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In force-current analogy, analogous of displacement is

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Draw and explain the displacement measurement system using LVDT.

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LVDT has a single primary winding P and two secondary windings S1 and S2 wound on a cylindrical former. S1 and S2 have equal number of turns and are connected in series opposition. A movable soft iron core is placed inside the cylindrical former. When a.c. supply is given to the primary winding, voltages are induced in both the secondary windings. When a displacement is applied to the movable core, the flux linking with both the secondary winding changes and produces output voltage which is proportional to the displacement applied. The output voltage is Vo = (VS1 -VS2) where VS1 is voltage induced in S1 and VS2 is voltage induced in S2.

Working: Case I: When there is no displacement. When no displacement is applied to the core, the core is at normal position. The flux linking with both the secondary windings is equal. Equal e.m.f. is induced in both secondary windings or VS1=VS2 So, Vo = VS1 -VS2 = 0 The output voltage Vo at null position is zero. 

Case II: When the core moves to the left due to some displacement: When the core is moved to left of null position due to some displacement applied, more flux links with winding S1 than winding S2 Hence e.m.f. induced in S1 is greater than the e.m.f. in S2, that is VS1>VS2 The output voltage Vo = VS1-VS2 and is in phase with the input primary voltage.

Case III: When the core moves to the right due to some displacement: When the core is moved to right of null position due to applied displacement, more flux links with winding S2 than winding S1. So e.m.f. induced with winding S2 is greater than S1.that is VS2>VS1 Hence the output voltage Vo= VS1-VS2 and is 1800 out of phase with the input primary voltage. In this way any physical displacement of core causes the voltage of one secondary winding to increase while simultaneously reducing the voltage in the other winding. Output voltage Vo measured is equivalent to the displacement.

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