# Sensor Sense: Variable-Reluctance Sensors

June 2, 2009
VR sensors use variations in magnetic-field densities created by changes in reluctance within a magnetic circuit.

Automobiles today contain a growing number of position and speed sensors that look at rotation. From transmission input and output shafts, crankshafts, and even individual tire speeds, these sensors provide signals to control transmission shift points, cruise controls, limited-slip or traction controls, and antilock-braking systems. Variable-reluctance (VR) sensors work well for these automotive applications because of their simplicity in design and their operational ruggedness.

Reluctance is defined as the ability of a material to pass a magnetic field, and is often likened to resistance in an electrical circuit. Ferrous materials possess a low reluctance as they help concentrate magnetic fields that easily pass through them. Mathematically, the equation for reluctance looks much like Ohm’s Law:

R = mmf/Φ

where R = value of reluctance, mmf = magnetomotive force in ampere-turns, and Φ = intensity of the magnetic field in Webers.

In its simplest form, a VR sensor consists of a coil of wire wound around a permanent-magnet armature. The target of the sensor is typically a gear or other toothed ring made from ferrous materials. As the ring rotates in front of the sensor, the teeth concentrate the magnetic flux when they align with the magnetic poles, but let the flux expand outward when the poles are over a gap between the teeth. The change in flux density created by the change of reluctance at the poles induces an electrical voltage in the coil, creating the output from the sensor.

The frequency of the output is controlled by the speed of rotation and the number of teeth in the target. For example, a 100-tooth gear turning at 1,800 rpm generates an output frequency of 3,000 Hz. This type of sensor arrangement is often referred to as a tone wheel, as the sensor output creates an audio tone.

A variation on VR-sensor design replaces the permanent magnet with a small dc-bias current through the coil creating an electromagnetic field. The sensor output is read as an ac signal riding on top of the dc bias. Besides generating the sensor’s magnetic field, the dc bias can also detect whether the connection to the sensor is broken for a confidence check on sensor operation.

Edited by Robert Repas

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