EE3901/EE5901 Sensor Technologies
Week 9 Tutorial

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College of Science and Engineering, James Cook University
Last updated: 02 March 2022

Question 1

An eddy current sensor is used to detect defects on a steel target. Steel has resistivity ρ=1.18×107\rho=1.18\times10^{-7} Ω.m and relative permeability μr=100\mu_{r}=100. If the driving frequency is 50 Hz, what is the minimum thickness of the steel target to ensure proper sensing with the eddy current sensor?

Hint: the magnetic permeability of free space is μ0=4π×107\mu_{0}=4\pi\times10^{-7} H/m and the formula for the eddy current skin depth is given by

δ=2ρωμ.\begin{equation} \delta=\sqrt{\frac{2\rho}{\omega\mu}}. \end{equation}

Question 2

A thin metal tape is being affixed to a non-conductive target to facilitate distance measurements using an eddy current sensor. The tape is made of aluminium, which has a resistivity of ρ=2.65×108\rho=2.65\times10^{-8} Ω.m and a relative permeability of μr1\mu_{r}\approx1. The tape has a thickness of 0.3 mm. What is the required frequency for the eddy current power source?

Question 3

The inclination of a plane is measured with an LVDT that has a 2 kg mass attached to its rod (Figure Q3). The mass is supported by a spring which exerts a force


where k=2000k=2000 N/m and xx is the displacement from the zero point of the LVDT. Meanwhile the weight of the the mass in the direction of xx is


where g=9.81 m/s2g=9.81\ \text{m}/\text{s}^{2}. Assume that the friction between the mass and the plane is negligible. The LVDT has a sensitivity of 150 mV/cm/V when powered by a 2.5 kHz, 3 V RMS sine wave.

Derive the transfer function between output voltage and angle θ.\theta.

Hint: assume static equilibrium to find the relationship between θ\theta and xx, then use the sensitivity of the LVDT to find the relationship between xx and the output voltage.

Figure Q3: An angle sensor constructed from an LVDT, a mass, and a spring. Zoom:

Question 4

Figure Q4 shows the equivalent circuit of an LVDT. The device produces a no-load output voltage of V0=0.5V_{0}=0.5 V (RMS) when measuring a deflection of 10 mm. The power supply is Vi=5V_{i}=5 V (RMS) at 2 kHz. You would like to increase the output voltage (i.e. increase the sensitivity) by raising the excitation frequency.

Figure Q4: Equivalent circuit of an LVDT. Zoom:

(a) You measure the DC resistance of the primary winding to be R1=200R_{1}=200 Ω. Next you measure its inductance using an LCR meter and find that the primary windings have an inductance of L1=10L_{1}=10 mH. Calculate the impedance of the primary winding at 2 kHz and hence find the magnitude of the excitation current ii.

(b) Calculate the net mutual inductance M=M1M2M=M_{1}-M_{2} at 10mm deflection based upon the measured output voltage V0=0.5V_0 = 0.5 V.

Hint: write KCL around the output winding to obtain an expression for V0V_0 as a function of MM.

(c) Assume that MM is constant with respect to frequency (i.e. the magnetic media in the core is not saturated). Calculate the new output voltage when the excitation frequency is raised to 20 kHz.

Hint: you will need to recalculate the excitation current ii because the impedance of the primary winding will change.

Question 5

You are measuring the strength of an electromagnet with the Hall effect. Your sensor element is a 10 mm ×\times 10 mm ×\times 0.1 mm wafer of p-type silicon with doping density Nc=1018 cm3N_{c}=10^{18}\ \text{cm}^{-3}. The geometry is shown in Figure Q5.

Figure Q5: Measuring the magnetic field strength using the Hall effect. Zoom:

(a) Is VHV_{H} positive or negative as drawn?

(b) Suppose instead that the sensor material were n-type silicon. What would be the polarity of VHV_{H}?

(c) Returning to the p-type device, and assuming a geometry factor of GH=1G_{H}=1, calculate VHV_{H} for an injected current of i=50i=50 mA and a magnetic field strength of 100 mT.

(d) Suggest a type of amplification circuit that could be connected to this sensor to obtain a sensitivity of 3.1211-3.1211 V/T.

(e) The sensor is now rotated about the yy axis as shown by the angle θ.\theta. What is the minimum value of θ\theta such that VH=0V_{H}=0?

(f) What is the minimum value of θ\theta such that VHV_{H} has the opposite sign but the same magnitude?