Verlustwinkel

Verlustwinkel is a term used in physics and engineering to describe the phase angle by which a response lags behind a driving force or field in oscillatory systems. It quantifies the amount of energy dissipated as heat or other irreversible processes during cyclic loading or excitation.

In dielectrics, the loss angle arises from the complex permittivity ε* = ε' − iε''. When a dielectric is driven by a sinusoidal electric field, the polarization responds with a phase lag δ. The loss angle is defined as δ = arctan(ε''/ε'), and the loss tangent is tan δ = ε''/ε'. Materials with small δ exhibit low dielectric losses, while larger δ indicates stronger energy dissipation.

In viscoelastic materials, the concept is analogous. Under oscillatory shear, stress σ(t) and strain γ(t) have a phase difference δ, where δ = arctan(G''/G'), with G' the storage modulus and G'' the loss modulus. The loss angle thus reflects damping: a larger δ corresponds to greater energy dissipation per cycle. For small δ, the quality factor Q is approximately Q ≈ 1/tan δ.

Measurement and dependence: The loss angle is frequency- and temperature-dependent and is typically determined from frequency-domain measurements of ε' and ε'' (dielectric spectroscopy) or of G' and G'' (dynamic mechanical analysis).

Applications: It serves as a key material-characterization parameter across electronics, insulation, polymer science, and damping technologies, enabling comparisons of energy dissipation properties under specific conditions.

See also: dielectric loss, complex permittivity, viscoelasticity, damping, quality factor.