A linear displacement sensor consists of a linear potentiometer as shown in figure 1. The value of the displacement of the cursor is designated Ax. 1. The effective travel of the potentiometer is 21 = 10 cm and its total resistance is 2R0. Deduce the expression of the resistances Rb(Ax) and Rh(Ax) of the potentiometer for a displacement Ax of the cursor concerning the middle position. 2. The measurement voltage Vmes, the image of the cursor position, is measured by a system that has an input impedance Rapp. Express Vmes as a function of Rb(Ax), Rh(Ax), Rg, Rapp, and Vg. 3. What does this expression become for Rapp>>R0? Express Vmes as a function of RO, Rg, Ax, 1, Vg 4. The sensitivity of a sensor is defined as the change in output for a given change in input. Sensitivity represents the slope of the transfer function: s= d dx (f(x) Deduce the sensitivity Smes of the measurement. 0 Ar R R, (Ax) == 2R R (Ax) R(Ax) R (Ax) Figure 1: Position sensor