4427 Semester 1 – 2014 Page 2 of 6 Faculty of Engineering & Information Technologies INSTRUMENTATION – AMME2700 FOUNDATIONS OF INSTRUMENTATION – AMME5700 Semester 1 – 2014 Duration: Three hours and Ten mins reading time SEAT NUMBER: _______________________________ LAST NAME: _______________________________ FIRST NAME: _______________________________ SID: _______________________________ INSTRUCTIONS TO CANDIDATES 1. Please read each question carefully. The value of each question has been written next to the question. Note that questions are of unequal value. Total mark of this exam paper is 100. 2. This examination consists of three (3) QUESTIONS (Q1, Q2, and Q3). 3. ALL questions must be answered. 4. Write your response to questions in the answer booklet provided. 5. Use a separate answer sheet for each question. Note that you can request a new booklet if it is not enough for your solutions. 6. Please ensure that your Name and Student No are written on each booklet you use. 7. Please write on the front of each answer booklet the designated Questions (Q1, Q2, and Q3). 8. Please indicate the Question number/s on the front of each booklet you use. 9. Non programmable calculators permitted 9. Check that you have answered all THREE (3) questions. Please check your examination paper is complete (6 pages) and indicate you have done this by signing below. This paper is not to be taken from the examination room. I have checked the examination paper and affirm it is complete. Student Name ________________________________________________________Date:___________ Q1 (25 marks) The circuit shown in Fig. 1a has been divided into three parts. In Fig. 1b the rightmost part has been replaced with an equivalent circuit. In Fig. 1c the circuit is simplified further. Please: 1) Determine the value of the resistance R1 in Fig. 1b; (5 marks) 2) Determine the value of the resistance R2 in Fig. 1c; (5 marks) 3) Find the current i1 and the voltage v1 shown in Fig. 1c; (5 marks) 4) Find the current i2 and the voltage v2 shown in Fig. 1b; (5 marks) 5) Determine the power absorbed by the 12Ω resistor in Fig. 1a. (5 marks) Fig. 1 Q2 (40 marks) A second-order, lowpass filter is shown in Fig. 2, in which vs=0.25u(t) is a step input. The filter has the following specifications. · Cut-off frequency of 4 rad/sec · The passband gain k=1 Please: 1) Determine the Laplace transfer function from the circuit diagram; (12 marks) 2) The quality factor Q; (5 marks) 3) Design the resistor and capacitor values. (8 marks) 4) Determine the Laplace transfer function ; (8 marks) 5) Using Inverse Laplace transformation, determine vR in the time domain when t>0. (7 marks) Fig. 2 Q3 (35 marks) An accelerometer with a charge sensitivity of 83 pC/g and a capacitance of 1000pF is connected to a voltage follower with an input connector capacitance of 15pF (in parallel with the cable capacitance), a 10,000pF blocking capacitor and a 100MΩ resistance. A 3m long cable with a capacitance of 312pF connects the accelerometer and the voltage follower. Determine: 1) The schematic of the instrument; (5 marks) 2) The instrument’s voltage sensitivity in mV/g; (10 marks) 3) The time constant of the instrument; (5 marks) 4) The minimum sampling frequency required to sample the data; (5 marks) 5) The gain required in order that the instrument can measure the acceleration from 0.01g to 1g using a 12-bit ±5V A/D converter. (10 marks) SOME USEFUL FORMULAE 1. Current and Charge 2. Basic Electrical Components 3. Impedance a. For resistor: b. For capacitor: c. For inductor: 4. Laplace transfer function a. and 5. Filters a. First order: is the cut-off frequency b. Second order: where, k is the passband gain, ωo is the cut-off frequency, and Q is the quality factor 6. Integration where, a, b, D are constant 7. Time Response of RC and RL Circuits where, τ is the time constant, for an RC circuit , and for an RL circuit . 8. Laplace Transform Pairs 9. Charge Sensitivity Model for Piezoelectric Sensors q is the charge generated by the pizeoelectric senor (pC) is the chare sensitivity of the transducer (pC/g, pC/lb, pC/N, pC/psi, pC/pa) is the mechanical quantity being measured 10. A/D converter resolution R=1/2M * FSV where M is the length of the digital word, FSV is the full scale voltage range. 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