The loss tangent is an important parameter used to describe the energy loss in a dielectric material when it is subjected to an alternating electric field. It indicates how much of the electrical energy is dissipated as heat instead of being stored.
Table of Contents
Definition of Loss Tangent
The loss tangent \( (\tan \delta) \) is defined as the ratio of power lost in the dielectric to the power stored in the electric field. It is also called the dissipation factor.
Mathematical Expression
\[
\tan \delta = \frac{\sigma}{\omega \varepsilon}
\]
- \( \sigma \) = electrical conductivity (S/m)
- \( \omega = 2\pi f \) = angular frequency (rad/s)
- \( \varepsilon \) = permittivity of the material (F/m)
Alternative Form (Using Complex Permittivity)
For a lossy dielectric:
\[
\varepsilon = \varepsilon’ – j\varepsilon”
\]
\[
\tan \delta = \frac{\varepsilon”}{\varepsilon’}
\]
- \( \varepsilon’ \) = real part (energy storage)
- \( \varepsilon” \) = imaginary part (energy loss)
Physical Meaning
- Represents dielectric losses
- Higher \( \tan \delta \) → more energy loss
- Lower \( \tan \delta \) → better insulating material
Loss Angle \( (\delta) \)
- \( \delta \) is the angle between current and ideal capacitive current
\[
\delta = 0 \Rightarrow \tan \delta = 0
\]
Power Loss in Dielectric
\[
P = \omega \varepsilon E^2 \tan \delta
\]
- \( E \) = electric field intensity
Factors Affecting Loss Tangent
Frequency
- As frequency increases, \( \tan \delta \) may change depending on material
Temperature
- Higher temperature → higher losses
Material Properties
- Impurities and moisture increase loss tangent
Classification Based on Loss Tangent
| Material Type | Loss Tangent |
|---|---|
| Good dielectric | \( < 0.01 \) |
| Moderate loss | Medium |
| Lossy dielectric | \( > 0.1 \) |
Applications
- Insulation design
- High-frequency circuits
- Capacitors
- Microwave engineering