For directional sensing using an LVDT, it is necessary to determine the phase angle of the induced signal. In other words, phase-sensitive demodulation would be needed.
(a) First, consider a linear core displacement starting from a positive value, moving to zero, and then returning to the same position in an equal time period. Sketch the output of the LVDT for this "triangular" core displacement.
(b) Next, sketch the output if the core continued to move to the negative side at the same speed.
By comparing the two outputs, show that phase-sensitive demodulation would be needed to distinguish between the two cases of displacement