DIELECTRIC RESPONSE IN TIME VARYING (AC) FIELDS

 In dielectric materials, the polarization P, the electric field E and the flux density D are related by the equation 𝐷=𝜀𝑜𝐸+𝑃=𝜀𝑜[1+𝜒]𝐸⁄

where, χ – dielectric susceptibility of the material with a varying electric fields E(t),

The polarization P induces current in a dielectric due to charge migration whenever an electric field is suddenly applied. With dc, if the material has a conductivity σ, then the current density obtained is σE(t) and the polarization displacement current will be δD(t)/δt.

Hence, the total current density produced is 𝑗(𝑡)=𝜎𝐸(𝑡)+𝛿𝐷(𝑡)𝛿𝑡=𝜎𝐸(𝑡)+𝜀𝑜𝛿𝐸(𝑡)𝛿𝑡+𝛿𝑃(𝑡)𝛿𝑡 = {𝜎+𝜀𝑜(1+𝜒)𝛿(𝑡)+𝑓(𝑡)}𝐸(𝑡)

Where , δ(t) – instantaneous impulse response

f(t) – the further response obtained.

Hence, the polarization current obtained in terms of the geometrical capacitance C0 (without

material) is, 𝑖(𝑡)=𝐶𝑜𝑉[𝜎𝑜𝜀𝑜+(1+𝜒)𝛿(𝑡)+𝑓(𝑡)]

where, V – applied voltage that produces the electric field E(t)

If the equations are transformed into frequency domain (ω) and with the complex frequency

concept, we get 𝑗(𝜔)=𝐸(𝜔)[𝜎𝑜+𝑗𝜔𝜀𝑜(1+𝐹(𝜔))] 𝑋(𝜔)=𝐹(𝜔)=𝜒⁄(𝜔)−𝑗𝜒⁄⁄(𝜔)

where F(ω) – complex susceptibility.

Hence, the complex permittivity ε*(ω) may be written as

𝜀∗(𝜔)=𝜀⁄(𝜔)−𝑗𝜀⁄⁄(𝜔) =[1+𝜒(𝜔)]−𝑗𝜒⁄⁄(𝜔)

From this, the dissipation factor tan δ is obtained as tan𝛿(𝜔)=𝜀⁄⁄(𝜔)+𝜎𝜀𝑜𝜔⁄𝜀𝑟(𝜔)

where εr(ω) – effective dielectric constant ε(ω)/ε0.
The above equations show that the loss factor tan δ is a function of ω and hence is to be determined over a frequency range.