  Here, a generalized induction coil sensor model, more generalized than other
models, has been considered and the equivalent magnetic field of the coil
thermal noise and the sensor signal to noise ratio are calculated theoretically
based on the dimensions and geometry of the coil winding and its core. Our
calculations indicate that the equivalent magnetic field of the thermal noise
can be minimized by the coil to core weight ratio. Moreover, it is found that
the sensor signal to noise ratio can be maximized with only a special value of
core aspect ratio length to diameter of core ratio. The calculation results
here exhibit good agreement with the experimentally measured noise data.
