* and voltage *V* are measured with the system.

The magnetic field is

*B*(*t*) = √2 * *B*_{0} * sin(2*πf*_{M}*t*),

the current* I*(*t*) = √2 * *I*_{0}*sin(2*πf*_{H}*t*).

Then the Hall voltage becomes* V*(*t*) = *R*_{H} * *B*(*t*) * *I*(*t*)

= 2*R*_{H} * *B*_{0} * *I*_{0} * sin(2*πf*_{M}*t*) * sin(2*πf*_{H}*t*)

= *R*_{H} * *B*_{0} * *I*_{0} * {cos[2*π*(*f*_{H}–*f*_{M})*t*] – cos[2*π*(*f*_{H}+*f*_{M})*t*]}.

By measuring the current at frequency *f*_{H} and the Y-component of the voltage at *f*_{H}–*f*_{M} or *f*_{H}+*f*_{M} both *I*_{0} and *B*_{0} can be calculated.

The sum or difference of two arbitrary frequencies can be set for frequency 8. Both internally generated frequencies as well as PLL frequencies can be used.

Alternatively, if both frequencies have a greatest common divisor, a base frequency can be set to the greatest common divisor, and the frequencies can be selected as higher harmonics in the multiple harmonics mode.