Interim Exam 1 5AIB0 Sensing, Computing, Actuating 3-5-2015, 14.00-15.00 Location AUD 11 Name: ID: This interim exam consists of 1 question for which you can score at most 30 points. The fina grade for this interim exam is determined by dividing the number of points you scored by 3. The soutions to the exercises shoud be ceary formuated and written down propery. Do not ony provide the fina answer. Expain your choices and show the resuts of intermediate steps in your computation. The use of a simpe cacuator is aowed. No graphica cacuator or aptop may be used during the interim exam. 1 / 6
Exercise 1: resistive pressure sensor (30 points) Strain gauges are used amongst others to measure pressure. Figure 1 shows one strain gauge that is attached to a thin meta strip (E = 250 10 9 N/m 2 ). When unoaded, the strain gauge has a resistance of R 0 = 150 Ω. The strain gauge has a gage factor of 2.50. To prevent damage to the strain gauge, the maxima current through it shoud be imited to 10 ma. active strain gauge (tension) Figure 1: Meta strip with one active strain gauges. The strain gauge is combined with three fixed resistors in a bridge circuit (see Figure 2) with a votage suppy V r. The fixed resistors R 1 and R 2 have a resistance of k R 0, and the resistor R 4 has a resistance of 150 Ω. The eectrica equivaent circuit of this sensor is shown in Figure 2. R 1 R 2 V r v s R 4 R 3 =R 0 (1+x) Figure 2: Bridge circuit with one strain gauge. (a) Show that the output votage v s of the sensor circuit is equa to: kx v s = (1 + k)(k + 1 + x) V r 2 / 6
(b) Show that the reative non-inearity error in the output votage of the sensor circuit is equa to: ɛ = x k + 1 + x (c) What is the change in the resistance of the resistor R 3 when a pressure of 100 10 6 N/m 2 is appied to the meta strip? 3 / 6
(d) Assume that resistor R 3 has a resistance of 150.15 Ω when a pressure of 100 10 6 N/m 2 is appied to the meta strip. What resistance shoud the resistor R 2 have to minimize the non-inearity error to 0.01% of the reading when a pressure of 300 10 6 N/m 2 is appied to the meta strip? (e) Assume that k = 4. What vaue shoud the votage suppy V r have to maximize the sensitivity of the sensor circuit shown in Figure 2 for a change in x? 4 / 6
(f) Give a definition (maximay 100 words) for the foowing terms: Transducer Sensor Sensitivity of a sensor 5 / 6
Formuae sheet Characteristic temperature of materia: B T1/T 2 Resistance: R = Strain: ɛ = d m ne 2 τ Stress: σ = F A = E d A = ρ A Poisson s ratio: v = dt/t d/ = n ( R2 R 1 ) 1 T 1 1 T 2 Change in specific resistance due to voume change (for metas): dρ ρ = C dv V Change in resistance due to strain: dr R = Gɛ Capacitance of fat pate capacitor: C = q V = ɛ 0ɛ r A d Capacitance of cyindrica capacitor: C = q V = ɛ 0ɛ r 2π n(b/a) Energy stored in capacitor: E = C V 2 2 Reuctance: R = 1 µµ 0 A Inductance: L = N Φ i = N 2 R Fux: Φ = B S Magneto-motive force: F m = Φ R = N i 1 Ampitude response of Butterworth LPF: H (f) = 1+( f fn )2n Sideways force on eectron moving through magnetic fied: F = q v B Transverse Ha potentia: V H = 1 i B N c q d sin(α) Radius of warping of bimeta sensor: r 2j 3(α x α y)(t 2 T 1) Dispacement of bimeta sensor: = r(1 cos( 180L πr )) Fow veocity and temperature difference: v = K ρ ( e 2 R S 1 T s T 0 ) 1.87 Votage across P-N junction (quaity factor 1): V = kt q n ( ) I I 0 Saturation current through PN-junction (quaity factor 1): I 0 = BT 3 e Eg/kT Thomson effect: Q = I 2 R I σ dt dx Petier coefficient: π AB (T ) = T (α A α B ) = π BA (T ) 6 / 6