1. Advanced Sensor Technology Lecture 3
Jun. QIAN

2. A Review of Lecture 2 Characteristics of sensors Transfer function
Sensitivity
Dynamic Range
Hysteresis
Temperature Coefficient
Linearity
Accuracy
Noise
Resolution
Bandwidth

3. Lecture 3 Basic Intent
Review some background on electrical measurement of sensor outputs
Provide an overview of piezoresistive devices. Some examples are worked out using this sensing technique

4. Introduction to Sensors Electronics
The electronics which go along with the physical sensor element are very important:
Limit the performance, cost, and range of applicability
If carried out properly, the design can improve the characteristics of the entire device,
Focus on basic techniques for processing the signals most typically produced by a sensor
Most sensor act like passive device
Resistive
Capacitive
Inductive

5. Resistive Sensor Circuits
Resistive sensors obey Ohm’s law
How to get a voltage signal out of the sensor?
Need a constant current source
The easiest way to build a current source: voltage divider
Condition: load R>>sensor R
Shortcoming: small signal might need some amplification

6. Capacitance measuring circuits
Many sensors respond to physical signals by producing a change in capacitance
Impedance:
Very much like a resistor at AC, may measure capacitance by building voltage divider circuits, use either resistor or capacitor as the load resistance
Resistors have much smaller temp coeff. than caps: 0.3ppm/ºC v.s. 200ppm /ºC

7. Capacitance measuring circuits
A substantial hassle:
providing an AC bias
Converting the AC for microprocessor interface
Use clock signal or integrated clock/sampling circuit
Modulated signal creates an opportunity for use of some advanced sampling and processing techniques
Lock-in: bias the sensor and trigger the sampling, get the low noise signal
Disadvantage: clocked switch inject noise charge into circuit
Very accurate capacitance measurement still requires expensive precision circuitry

8. Inductance measurement circuits
Impedance: iL -> essentially resistive elements
Inductive sensors generally require expensive techniques for the fabrication of the sensor mechanical structure: 3D structure
Inexpensive circuits are not of much use, expensive anyway!

9. Limitations Limitations to resistance measurement
Lead resistace -> 4-wire configuration
Output impedance
The measuring network resistance places a lower limit on the value of a resistance which may across the output terminals
An example: 10K thermister+1M load, if connected to an 1K measuring instrument
-> output voltage would be reduced by ~90%

10. Limitations to measurement of capacitance
Stray Capacitance
Appear as additional capacitances in the measuring circuit
Wires moving about with respect to ground, causing capacitance fluctuations
These effects are due to pressure-induced vibrations in the positions of objects, referred to as microphonics.

11. Piezoresistive devices – an overview
Silicon-based
Specific advantages are:
High sensitivity, >0.5mV/mbar
Good linearity at constant temperature
Ability to track pressure changes without signal hysteresis, up to the destructive limit

12. Structure and Assembly
Principle of Operation
Deformation by applied pressure causes high levels of mechanical tension at the edge of diaphragm
Semiconductor resistors on the front side transduce this tension into resistance changes by means of the piezoresistive effect. .

13. Spec Sheet Nominal Pressure Range (mbar) 100 200 400 1000 Sensitivity
(mV/mbar)
0.5
0.25
0.12
0.06
Linearity
(%FSO)
<1
Bridge Resistance
(k)
5.6
Chip Size
(mm3)
3 x 3 x 1
2.2 x 2.2 x 1
Diaphragm Size
(mm2)
2 x 2
1.5 x 1.5
1.1 x 1.1
0.8 x 0.8

14. Theoretical background: piezoresistance
A piezoresistor: a device which exhibits a change in resistance when it is strained.
There are two components of the piezoresistive effect
the geometric component
the resistive component.
The geometric component of piezoresistivity:
a strained element undergoes a change in dimension. These changes in cross sectional area and length affect the resistance of the device.

15. Strain: Definition
Strain is the amount of deformation of a body due to applied force
Dimensionless: mm/mm
strain is often expressed as microstrain (), which is  x 10-6.

16. Classical Device: Mercury Tube
An elastic tube filled with a incompressible conductive fluid, such as mercury (really!)
R = (Resistivity of mercury)(length of tube)/(cross sectional area of tube)
Gauge factor: K=2 for liquid strain gauge
What does it mean?
if a liquid strain gauge is stretched by 1%, its resistance increases by 2%.

17. Metal wire based strain gauge
To find K:
Metal wires:
stretching of the wire changes the geometry of the wire in a way which acts to increase the resistance:
Gauge factor K=2~4 4
= Poisson’s ratio 

18. Poisson’s Ratio Poisson’s ratio
When a bar is strained with a uniaxial force, a phenomenon known as Poisson Strain causes the girth of the bar, D, to contract in the transverse direction.
The magnitude of this transverse contraction is a material property indicated by its Poisson's Ratio:
Defined as the negative ratio of the strain in the transverse direction (perpendicular to the force) to the strain in the axial direction (parallel to the force),
Poisson’s ratio = eT/ eL
Poisson's Ratio for steel, for example, ranges from 0.25 to 0.3

19. Metal wire based strain gauge
Issues in design
we would prefer to have a large change in resistance to simplify the design of the rest of a sensing instrument,
so we generally try to choose small diameters, small young's modulus, and large gage factors when possible.
The elastic limits of most materials are below 1%, so we are generally talking about resistance changes which are in the 1% % range.
Clearly, the measurement of such resistances is not trivial, and we often see resistance bridges designed to produce voltages which can be fed into amplification circuits.

20. Wheatstone bridge
The Wheatstone bridge is widely used for precision measurements of resistance
How to choose R?
Rx=R+R
R1=R2=R3=R
V=-R*(V/4R)

21. Metal Wire Strain Gauge: thin film pattern
The metallic strain gauge consists of a very fine wire or,
more commonly, metallic foil arranged in a grid pattern.
The grid pattern maximizes the amount of metallic wire or foil
subject to strain in the parallel direction

22. A variety of shapes available

23. Strain Gauge Measurement
In practice, the strain measurements rarely involve quantities larger than a few millistrain( x 10-3).
To measure the strain requires accurate measurement of very small changes in resistance
For example, suppose a test specimen undergoes a strain of 500 . A strain gauge with a gauge factor of 2 will exhibit a change in electrical resistance of only 2 (500 x 10-6) = 0.1%. For a 120  gauge, this is a change of only 0.12 .

24. Foil Strain Gauge Gauge factor: a little over 2 Output
single gauge+3 dummy resistors
Area: 2-10 mm2

25. Measurement: Quarter-bridge circuit
If the nominal resistance of the strain gauge is designated as RG,
then the strain-induced change in resistance, R, can be expressed as
R = RG·K·.
Assuming that R1 = R2 and R3 = RG,
VO/VEX = - K/4(1+K·/2)
4(1+K·/2) term that indicates the nonlinearity of the quarter-bridge output with respect to strain

26. Increase Sensitivity
Half-bridge circuit
Full-bridge

27. Tackle Temperature Effect
Strain gauge material also respond to changes in temperature
Minimize sensitivity to temperature by processing the gauge material
Using two strain gauges in the bridge, the effect of temperature can be further minimized

28. Strain Gauge in Industry
adf

29. Strain Gauge in Industry
Packaged foil strain gauge

30. Signal Conditioning Bridge completion Excitation Remote sensing
Amplification
Filtering
Offset

31. Specifications Performance Hysteresis< 0.02 % Rated Output (R.O.)
Long Term Stability< 0.04 % Rated Output (R.O.)
Nonlinearrity< 0.1 % R.O. / Year
NonRepeatability< 0.01 % R.O
Creep/Creep Recovery, 20 minutes< 0.05 % R.O.
Temp. Effect on Zero Balance
Standard< 0.03 % R.O. / °C
Optional< % R.O. / °C
Temp. Effect on Output 
Standard< % Reading / °C
Optional< % Reading / °C
As oppose to P handbook

32. Bridge Completion
Unless you are using a full-bridge strain gauge sensor with four active gauges, you will need to complete the bridge with reference resistors.
Therefore, strain gauge signal conditioners typically provide half-bridge completion networks consisting of high-precision reference resistors.

33. Other Issues
Excitation –typically provide a constant voltage source to power the bridge. 3 ~ 10 V are common.
While a higher excitation voltage generates a proportionately higher output voltage, the higher voltage can also cause larger errors because of self-heating. .
Remote sensing
Long lead needs wire compensation

34. Other Application: Data Storage
A 100 micron-long piezoresistive cantilever is dragged along a polycarbonate disk at 10 mm/s, bouncing up and down as it passes over sub-micron indentations in the surface of the disk. This idea is essentially a high-performance phonograph needle

35. Example Calculation: Piezoresistive Cantilever
Here, L is the length, T is the thickness, and w is the width. Since F = kZ, we have stiffness
=3x10-6 or 0.03% for K=100
T = 4m, L = 100 m, w = 4 m ,
E = 2 x 1011 N/m2, and F = 10-7 N.

36. Optical Strain Gauges?

37. Example: Fiber Bragg Grating based strain sensor

38. Cascaded up to 13 sensors, gauge factor is still low

39. For extreme pressure in hostile environment
Option 1:
single wavelength, observe fringes resulting from interference
Option 2:
white light source, observe spectrum change due to pressure-sensing wavelength dependent rotator

40. Mechanism: it’s all what it matters!
For fused silica

42. Summary Basic circuits for sensors Piezoresistive Device-strain gauge
resistance
capacitance
Piezoresistive Device-strain gauge
strain
Poisson’s ratio
Mercury tube
Metal wire based strain gauge
Structure
Measurement: various bridge circuits
Temp compensation
Other applications: data storage
Optical strain gauges
FBG
Polarization