Dielectric Loss Tangent
The loss tangent measures how lossy a dielectric is — the ratio of its imaginary to real permittivity. From it you get the dielectric Q, the attenuation a wave suffers travelling through the material, and the wavelength and velocity inside it. Enter the relative permittivity, loss tangent and frequency; add a length to get the total dielectric loss.
Equations & Parameters ▸
\(\varepsilon'' = \varepsilon'\tan\delta,\qquad Q_d = \dfrac{1}{\tan\delta}\)
\(\alpha \approx 27.3\,\dfrac{\sqrt{\varepsilon'}\,\tan\delta}{\lambda_0}\ \text{dB/m},\qquad \lambda = \dfrac{\lambda_0}{\sqrt{\varepsilon'}},\quad v_p = \dfrac{c}{\sqrt{\varepsilon'}}\)
\(\alpha \approx 27.3\,\dfrac{\sqrt{\varepsilon'}\,\tan\delta}{\lambda_0}\ \text{dB/m},\qquad \lambda = \dfrac{\lambda_0}{\sqrt{\varepsilon'}},\quad v_p = \dfrac{c}{\sqrt{\varepsilon'}}\)
| ε′ | Real relative permittivity (dielectric constant). |
| tanδ | Loss tangent = ε″/ε′. FR-4 ≈ 0.02, PTFE ≈ 0.0002, alumina ≈ 0.0001. |
| f | Frequency (GHz). |
| ℓ | Path length in the material (mm), optional — gives the total dielectric loss. |
| α, Qd | Attenuation (low-loss approximation) and dielectric quality factor. |
References: D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, §1.6. · R. E. Collin, Foundations for Microwave Engineering, 2nd ed., Wiley, 2001.
Inputs
Dielectric constant
ε″/ε′
GHz
Operating freqmm
For total lossResults
Material
Imag. permittivity ε″—
Dielectric Q—
Wavelength in material—
Loss
Attenuation—
Loss over ℓ—
Velocity—
Diagram