ELEC 5516 ELECTRICAL AND OPTIMAL SENSOR DESIGN
ELECTRICAL AND OPTIMAL SENSOR DESIGN
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ELEC 5516 ELECTRICAL AND OPTIMAL SENSOR DESIGN
MID-SEMESTER ASSIGNMENT
This assignment consists of six questions, please answer them with
detailed solution steps and submit the answer by Sunday 23 April, 2023
Question 1
Four strain gauges are bonded onto a cantilever as shown in Figure 1. Given that the
gauges are placed halfway along the cantilever and the cantilever is subject to a
downward force of 0.5 N, use the data given below to calculate the resistance of each
strain gauge:
Figure 1
Cantilever data: Strain gauge data:
Length l = 25 cm Gauge factor G = 2.1
Width w = 6 cm Unstrained resistance R0 = 120 Ω
Thickness t = 3 mm
Young’s modulus E = 70 × 109 Pa
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Question 2
A variable dielectric capacitive displacement sensor consists of two square metal plates of
side 5 cm, separated by a gap of 1 mm. A sheet of dielectric material 1 mm thick and of
the same area as the plates can be slid between them as shown in Figure 2. Given that the
dielectric constant of air is 1 and that of the dielectric material 4, calculate the
capacitance of the sensor when the input displacement x = 0.0, 2.5 and 5.0 cm.
Figure 2
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Question 3
By taking a central flux path, estimate the inductance of the sensor shown in Figure 3
(a) for zero air gap;
(b) for a 2 mm air gap.
Assume the relative permeability of core and armature is 104 and that of air is unity.
Figure 3
6.0cm
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Question 4
An iron v. constantan thermocouple is to be used to measure temperatures between 0 and
300o C. The e.m.f. values are as given in Table 4.
(a) Find the non-linearity at 100 o C and 200 o C as a percentage of full scale.
(b) Between 100 o C and 300 o C the thermocouple e.m.f. is given by ET,0 = a1T + a2T
2.
Calculate a1 and a2.
(c) The e.m.f. is 12500 μV relative to a reference junction of 20o C and the corresponding
reference junction circuit voltage is 1000 μV. Use the result of (b) to estimate the
measured junction temperature.
Table 4
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Question 5
The resistance Rθ kΩ of a thermistor at θ K is given by:
Rθ = 1.68 exp[3050×(1/θ-1/298)]
The thermistor is incorporated into the deflection bridge circuit shown in Fig. 5.
(a) Assuming that VOUT is measured with a detector of infinite impedance, calculate:
(i) the range of VOUT corresponding to an input temperature range of 0 to 50 o C;
(ii) the non-linearity at 12 o C as a percentage of full-scale deflection.
(b) Calculate the effect on the range of VOUT of reducing the detector impedance to 1
kΩ.
Figure 5
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Question 6
An analogue-to-digital converter has an input range of 0 to 5 V and incorporates a 12-bit
encoder.
(a) Assuming a binary encoder, find:
(i) the maximum percentage quantisation error;
(ii) the digital output signals corresponding to input voltages of 0.55 V and 2.63 V.
(b) Convert the binary codes of (a) (ii) into hexadecimal form.
(c) Repeat (a) assuming a three-decade, 8:4:2:1 binary-coded decimal (b.c.d.) encoder.