Question

The output of LVDT with input mechanical motion of 10 Hz and excitation frequency of 400 Hz will contain frequencies:

• A. 10 Hz and 400 Hz
• B. 400 Hz only
• C. 10 Hz only
• D. 390 Hz and 410 Hz

Hint:

LVDT output = AM signal with frequencies: carrier \(\pm\) modulation → \(f_c \pm f_m\)

Answer 1

The Correct Option is D

To determine the output frequency of a Linear Variable Differential Transformer (LVDT) given an input mechanical motion and an excitation frequency, we need to consider the concept of frequency modulation. When an LVDT is excited with a specific frequency, and there is a mechanical displacement (or vibration) present, the output typically presents frequency components that result from mixing these two frequencies. This results in frequency sidebands around the excitation frequency.

For the given problem, the LVDT's excitation frequency is 400 Hz, and the input mechanical motion frequency is 10 Hz. The output frequency will consist of sidebands due to modulation:

1. The frequency of the mechanical motion is mixed with the excitation frequency, resulting in the generation of sum and difference frequencies.
2. The sidebands are calculated as:
   • Upper sideband: 400 Hz + 10 Hz = 410 Hz
   • Lower sideband: 400 Hz - 10 Hz = 390 Hz
3. Thus, the output will contain the frequencies 390 Hz and 410 Hz.

Therefore, the correct answer is: 390 Hz and 410 Hz