EE3901/EE5901 Sensor Technologies
Week 6 Tutorial

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College of Science and Engineering, James Cook University
Last updated: 04 February 2022

Question 1

A four-wire resistance measurement is performed using the circuit shown in Figure Q1.

Figure Q1: A circuit intended for resistance measurement. The op-amp works as a constant current source, as you will prove in part (a). The component VV is a voltage meter, measuring the voltage drop across the sensor RR. The resistors RwiR_{w_i} represent the unwanted resistances in the wires that connect to the sensor. Zoom:

The wires connecting the interface circuit to the sensor have resistance Rw1=Rw2=Rw3=Rw4=1R_{w_{1}}=R_{w_{2}}=R_{w_{3}}=R_{w_{4}}=1 Ω. The device VV is a voltmeter, which has an input impedance of Zmeter.Z_{meter}. The circuit is designed to measure resistances in the range 10 ΩR500 kΩ10\ \text{Ω}\leq R\leq500\ \text{kΩ}.

(a) Find the excitation current iexcitei_{excite}. Assume that the op-amp is ideal.

(b) Notice that some current will be diverted through the voltmeter, so the measured voltage VV will not be the expected value of V=RiexciteV=Ri_{excite}. If the current flowing into the meter is isensei_{sense} then the measured voltage is actually V=isenseZmeterV=i_{sense}Z_{meter}. Find the minimum value of ZmeterZ_{meter} such that the relative measurement error is no worse than ±\pm0.01%.

(c) In next week’s practical, you will use a Texas Instruments INA826 instrumentation amplifier. This device has an input impedance of approximately 20 GΩ. Would this device be a suitable buffer for the analog front end of the voltage meter?

Question 2

The Wheatstone Bridge can be used to compensate for changes in temperature. Suppose that you have two identical strain gauges. The “active gauge” is glued to the stressed material, and the “dummy gauge” is kept away from any mechanical stress. If the gauges are at equal temperature, then the effects of temperature will be the same on both.

Suppose that the strain gauges have a nominal resistance of R0R_{0} at a temperature T0T_{0}. Also, they have a temperature coefficient of resistance (TCR) of α\alpha and a gauge factor of GG.

(a) Write down the transfer function for the gauges as a function of strain (ϵ\epsilon) and temperature (TT).

Hint: a TCR represents a relative change per Kelvin. In other words, to account for temperature, multiply the entire resistance by a correction factor (1+α(TT0))\left(1+\alpha(T-T_{0})\right).

(b) Suppose that these gauges are placed in a half-bridge configuration as shown below:

Figure Q2: The circuit for Question 2. Zoom:

Sensor R1R_{1} is the dummy gauge (with zero strain), and sensor R2R_{2} is the active gauge (with strain of ϵ\epsilon).

Analyse this circuit and show that V0V_{0} is independent of temperature.

(c) Find the sensitivity of this circuit for small values of strain.

Question 3

A quarter-bridge circuit is used to interface with a resistive sensor as shown below:

Figure Q3: The circuit for Question 3. Zoom:

The sensor is placed at position R3R_{3} and is described by a transfer function of the form


where R0R_{0} is a large fixed constant, and xx is the sensor response that we seek to measure.

(a) Analyse each side of the voltage divider and prove that the bridge is balanced (i.e. V0=0V_{0}=0) when


(b) Suppose that the resistances satisfy a relationship


Find an expression for the output voltage in terms of xx and kk.

(c) Find the sensitivity of V0V_{0} to changes in xx.

(d) Find the value of kk that maximises the sensitivity at x=0x=0.

Question 4

The circuit below is used to perform a resistance measurement. Balanced current sources i1=i2i_{1}=i_{2} inject power into the circuit. There is a sensor RR with transfer function


where xx is a small relative change in resistance that we seek to measure. The circuit also has a fixed resistance RzR_{z}.

Figure Q4: The circuit for Question 4. Zoom:

(a) Assuming perfectly balanced current sources (i1=i2i_{1}=i_{2}), find the value of RzR_{z} such that V0=0V_{0}=0 when x=0x=0.

(b) Write the transfer function for this circuit (i.e. the relationship between V0V_{0} and xx).

(c) Discuss the practical issues that would be associated with this design.