MEASUREMENT OF DIELECTRIC CONSTANT AND LOSS FACTOR

 Insulating substances will have a dielectric constant greater than unity and dielectric

loss when subjected to ac voltages. These two quantities, depend on the magnitude of the

voltage stress and on the frequency of the applied voltage.

The microscopic properties of the dielectric are described by combining the variation

of the two quantities into one ‘complex quantity’ known as ‘complex permittivity’ and can be

determined at various frequencies.

A capacitor connected to a sinusoidal voltage source

v = v0 exp (jωt)

with an angular frequency ω= 2πf stores a charge Q = C0v and draws a charging current

𝐼𝑐 =

𝑑𝑄

𝑑𝑡

= 𝑗𝜔𝐶𝑜𝑣.

When the dielectric is vacuum

➢ C0 is the vacuum capacitance or geometric capacitance of the capacitor, and the current

leads the voltage vc by 90°.

If the capacitor is filled with a dielectric of permittivity ε',

➢ Capacitance is increased to 𝐶 =

𝐶0𝜀/

𝜀0

= 𝐶0𝐾/

where K’ is the relative dielectric constant of the material with respect to vacuum.Under these conditions, if same voltage V is applied, there will be a charging current Ic and loss component of the current, I1 and will be equal to GV

where G is conductance of the dielectric material.

The total current

𝐼= 𝐼𝑐+𝐼𝑙=(𝑗𝜔𝐶+𝐺)𝑉.

Current leads the

 voltage by an angle θ which is less than 90°. The loss angle δ is equal to (90 − θ) °.The frequency response of this circuit which can be expressed as the ratio of the loss current to the charging current, i.e., the loss tangent tan𝛿=𝐷=𝐼𝑙𝐼𝑐=1𝜔𝐶𝑅

Does not agree with the result observed, as the conductance need not be due to the migration of charges or charge carriers but may represent any other energy consuming process.

Hence, the existence of a loss current in addition to the charging current is referred by introducing ‘complex permittivity’

𝑘∗=𝜀/−𝑗𝜀⁄⁄

current I can be written as 𝐼=(𝑗𝜔𝜀/+𝜔𝜀⁄⁄)𝐶𝑜𝜀𝑜𝑣 =𝑗𝜔𝐶𝑜𝐾∗𝑣

𝐾∗=(𝜀⁄−𝑗𝜀⁄⁄)𝜀𝑜=𝐾⁄−𝑗𝐾⁄⁄

Where

K* - complex relative permittivity or complex dielectric constant,

ε' and K' – permittivity, and relative permittivity

ε'' and K'' – the loss factor and relative loss factor

The loss tangent tan𝛿=𝜀⁄⁄𝜀⁄=𝐾⁄⁄𝐾⁄