Telemetry system, current sensor, and related methods for a drilling system

A current sensor configured to detect a signal current in a drilling system component of a drilling system, the signal current including encoded data, the drilling system configured to form a borehole in an earthen formation, the current sensor comprising:

• a magnetic body at least partially composed of a magnetic material, the magnetic body including a first portion that defines a gap and a second portion attached to the first portion such that the second portion spans the gap;
• at least one field coil positioned on the first portion of the magnetic body, the at least one field coil configured to detect a first magnetic field that passes within the magnetic body, the first magnetic field being induced by the signal current carried by the drill system component when the current sensor is positioned in proximity to the drilling system component carrying the signal current;
• and
• at least one drive coil positioned on the second portion of the magnetic body, the at least one drive coil configured to generate a second magnetic field,
• wherein when the current sensor is positioned in proximity to the signal current and the at least one drive coil generates the second magnetic field, the current sensor is adapted such that 1) the second magnetic field causes the second portion of the magnetic body to alternate into and out of magnetic saturation so as to modulate the first magnetic field that passes within the magnetic body, and 2) modulation of the first magnetic field induces a modulated signal in the at least one field coil.