Dielectric constant

Describes how an electric field affects, and is affected by a dielectric medium.

Determined by the ability of a material to polarize in response to the field.

It is directly related to electric susceptibility as:

Measured in farad per meter (F/m)

Vary with the frequency of the field applied, humidity, temperature etc.

Dielectric spectroscopy

Measures the dielectric properties of a medium as a function of frequency.It is based on the interaction of an external field with the electric dipole moment of the sample.

Polarization mechanisms:1. Electronic polarization.2. Ionic polarization.3. Orientation polarization.4. Space charge polarization

The net polarization of the material is due to the contribution of all four polarization mechanisms.

P = Pe + Pi + Po + Ps

Complex Dielectric Constant

,

A material is called dispersive if its characteristics are frequency dependent.

On taking time dependence of e m field as e jt

× H = j ε* E Where ε* = (ε - j σ/ ) is called complex dielectric constant.

Where tanδ is known as the loss tangent of the dielectric and represents the ratio of power loss in dielectric.

The complex relative permittivity of a material is defined as follows:

Figure: Measured dielectric constant (a) real part, and (b) imaginary part, of 0.5-mm thick Teflon.

(b)(a)

Applications of Dielectric Materials

Plastic and Rubber dielectric are used for the insulations of electrical conductors.

Ceramic beads are used for the prevention of electric short circuiting and also for the purpose of insulation.

Mica and Asbestos insulation is provided in electric Iron in order to prevent the flow of electric current to outer body.

Varnished cotton is used insulators in transformers.

Dielectric materials are used in the energy storage capacitors.

Piezoelectric crystals are used in oscillators and vibrators.

An essential piece of information when designing capacitors, and in other circumstances where a material might be expected to introduce capacitance into a circuit.

The dielectric constant of a solvent is a relative measure of its polarity.

There are several ways in which dielectric measurements may be made at microwave frequencies.

Von-Hipple or shorted waveguide method.

Corfield coaxial line method. The two point method.

Applications of Dielectric Materials

Two point method of measuring dielectric constant:

Fig: Illustration of two point method for measuring dielectric constant

Considering the position of minima in a waveguide with and without a dielectric,

It suggests a method for measuring dielectric constant.

When approximate value of dielectric constant is known, select that value, say βε, and compute dielectric constant from the relation,

If approximate value of the dielectric constant is not known, a second identical experiment is to be performed with the sample of a different length.

The proper solution of the transce-dental Eq. is common to the two sets of solutions and is thus the point of intersection of the two curves drown for each sample between dielectric constant ε and the solutions for βεlε as shown in fig.

Experimental set up

Reflex Klystron,

Klystron Power supply,

Isolator,

Frequency meter,

Variable Attenuator,

Slotted wave guide section, Dielectric sample holder cell,

S.W.R. detector,

V.S.W.R. measurement.

Dielectric constant measurement

Low-loss Solid dielectric:

Figure: Set-up for measuring dielectric constant of a solid using two point method.

Table : Measurement for Solid sample

S. No. Thickness of sample

lε (cm)

Positions of standing wave minima Possible

values of XCalculated values of

εr

Waveguide unloaded

DR (cm)

Waveguide loaded with Dielectric D(cm)

1. 1.5 0.76 1.37 1.48X1

’= 0.15

X1’’= 4.45

X1’’’=8.88

ε1’=0.505

ε1’’=2.66

ε1’’’=9.13

2. 2.0 0.76 0.53 0.0088X2

’= 2.01

X2’’= 4.98

X2’’’= 7.95

ε2’=0.751

ε2’’=2.029

ε2’’’=4.392

3. 2.5 0.76 0.53 0.254X3

’= 1.75

X3’’= 4.9

X3’’’= 8.05

ε3’=0.623

ε3’’=1.448

ε3’’’=3.053

Graph between relative dielectric constant ε and the solutions for ε

Liquids and Solutions

Figure: Set-up for measuring dielectric constant of a liquid using two point method.

Table : Measurement for Liquid sample

S. No. Height of sample

lε (cm)

Positions of standing wave minima Possible

values of XCalculated values of

εr

Waveguide unloaded

DR (cm)

Waveguide loaded with Dielectric D(cm)

1. 1.0 1.2 2.5 -0.317X1

’= 2.4

X1’’= 5.2

X1’’’=8.0

ε1’=1.97

ε1’’=7.35

ε1’’’=16.68

2. 1.5 1.2 2.4 0.211X2

’= 1.8

X2’’= 4.95

X2’’’= 8.1

ε2’=0.88

ε2’’=3.183

ε2’’’=7.88

3. 2.0 1.2 2.43 0.629X3

’= 1.25

X3’’= 4.75

X3’’’= 8.45

ε3’=0.614

ε3’’=1.94

ε3’’’=5.024

Graph between relative dielectric constant ε and the solutions for ε

Result and conclusionFrom the graph,

The correct value of dielectric constant is equal to 0.75 for Teflon and

0.85 for Carbon Tetra Chloride (CCl4).

The dielectric constants measured by two point method are near to absolute values. This method provides a better graphical tool to determine the dielectric constants of liquids and solids.

This method can be applied to loss-less or low loss dielectric materials. It has been observed from the results that the dielectric parameters of the material can be measured with existing waveguide with good accuracy.