1. ECE699 – 004 Sensor Device Technology
Chapter 3 Physical Principles of Sensing
Fall 2018
George Mason University

2. 3.1 Electric Charge, Fields and Potentials

5. 3.2 Capacitance
When it is connected into a circuit

6. Capacitors

7. Dielectric constant

8. Can be a function of temperature

10. Can be used to detect humidity

11. 3.3 Magnetism

14. Flux of magnetic field
Deflecting force

15. Solenoid

16. 3.4 Induction
For a coil with cross-section area A:

17. Mutual inductance M:

18. 3.5 Resistance

19. Specific resistivity

20. Temperature Sensitivity

21. Αe is the temperature coefficient of resistance (TCR)

23. Strain Sensitivity
Electrical resistance changes when the materials is mechanically deformed: Piezoresistive effect

24. Moisture sensitivity

25. 3.6 Piezoelectric Effect

27. Polarization: dmn is piezoelectric coefficients (unit: coulomb/newton)
g coefficient: represents a voltage gradient (electric field) generated by the crystal per unit applied pressure
Unit:

28. h coefficient: hmn is obtained by multiplying gmn with the corresponding Young’s moduli for the corresponding crystal axes, unit:
k coefficient: coupling coefficient kmn
For a piezoelectric crystal capacitor:
a is the area

29. Good examples: PZT and PVDF (organic) film
The materials is cooled down while the E field across its thickness is maintained
After removing the E field below Curie temperature, the dipoles stay “frozen”

31. Piezoelectric films unique properties

32. Piezoelectric films
polyvinylidenePVDF
PVDF maintains higher strain than PZT and has 100 times higher maximum permissible field

33. 3.7 Pyroelectric Effect
Generating an electrical charge in response to heat flow

34. Example materials include PbTiO3 BaTiO3 and polyvinyl fluoride (PVF), PVDF
The charge generated is
A is the sensor area, µ is dipole moment per unit volume, a function of both temperature and incremental thermal energy

35. Output voltage
PQ is pyroelectric charge coefficient

36. 3.8 Hall Effect

39. A linear Hall effect sensor is usually packaged in a four-terminal housing

40. An example Hall sensor

41. 3.9 Seebeck and Peltier Effect

42. Change of conductivity thermal gradient
αa is absolute Seebeck coefficient
If the material is homogeneous, αa is not a function of length

44. A differential Seebeck coefficient
If a T-type thermal couple

46. For a n-type Si
Peltier effect: voltage  temperature difference

47. 3.10 Sound Waves Generate physical compression and expansion
With certain frequencies: 20Hz to 20 kHz can be heard by human ears; above 20 kHz is ultrasound
bulk modulus of elasticity
ρ0 is the density outside the compression zone, v is the speed of sound in the medium

48. For a sound wave, the displacement of a particle from the equilibrium position:
The pressure exerted by the sound wave:
where k=2π/λ
Acoustic pressure: P = the difference between the instantaneous and the average pressure
Instantaneous velocity: ξ, Acoustic impedance: Z

49. For an idealized medium (no loss)
The intensity I of a sound wave as the power transferred per unit area:
Sound level β (unit dB) (represent the intensity)
If I=I0, β=0
Pressure level:

51. 3.11 Temperature and Thermal Properties of Materials
Every single particle in the universe exists in perpetual motion!
Can be described as a measure of kinetic energy of vibrating particles – the stronger movement, the higher the temperature of that particles
Thermometer: by contacts the object or receives its electromagnetic radiation

52. Temperature scales Thermal expansion Linear expansion
Linear expansion coefficient

54. The fractional change in area and volume
For Fig. 3.38A: the radius of warping
The biomaterial plate deflection:

55. Heat capacity C=c m, where c is a constant, specific heat:
c also changes slightly with temperature and dramatically for phase change
Heat, once produced, has not origin,
Heat can not be contained

56. Heat conduction

57. Heat flow rate (thermal current)
k is call thermal conductivity, A is area
For an electric wire with T1 and T2 at both ends
Thermal resistance:

58. RC is contact resistance
hC is contact coefficient

59. Thermal convection: depend on intermediate agents: gas or liquid
For an horizontal plate
For a vertical plate

60. Thermal Radiation Every atom and every molecule vibrate
The radiation flux density
At room temperature fm=30 THz

62. visible
infrared

63. Light

64. Dynamic models of sensor elements
Input s(t) and output S(t)
Zero order response: (G is a constant transfer function)
First order response: a1 and a0 are constants
For a step function input

65. Second-order response
The response depends on several factors: natural frequency ω0 and damping coefficient b
Overdamp (b>1), underdamped (b<1) (damping is the progressive reduction or suppression of the oscillation in the sensors having higher than a first-order response

67. Mechanical, thermal and electrical elements

68. Mechanical elements

69. Thermal elements

70. Electrical elements:
Kirchhoff’s first law and second law