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Exercise 1: resistive pressure sensor (30 points) Strain gauges are used among others to measure pressure. Figure 1 shows one strain gauge that is attached to a thin metal strip (E = 200-10° N/m²). The strain gauge is combined with three resistors with a fixed value into a complete bridge. When unloaded, the strain gauge has a resistance of 200 2. The fixed resistors also have a resistance of 200 2. The strain gauge has a gage factor of 2.00. To prevent damage to the strain gauge, the maximal current it them should be limited to 25 mA. Figure 1: Metal strip with one active strain gauge. The strain gauge and the three fixed resistors are connected in a bridge circuit with a voltage supply V₂. The electrical equivalent circuit of this sensor is shown in Figure 2. V₂C active strain gauge (tension) R₁ R₁ R₁ R₁ Figure 2: Bridge circuit with one strain gauge. (5p) (a) Show that the output output voltage u, of the sensor circuit shown in Figure 2 is equal: 2₁ = 1₂ = -V₂ (5p) (b) The sensor output voltage , has a non-linearity error in terms of the signal z. How could this non-linearity error be removed? (Explain your answer) (5p) (e) Show that the output voltage , of the sensor circuit shown in Figure 2 is equal to 2.5 mV when a pressure of 100-106 N/m² is applied to the metal strip and V, = 10 V. R3-R0(1+x) V2 -I 4+2x R₂ R₁ R₁=Ro(1+x) ww {2²² 2²³ Re Re www V₂ Vb R₂ www R7 www he -O Vo Figure 3: Sensor circuit with processing circuit. (5p) (d) The sensor circuit from Figure 2 i connected to an instrumentation amplifier (see Figure 3). Show that the output voltage , of the circuit shown in Figure 3 is equal to: 2R6 Rs -z -V. R+ 4 + 2x 6 = (1 + 2²/²6 ) ² Rs