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CHAPTER 7 Dielectric Materials and Insulation

CHAPTER 7 Dielectric Materials and Insulation. Relative Permittivity Dipole moment Polarization Vector P Local field Loc and CLASIUS-MOSSOTTI equation. CHAPTER 7 THE RECORDING PROCESS. Polarization Mechanism Debay equation, Cole cole plot’s and equivalent series circuit:.

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CHAPTER 7 Dielectric Materials and Insulation

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  1. CHAPTER 7Dielectric Materials and Insulation • Relative Permittivity • Dipole moment • Polarization Vector P • Local field Loc and CLASIUS-MOSSOTTI equation

  2. CHAPTER 7THE RECORDING PROCESS • Polarization Mechanism • Debay equation, Cole cole plot’s and equivalent series circuit: After studying this chapter, you should be able to:

  3. 7.1.1:Relative Permittivity: Definition • The relative permittivity or the dielectric constant єr is defined to reflect this increase in the capacitance or charge storage ability by virtue of having a dielectric medium. If C is the capacitance with the dielectric medium as Fig 7.1, then by definition , Єr=Q/Q○=C/C○

  4. Figure 7.1:(a) parallel port capacitor with free space between the plates. • (b) As a slab of insulating material inserted between the plates, there is an external current flow indicating that more charge is stored on the plates. • (c) The capacitance has been increased due to the insertion of a medium between the plates.

  5. 7.1.2: Dipole moment: • An electrical dipole is simply a separation between a negative and positive charge of equal magnitude Q as shown in Fig 1, if a is the vector from the negative to the positive charge the electric dipole moment is defined as a vector by P=QA

  6. Figure 7.2: The definition of electric dipole moment Figure 7.3: A neutral atom in E=0 and induced dipole moment in a field

  7. Art :7.1.3.Polarization Vector P:

  8. Let us consider a dielectric material is placed in an electric field, as shown in fig. (a) Which is bound polarization charge appear on the opposite surface. Again consider the alone polarized medium as shown in fig. (b).Here the positive surface charge +Qp & the negative surface charge -Qp on the left & right hand face respectively.Now the polarization vector P can be defined asP=1/vloume[P1+P2+P3+………+Pn] [Where P1,P2,P3,Pn are the dipole moments]

  9. Or P=NPav,[where N=no. of molecules per unit volume Pav= average dipole moment]Now we calculate the total dipole moment Ptotal from –Qp+Qp i.e.Ptotal=QpdNow the magnitude of polarization vector P isP=Ptotal/Volume =Qpd/Ad = Qp/A=ςp [where ςp= surface polarization charge density]Again we know,ε Pα E or, P=XeoE [Where Xe=Electronic Susceptibility and εo =permittivity]

  10. Again here, Pinduced=αθE [Where αθ=Electronic polarizability ] So, P=NPinduced=NαθE Or, XeoEP=NαθE Or, Xe=1/eo(NαθE) The above equation shows the relation between [Where Xe=Electronic Susceptibility & αθ=Electronic polarizability ]. Again the electric field E before the dielectric was inserted is given by, E=Qo/Cod=V/d=Qo/εoA=σo/εo [where Qo/Cod=V,Qo/εoA= σo, σo= free surface charge density] Now,

  11. Now, Qo=Q-P Or, Q=Qo+P Or,Q/A=Qo/A=Qp/A; [Dividing by A in both side] or, σ= σo+ σp Or, σ= εoE+P Or, σ= εoE+XeoE or, σ= εoE(1+Xe) Now we can write from the define of relative permittivity εr we get, εr =Q/Qo= σ / σo or, εr=εoE(1+Xe)/ εoE or,mεr=(1+Xe)……………………..(1) or, εr=1+(Nαo/ εo)……………….(2) The above two equation shows the relation between εr = relative permittivity & Xe=Electronic Susceptibility & αθ=Electronic polarizability

  12. Art.7.1.4 Local field Eloc and CLASIUS-MOSSOTTI equation: • A dielectric is defined as the local fiel d and denoted by Eloc.In the simplest case of the material with a cubic crystal structure or a liquid the local field Eloc acting on a molecule increases with polarization as Eloc=E+1/3εP

  13. Is called the Lorenz field. Induced polarization in the molecule now depends on the local field Eloc rather than the average field E.thus, Pinduced=αc Eloc The fundamental definition pf electric susceptibility by the equation P=xeεE This equation is unchanged with means that ε=1+x .The polarization is defined by p=Npinduced and pinduced can be related to Eloc hence to the E and p.Then P=(ε-1) ε E E and P and obtain a relationship between and .This is the CLAUSIUS –MOSSOTTI equation. (ε-1)/(ε+2) =Nα/3 ε

  14. Example:7.2: The electric polarizability of the Ar atom is 1.7 *10^40 Fm .What is the static dielectric constant of solid Ar(84k)if it’s density is 1.8gcm -3 Solution: Mat=39.95 N= NAd/Mat =2.71*10^22 cm-3 αe = 1.7×10^40Fm^2 we have , εr=1+Nαe/εo=1.52 Using the CLAUSIUS –MOSSOTTI equation εr =1.63 The values are different by 7 percent.(Ans.)

  15. Art.7.3Polarization Mechanism • Ionic polarization. • Dipolar polarization. • Interfacial polarization.

  16. 7.4 Frequency Dependence: Dielectric Constant and Dielectric Loss • The static dielectric constant is an effect of polarization under dc condition • For Ac signal this constant generally different than the static case. • The sinusoidally varying field changes magnitude and direction continuously. • It tries to line up the dipoles one way and then the other way and so on.

  17. 7.4 Frequency Dependence: Dielectric Constant and Dielectric Loss • There are two factors opposing the immediate alignments of the dipoles with the fields. • Thermal agitation tries to randomize the dipole orientation • Dipole can not response instanteously to the changes in the applied field. • At high frequency αd will be zero but at low frequency αd has its maximum vale.

  18. Art.7.4.2Debay equation, cole-cole plots and equivalent series circuit • A dipolar dielectric with both oriental and electronic polarization is considered. • αd and αe are contributing to the overall polarizibility. • αe is independent of frequency where αd is totally dependent of frequency. • At high frequency αd = 0 and εr will be εr∞ (the subscript ∞ means high frequency) • The dielectric constant εr= 1+(N/εo)*αe +(N/εo)*αd(ω) εr= εr∞+ (N/εo)*αd(ω)

  19. Art.7.4.2 • The dielectric constant εr= εr∞+ (N/εo)*αd(ω) εr ‘ – jεr “ = εr∞+ (N* /εo)*αd(0)/(1+jωτ) = εr∞+ (εrdc - εr∞)/(1+jωτ) = εr∞+ (εrdc - εr∞)(1-jωτ) /[1+(ωτ)2 ] εr ‘ = εr∞+ (εrdc - εr∞)/[1+(ωτ)2 ] εr “ = (εrdc - εr∞)(ωτ) /[1+(ωτ)2 ]

  20. Figure: colecole plot εr ‘ = εr∞+ (εrdc- εr∞)/[1+(ωτ)2 ] εr “ = (εrdc- εr∞)(ωτ) /[1+(ωτ)2 ]

  21. C∞ = ε0εr∞ A /d Cs = ε0(εrdc- εr∞)A/d Rs = τ / Cs tanδ = εr “/εr ‘ Figure: Equivalent Circuit

  22. 7.6 Dielectric Strength and Insulation Breakdown • Dielectric materials are widely used as insulating media between conductors at different voltages to prevent the ionization of air & hence currents flashovers between conductors. • If the voltage across a dielectric materials is increased without limit. • A substantial current is flown between the electrodes, which appears as a short between the electrodes and leads to what is called dielectric breakdown.

  23. Dielectric strength : • Dielectric strength is the maximum field that can be • Applied to an insulating medium without causing dielectric breakdown. • Dielectric strength of a solid depends on • The molecular structure. • Micro structural defects • Sample geometry • Nature of the electrodes • Temperature • Ambient condition • Duration and the frequency of the applied field. • Dielectric strength is different under dc and ac onditions.

  24. Dielectric Breakdown: Gases • Dielectric Breakdown: liquids • Dielectric Breakdown: solids • Intrinsic or Electronic Breakdown • Thermal Breakdown • Electromechanical and Electro fracture Breakdown • Internal Discharges • External Discharges

  25. Piezoelectricity: • Certain crystals become polarized when they are mechanically stressed. • Charges appear on the surface of the crystal. • Appearance of surface charges leads to a voltage difference between the two surfaces of the crystal. • The same crystal also exhibit mechanical strain or distortion when they experience an electric field. • Direction of mechanical distortion depends on the direction of the applied field. • The two effects are complementary and define piezoelectricity.

  26. Piezoelectricity:

  27. Piezoelectricity: QUARTZ OSCILLATORS AND FILTERS • One of the most important applications of the piezoelectric quartz crystal in electronics is in the frequency control of oscillators and filters.

  28. Series and parallel resonant frequencies • The mechanical resonant frequency : • The antiresonant frequency : Where, • Quality factor: ƒѕ=1/2π√(LC) ƒa=1/2π√(LC’) 1/C’=1/cO+1/C Q=1/2πƒѕRC

  29. A typical 1Mhz quartz crystal has the following properties:fs =1Mhz fa =1.0025Mhz C0 =5pF R=20ΩWhat are C and L in the equivalent circuit of the crystal? What is the quality factor ? Solution: The expression for fs is fs =1/2π√(LC) From the expression fa we have fa =1/2π√(LC’)=1/2π√(LCC0/(C+C0)) Dividing fa by fs eliminates L, and we get fa/fs =√((C+C0)/C0)

  30. So that C is C= C0 [(fa/fs )^2-1] = 0.025pF Thus, L=1/C(2πfs)2 = 1.01H The quality factor, Q = 1/2πƒsRC = 3.18×10^2

  31. Mathematical Problems 7.2,7.3,7.4,7.8,7.13,7.14,7.15

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