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A Name_________________________ Date__________________________ Mailbox #_____________________ MAE 411 Spring 2019 Mid Semester Test #1 This test is closed book and closed notes. Show all work to receive full credit. Numerical answers should be rounded to 3 significant figures and must include proper units . Use of cell phones and large memory/programmable calculators is NOT allowed. 1). An analogue to digital converter has an output word length of 10 bits and a quantization error of ±0.0195 V. 1a). Calculate the resolution in Volts. (5 pts) 1b). As part of the analogue-to-digital conversion process, the assumed input range is partitioned in subintervals. What is the size of a partition subinterval? (2 pts) 1c). The assumed or expected range of the input signal could be (consider rounding off)… (circle one) (3 pts) a) ±40 V b) ±20 V c) ±10 V d) ±0.039 V e) ±0.0195 V 1d). What should be the assumed input span to obtain a resolution equal or better than 2.45 mV, with 10 bits? (5 pts)

2). A Wheatstone bridge has a single strain gauge in one arm (R1). The nominal resistance of the strain gauge is R = 100 Ω and the gauge factor 2.2. The power supply of the bridge provides 5V. 2a). Assume that you need to locate the sensor at a distance using long leads. Explain what do you need to do to eliminate the undesirable effects of the long leads resistances and their variation with temperature. (5 pts) Note that the general input/output relationship for a Wheatstone bridge circuit is: 𝑉 𝑜?? = 𝑉 ? ( ? 1 ? 1 +? 2 − ? 3 ? 3 +? 4 ) . 2b). Draw the Wheatstone bridge circuit (5 pts) and determine the values at balance of all resistances for the scenario at 2a. (5 pts) 2c). For the calculation of the output of the Wheatstone bridge, two linear relationships are available: Rel. #1: 𝛿𝑉 𝑜?? = 𝑉 ? 𝛿? 1 ? 1 +? 2 Rel. #2: 𝛿𝑉 𝑜?? = 𝑉 ? 𝛿? 1 ? 1 +? 2 ∙ ? 2 ? 1 +? 2 If the measured strain is 0.0001, calculate the output of the Wheatstone bridge for the resistance values obtained at 2b (5 pts) . Explain which relationship you use and why. (5 pts)

4). Fill in the blanks (1 pt each) : 4a). The ratio of the difference amplifier gain and the common mode gain is called ……………………………..………………………….. 4b). If the sensor input range is [-15, 15] Volts, then the span of the input is ……………………….. 4c). A piezoelectric sensor can be typically used to measure ……………………….. 4d). An absolute optical encoder with an 8-bit output must have ………… tracks. 4e). Give an example of an 8-bit word with the least significant bit equal to 0 and the most significant bit equal to 1: ……………………. 4f). Protection against wrong polarity can be achieved using a …………………..……diode. 4g). The feedback loop of a logarithmic amplifier contains instead of the feedback resistor a……………… 4h). To use the standard conversion tables directly, the reference junction of a thermocouple must be at ………..degrees Celsius. 4i). A sinusoidal signal with frequency 400 Hz and amplitude 2 V is the input to a low-pas filter with cut-off frequency equal to 400 Hz. The amplitude of the output will be…………….. 4j). A band-pass filter with cut-off frequencies of 1000 and 2000 Hz can be used to eliminate frequencies that are………….……..the range [1000, 2000] Hz. 5). For the figure below, answer each of the following questions by circling one correct answer (2 pts each). 5.1). The figure represents……. a). an inverting amplifier. b). a non-inverting amplifier. c). a difference amplifier. d). a comparator. e). a voltage follower. f). a Wheatstone bridge. 5.2). Which statement is true in general for the electrical potential at X?

a). Potential at X is equal to zero. b). Potential at X is infinite. c). Potential at X is equal to potential of the ground. d). Potential at X is virtually equal to the output voltage. e). Potential at X is virtually equal to the input voltage. 5.3). The resistor R 2 is typically called….. a). input resistor. b). output resistor. c). feedback resistor. d). ground resistor. e). input/output resistor. 5.4). The current flowing into the operational amplifier from X is….. a). very large. b). virtually zero. c). dependent on the input voltage. d). dependent on the output voltage. e). dependent on the values of the two resistances. 5.5). The impedance between the input ports of the operational amplifier is….. a). extremely large. b). extremely small. c). virtually zero. d). dependent on the output voltage. e). dependent on the input voltage.