Lecture 3

1. Lecture 3 • Demos: capacitor separation with distance • Introduce dielectrics (foam,glass) and see the voltage decrease as the capacitance increases.

2. Electrical Sensors • Employ electrical principles to detect phenomena. • May use changes in one or more of: • Electric charges, fields and potential • Capacitance • Magnetism and inductance

3. Some elementary electrical sensors Thermocouple Thermistor Variable Capacitor

4. Review of Electrostatics • In order to understand how we can best design electrical sensors, we need to understand the physics behind their operation. • The essential physical property measured by electrical sensors is the electric field.

5. Electric Charges, Fields and Potential Basics: Unlike sign charges attract, like sign charges repel Coulombs’ Law: a force acts between two point charges, according to: The electric field is the force per unit charge: How do we calculate the electric field?

6. Electric Field and Gauss’s Law We calculate the electric field using Gauss’s Law. It states that: Seems very abstract, but is really useful

7. Point or Spherical charge What is the field around a point charge (e.g. an electron)? The electric field is everywhere perpendicular to a spherical surface centred on the charge. Electric field vectors So Gaussian surface We recover Coulombs Law! The same is true for any distribution of charge which is spherically symmetric (e.g. a biased metal sphere).

8. Line of Charge For a very long line of charge (eg a wire), the cylindrical surface has electric field perpendicular to a cylindrical surface. So Where  = linear charge density (Coulombs/meter)

9. Plane of Charge For a very large flat plane of charge the electric field is perpendicular to a box enclosing a segment of the sheet So Where  = Charge/Unit area on the surface

10. Electric Dipole • An electric dipole is two equal and opposite charges Q separated by a distance d. • The electric field a long way from the pair is • p = Q d is the Electric Dipole moment • p is a measure of the strength of the field generated by the dipole.

11. Electrocardiogram • Works by measuring changes in electric field as heart pumps • Heart can be modeled as a rotating dipole • Electrodes are placed at several positions on the body and the change in voltage measured with time

12. Electrocardiogram • Interior of Heart muscle cells negatively charged at rest • Called “polarisation” • K+ ions leak out, leaving interior –ve • Depolarisation occurs just proir to contraction: Na+ ions enter cells Occurs in waves across the heart Re-polarisation restores –ve charge in interior + + + + - - - - - • - - • - + + + + Polarisation Depolarisation

13. Electrocardiogram • Leads are arranged in pairs • Monitor average current flow at specific time in a portion of the heart • 1 mV signal produces 10 mm deflection of recording pen • 1 mm per second paper feed rate A A - - + B C + - C B +

14. Electric Potential The ECG measures differences in the electric potential V: The Electric Potential is the Potential ability to do work. Alternatively: Work = Q  V Where V = For uniform electric fields:

15. Electric fields on conductors. • Conductors in static electric fields are at uniform electric potential. • This includes wires, car bodies, etc. • The electric field inside a solid conductor is zero.

16. Dielectric Materials • Many molecules and crystals have a non-zero Electric dipole moment. • When placed in an external electric field these align with external field. • The effect is to reduce the strength of the electric field within the material. • To incorporate this, we define a new vector Field, the electric displacement,

17. Electric Displacement is independent of dielectric materials. Then the electric field is related to by: Are the relative permittivity, the permittivity of free space and the absolute permittivity of the material. As shown in the diagram, there is torque applied to each molecule. This results in energy being stored in the material, U. This energy is stored in every molecule of the dielectric:

18. Capacitance. Remember that the electric field near a plane of charge is: In the presence of a dielectric: So the Potential difference is proportional to the stored charge.

19. Cylindrical Capacitor Can make a capacitor out of 2 cylindrical conductors

20. Sensing using capacitance. So the charge Q = CV Where C = Capacitance, V = Potential difference. For a parallel plate capacitor: Area of plate Easily Measured Properties of Material Distance between plates We can sense change in A, ε, or d and measure the change in capacitance.

21. Measurement of Capacitance Capacitors have a complex resistance We measure capacitance by probing with an AC signal. Directly measure current i(t) with known V(t) and frequency ω. For extreme accuracy, we can measure resonant frequency with LC circuit.

22. Example: water level sensor Measures the capacitance between insulated conductors in a water bath Water has very different dielectric properties to air (a large ) As the bath fills the effective permittivity seen increases, and the capacitance changes according to:

23. Example: The rubbery Ruler Invented by Physicists here to measure fruit growth. http://www.ph.unimelb.edu.au/inventions/rubberyruler/ Spiral of conductor embedded in a flexible “rubbery” compound As the sensor expands, the distance between the plates increases causing capacitance to decrease.

24. The rubbery ruler Spiral of conductor embedded in a flexible “rubbery” compound Invented by Physicists here to measure fruit growth. http://www.ph.unimelb.edu.au/inventions/rubberyruler/ As the sensor expands, the distance between the plates increases causing capacitance to decrease.

26. Lecture 4 • Piezoelectric demo (stove lighter and voltmeter)

27. Piezoelectric sensors Mechanical stress on some crystal lattices results in a potential difference across the solid. This is an extremely useful effect. Reversible too!

28. For quartz, stress in x-direction results in a potential difference in the y-direction. • This can be used as a traffic weighing and counting sensor! • A piezoelectric sensor can be thought of as a capacitor, with the piezoelectric material acting as the dielectric. The dielectric acts a generator of electric charge resulting in a potential V across the capacitor. • The process is reversible. An electric field induces a strain in the material. Thus a very small voltage can be applied, resulting in a tiny change in the size of the crystal.

29. Characterisation of Piezoelectrics We quantify the piezoelectric effect using a vector of Polarisation. Where dmnare coefficients, i.e. numbers that translate applied force to generated charge and are a characteristic of the piezoelectric material. Units are Coulomb/Newton.

30. The conversion efficiency is given by the coupling coeffient: Characterisation of Piezoelectrics Piezo crystals are transducers; They convert mechanical to electrical energy. Where Y is Young’s Modulus = Stress/strain

31. Area of electrodes So the Voltage is The charge generated is proportional to the applied force The charge generated in the X-direction from an applied stress in y Using our Q = CV, we get a generated voltage The capacitance is: Thickness of crystal

32. Some piezoelectrics

33. Volts/Newton C = Numerical Example. What is the sensitivity of 1 mm thick, BaTiO3 sensor with an electrode area of 1 square cm? = So This is a big number because the effective capacitance is so small. In the real world the voltage is smaller. Very Small!

34. Atomic Scale Microscopy Use Piezoelectric crystals as transducers to do atomic scale microscopy

35. A Resitance l Piezoresistive Sensors The stress on a material is Strain = dl/l A cylinder stretched by a Force F keeps constant volume but l increases and A decreases. Sensitivity of the sensor is Longer wires give more sensitivity

36. Characterizing Piezoresistors is the gauge factor or sensitivity of the strain. Metals Semiconductors Normalised resistance is a linear function of strain: Where e is the strain, and Semiconductor strain gauges are 10 to 100 times more sensitive, but are also more temperature dependent. Usually have to compensate with other types of sensors.

37. Piezoresistive Heat Sensors. Resistive Temperature Detectors: on demand “RTD”s RTD’s used at Belle Thin platinum wire deposited on a substrate.

38. Other piezoresistive issues • Artificial piezoelectric sensors are made by poling; apply a voltage across material as it is heated above the Curie point (at which internal domians realign). • The effect is to align natural dipoles in the crystal. This makes the crystal a Piezoelectric. • PVDF is of moderate sensitivity but very resistant to depolarization when subject to high AC fields. • PVDF is 100 times more resistant to electric field than the ceramic PZT [Pd(Ze,Ti)O3] and useful for strains 10 times larger.

39. Example: acceleration Sensor. • Piezoelectric cable with an inner copper core. • The piezoelectric acts as an insulator, clad by an outer metal sheath and flexible plastic and rubber coating. • Other configurations exist: see • www.pcb.com/techsupport/tech_accel.aspx Inner copper core Piezoelectric Outer metal sheath or braid Plan view of cable Remember that F=ma , so if the sensor mass is known, then the force measured can be converted into an acceleration.

40. Applications for piezoelectric accelerometers • Vibration monitor in compressor blades in turboshaft aircraft. • Detection of insects in silos • Automobile traffic analysis (buried in highway): traffic counting and weighing. • Force and pressure sensors (say, monitoring jolts to packages). • Tactile films: thin silicone rubber film (40 m) sandwiched between two thin PVDF films. If tactile sandwich is compressed, the mechanical coupling in the PVDF/rubber/PVDF sandwich changes, the measured AC signal changes, and the demodulation voltage changes

41. Lecture 5

42. Pyroelectric Effect. Generation of electric change by a crystalline material when subjected to a heat flow. Closely related to Piezoelectricity. BaTiO3, PZT and PVDF all exhibit Pyroelectric effects

43. Primary Pyroelectricity. Temperature changes shortens or elongates individual dipoles. This affects randomness of dipole orientations due to thermal agitation.

44. Secondary Pyroelectricity

45. Quantitative Pyroelectricity. Pyroelectric crystals are transducers: they convert thermal to electrical energy. The Dipole moment of the bulk pyroelectric is: M =  A h Where  is the dipole moment per unit volume, A is the sensor area and h is the thickness From standard dielectrics, charge on electrodes, Q =  A The dipole moment, , varies with temperature.

46. Is the pyroelectric charge coefficient, and Ps is the “spontaneous polarisation” The generated charge is Q = PQ A T Pv = is the pyroelectric voltage coefficient and E is the electric Field. The generated voltage is QV = Pv h T (h is the thickness) The relation between charge and voltage coefficients follows directly from Q = CV

47. Seebeck and Peltier Effects. Seebeck effect: Thermally induced electric currents in circuits of dissimilar material. Peltier effect: absorption of heat when an electric current cross a junction two dissimilar materials The dissimilar materials can be different species, or the the same species in different strain states. The Peltier effect can be thought of as the reverse of the Seebeck effect

48. Seebeck effect Free electrons act as a gas. If a metal rod is hot at one end and cold at the other, electrons flow from hot to cold. So a temperature gradient leads to a voltage gradient: Where  is the absolute Seebeck coefficient of the material. When two materials with different  coefficients are joined in a loop, then there is a mis-match between the temperature-induced voltage drops. AB = A - B The differential Seebeck coefficient is:

49. Thermocouples The net voltage at the junction is So the differential Seebeck coefficient is also This is the basis of the thermocouple sensor Thermocouples are not necessarily linear in response. E.g. the T – type thermocouple has characteristics Where the a’s are material properties:

50. The sensitivity is the differential Seebeck coefficient Independent of geometry, manufacture etc. Only a function of materials and temperature. Seebeck effect is a transducer which converts thermal to electrical energy. Can be used as solid state thermal to electrical energy converter (i.e. engine)as well as an accurate temperature sensor. Seebeck engines are currently not very efficient but are much more reliable than heat engines. They are used by NASA for nuclear powered deep-space probes.