Question

An ideal LVDT shows $2\,\text{V}_{\text{RMS}}$ from each secondary at zero displacement. One secondary has a phase deviation of $1^\circ$ from the expected $180^\circ$ opposition; otherwise the LVDT is ideal. If the differential output sensitivity is $1\ \text{mV(RMS)}/\mu\text{m}$, the output for zero displacement is _____(rounded off to one decimal place)} $\mu$m.

Hint:

At LVDT null, any small phase/amplitude mismatch leaves a residual differential voltage. Convert that residual to an equivalent displacement using the sensor sensitivity.

Answer 1

Correct Answer: 34.5

At null: $V_1=2\angle 0^\circ$ V and $V_2=2\angle 179^\circ$ V (series opposing, so differential output is vector sum).
\[ V_{\text{diff}} = V_1+V_2 =2\angle 0^\circ + 2\angle 179^\circ \approx 0.0349\ \text{V}_{\text{RMS}}=34.9\ \text{mV}. \] With sensitivity $1\ \text{mV}/\mu\text{m}$, equivalent displacement \[ x=\frac{34.9\ \text{mV}}{1\ \text{mV}/\mu\text{m}} \approx \boxed{35.0\ \mu\text{m}}. \]