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April 1, 2014

Capacitance and Dielectrics

• Capacitance• Capacitance examples• Energy stored in capacitor• Dielectrics• Nat’s research (just fun stuff)

Capacitance• Electric potential always proportional to charge

– Point – Sheet – Wire

• Define capacitance as ratio:

– )

• Measure of geometry’s ability to store charge• Charge create a voltage, but voltage requires charge

Capacitance of Parallel Plate

Constant electric field between two conducting sheets

Potential between sheets

Capacitance across sheets

With Dielectric between

Capacitance

• Typical capacitors

Capacitance examples

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Capacitance examples

Capacitance examples

• Materials can do 2 things:

• Polarize– Initial alignment of charge

with applied voltage– Charge proportional to

voltage– Temporary short-range

alignment

• Conduct– Continuous flow of charge

with applied voltage– Current proportional to

voltage– Continuous long-range

movement

Electrical Properties of Materials

Dielectrics• Polarizable material increases capacitance

• Ability to “cancel” charge on plates draws more charge for given voltage, increases capacitance

• Capacitance becomes

• Actually k isn’t a “constant”. Can vary with frequency, temperature, orientation, etc.

Dielectric constants

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Dielectric Spectroscopy (Nat’s Research)• Most insulators contain polar molecules and free ions

• These can align as a function of frequency (up to a point)• Where they fail to align is called “relaxation frequency”• Characteristic spectrum

2010-12-03

13

TDR Dielectric Spectroscopy

• Sensor admittance from incident and reflected Laplace Transforms.

• Sample complex permittivity from sensor admittance.

• Differential methods

• Bilinear calibration methods.1

• Non-uniform sampling.2

)()(

)()()(

rv

rvGY

oCi

Y

)(

)(

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Dielectric Permittivity in Epoxy Resin 1 MHz -1 GHz

• Aerospace resin Hexcel 8552.

• High frequency range 1 MHz – 1 GHz.

• Temperature constant 125°C, transition decreases with cure.

• TDR measurement method.

www.msi-sensing.com

Permittivity in Epoxy Resin during Complete Cure Cycle

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Application to cement hydration• Cement Conductivity - Variation with Cure

• Imaginary counterpart of real permittivity (’’).

• Multiply by to remove power law (o’’).

• Decrease in ion conductivity, growth of intermediate feature with cure

• Frequency of intermediate feature does not match permittivity

17

Basic signal evolution in cement paste3

• Permittivity (ε’ ) and conductivity (εoωε’’) from 10 kHz to 3 GHz.

• Initial behavior at zero cure time.

• Evolution with cure time.

• Low, medium, and high (free) relaxations.

www.msi-sensing.com

Dielectric modeling in cement paste

• 1 Cole-Davidson, 2 Debye relaxations4-7

2010-12-03

Model evolution with cement cure

• Free-relaxation decreases as water consumed in reaction.

• Bound-water8, grain polarization9 forms with developing microstructure.

• Variations in frequency and distribution factor.

• Conductivity decrease does not match free-water decrease.2010-12-03 www.msi-sensing.com

Energy stored in capacitor• Work to move charge across V

• Define

• Example 17-11

• Energy Density

• Energy Density proportional to field squared!

V

0

+