Loss factor

Equivalent circuit diagram of a capacitor at a higher frequency (above);
Representation of the loss angle δ and the impedance Z as a vector diagram in the complex plane (bottom)

The loss factor (engl .: dissipation factor , abbreviated DF ) describes in physical vibrations , the ratio of the lossy nature of different real part for the lossless imaginary part of a complex quantity. The loss factor is equal to the tangent of the loss angle between the complex quantity and its imaginary part. It finds practical application in electrical engineering and rheology, among others . ${\displaystyle \delta }$

Applications

Electrical components

The loss factor indicates how large the losses are in electrical components such as chokes and capacitors or when electromagnetic waves propagate in matter (e.g. air ). “Loss” here means the energy that is converted electrically or electromagnetically and, for example, is converted into heat ( dissipation ). The electromagnetic wave is dampened by these losses .

For a more precise representation of the loss factor, a capacitor is considered which is connected to a voltage source with a sinusoidal voltage curve over time. A phase shift between voltage and current occurs at such a capacitor : An ideal capacitor that does not show any losses has a phase shift of ( radians ). In the case of a real capacitor that has losses, the phase shift by the loss angle is smaller than : ${\displaystyle \varphi }$ ${\displaystyle \varphi =90^{\circ }={\tfrac {\pi }{2}}}$ ${\displaystyle \varphi }$ ${\displaystyle \delta }$ ${\displaystyle 90^{\circ }}$

${\displaystyle \varphi =90^{\circ }-\delta \Leftrightarrow \delta =90^{\circ }-\varphi }$

According to the complex alternating current calculation in electrical engineering, the loss factor is defined as the tangent of this loss angle:

${\displaystyle DF=\tan \delta }$

Resonant circuit

The reciprocal value of the quality factor Q for resonant circuits and filters  is also referred to as the loss factor  d (damping; in English, dissipation factor DF) :  

${\displaystyle d={\frac {1}{Q}}}$.

See also coil quality .

Material damping

In the case of internal damping of materials, the loss factor µ describes the ability of the material to dampen vibrations and structure-borne noise. This is relevant, for example, in vehicle and mechanical engineering as well as in building acoustics and dynamics .

Rheology

See also : Complex shear modulus # storage and loss modulus

In rheology , the loss factor describes the relationship between loss modulus (imaginary part) and storage modulus (real part): ${\displaystyle \tan \delta }$ ${\displaystyle G''}$ ${\displaystyle G'}$

${\displaystyle \tan \delta ={\frac {G''}{G'}}}$

• the higher the loss factor, the more the behavior approaches a sample to an ideal- viscous liquid with Newtonian flow behavior of

(Example water: storage module ) ${\displaystyle G'=0\Leftrightarrow \cos \delta =0\Leftrightarrow \delta =90^{\circ }\Rightarrow \tan \delta \to \infty }$

• the lower the loss factor, the more the behavior of a sample corresponds to that of an ideally elastic solid

(Example steel : loss module ). ${\displaystyle G''=0\Leftrightarrow \sin \delta =0\Leftrightarrow \delta =0^{\circ }\Rightarrow \tan \delta =0}$

literature

• Karl Küpfmüller, Wolfgang Mathis, Albrecht Reibiger: Theoretical Electrical Engineering - An Introduction . 18th edition. Springer, 2008, ISBN 978-3-540-78589-7 .