Biosensors and Instrumentation: Tutorial 2

Transcription

1 Biosensors and Instrumentation: Tutorial 2. One of the most straightforward methods of monitoring temperature is to use the thermal variation of a resistor... Suggest a possible problem with the use of a standard Wheatstone bridge setup in a remote application like an implanted sensor?.2. Can you suggest a possible solution?.3. The alternative might be to locate the resistor at the remote sensing position while the instrumentation is in a stable environment. Why does this lead to a problem?.4. Why does a Kelvin measurement improve measurements of small resistances? 2. The circuit shown in figure can be used to compensate for the error in the output voltage which results from the fact that the cold junction is not at 0. There are two parameters which can control this compensation (assuming all of the resistors in the Wheatstone bridge are equal when the cold bridge temperature is 0 ), which are the voltage used to power the bridge and the position of the potentiometer. If we have the following parameters suggest values for in, and the ratio of P to P2 to correct for an observed error in the thermocouple output EMF of 0m when the cold junction is at room temperature (20 ): TD = 00 Tjunction = 0 αtd = Ω Ω K = 00 Ω (Wheatstone bridge resistor) Pot = P P2 = 00 kω Thermocouple TD P Cold Junction P2 EMF Figure. Thermocouple compensation circuit Hint for Q2, if TD is greater than then think about the size and direction of the voltage output from the Wheatstone bridge then about how that adds/subtracts from the EMF from the thermocouple and the cold junctions in order to correct for any error. It might be useful to redraw the circuit with voltage sources replacing these components.

2 " 3. The basic formula for resistance is = ρ L/A. From this we can work out the fractional change in resistivity for a strain gauge: = A A L L The first term there deals with the change in the material resistivity due to applied strain. The piezoresistive coefficient π is defined as: = / E Where E is the Young s modulus of the material and ε is the strain (ε = ΔL/L). Poisson s ratio ν is another material parameter that defines the change in the transverse strain due to an applied axial strain, for our resistor we can say that: A/A L/L = Combine all of this information with the equation for the gauge factor of a piezoresistor (given below) to produce an expression for GF in terms of ν, π and E. GF = 3.2. In most metals the poisson ratio is between 0 and 0.5, while the effect of π is negligible, what does that mean for the possible range of values for GF? 3.3. Polycrystalline silicon can have a gauge factor as high as 40. What is the source of this? G 2 4. A platinum based strain gauge with an unstrained resistance (G) of kω has a gauge factor (GF) of 2. The formula for gauge factor is covered in the previous question. 4.. If the gauge is securely fixed to a measured structure undergoing a strain (ε) of 0%, what will be the maximum change in resistance ( )? 4.2. You have 4 gauges to measure a structure with a maximum strain of %. How would you arrange the gauges in a Wheatstone bridge in order to maximise the output voltage and what will be be the output voltage range? 4.3. Assuming it s only possible to attach two of the 4 gauges to the structure under test, how would you do this and what effect would it have on the sensitivity? 4.4. How could you add to the Wheatstone bridge circuit in order to allow small mismatches in the gauge resistors to be corrected? 5. Piezoelectric acoustic wave devices are now widely used in F filters in mobile communications and in passive F-ID tags. Surface acoustic wave filters can also be adapted into sensitive detectors. The frequency of the acoustic wave is proportional to the wave velocity in the material. 5.. Suggest how this could be used in a biosensor What factors can also affect the frequency? 5.3. How can these be corrected for? Sketch a SAW sensor setup that could avoid these problems which only uses one driven IDE Why are ayleigh wave type SAW devices unsuitable for use in liquid environments?

3 6. The capacitive bridge circuit shown in figure 2 is used to convert changes in the capacitance of a MEMS accelerometer with a differential sensing setup. It has the following output voltage amplitude, when driven with an ac voltage with amplitude : 3 out = 2 = x 2d When C2 = C4 = C0, C = Cw and C3 = Cw2 where and C w = C 0 x d C w2 = C 0 x d = C 0 C = C 0 C () (2) C 2 C4 C3 Figure 2. Capacitive Wheatstone bridge. 6.. Using equations () and (2), define the change in capacitance ΔC. Is this the same for Cw and Cw2? 6.2. If we can arrange for this to be a full bridge where C = C4 = Cw and C2 = C3 = Cw2 what will the equation for the output voltage be in terms of the displacement x? 6.3. If the area of one of the differential capacitors is μm and the separation d =μm calculate the output voltage from the bridge when the deflection x =0nm and = If there are parasitic capacitances Cp on the two output terminals what is the equation for the output voltage? (hint, use the C version of the working capacitor equations) 6.5. What are the possible sources of parasitic capacitance in MEMS sensors? 6.6. The main contribution to the parasitics is from the bond pads used to connect to the bridge. The pads are 80 80μm and are separated from the grounded silicon substrate by a 2μm thick dielectric (ε = 7). Calculate the value of Cp ecalculate the output voltage for the same deflection as question.2 including the effect of the parasitics.

4 7. The alternative to the capacitive bridge for displacement sensing is current measurement using the circuit in figure 3. 4 B i - Figure 3: Current measurement of capacitive sensor. 7..What effect does this have on a grounded parasitic capacitance connected to node B? 7.2. If Cw and Cw2 are characterised by equations () and (2) in the previous question, derive the equation for the output current in terms of x, d and C0. Please don t just copy it down from the slides! 7.3. If this circuit is used to measure a micromachined accelerometer with nominal gap d = 2.5 μm and area A =.2 mm.2 mm calculate the output current when the displacement is 0.46 μm and the device is driven with an ac voltage = 0., f = 00 khz If a current-follower op-amp circuit is used to amplify and convert this current, what value of resistor is required to give a p-p voltage output? 8. Switched capacitor circuits may be more appropriate for use in IC based sensor interfaces. 8.. Give as many reasons as you can come up with why resistors are a problem in integrated electronics, particularly if an amplifier circuit such as that in question 3.4 is required. What are the advantages of capacitors? 8.2. The circuit shown in figure 4 is controlled by two non-overlapping clock signals such that when s and s3 are closed, s2 is open and vice-versa. With the help of sketches of the circuit during the two different phases, describe the operation of the amplifier and state the transfer function. s 3 s s 2 C out Figure 4. Switched Capacitor Amplifier

5 8.3. Figures 5 and 6 show two more switched capacitor circuits driven by non-overlapping clock signals Φ and Φ2. What is the difference between the transfer functions of each? 5 Φ Φ C Φ out Figure 5. SC amplifier number Φ C Φ Φ out Figure 6. SC amplifier number 2