Loss angle

The loss angle describes the proportion of the active power of electrically reactive components such as coils or capacitors with sinusoidal voltage and current curves.

In oscillating mechanical examinations, the loss angle occurs as a phase difference between deformation and applied (e.g. shear) stress. Sa complex shear modulus .

description

The loss angle is defined as the arctangent of the ratio of active power to reactive power . A distinction must be made between this and the cosine of the angle of the phase shift φ as the ratio of real power to apparent power .

The smaller the loss angle, the closer the real components come to an ideal behavior. An ideal inductance has a loss angle of 0 °. An ideal capacitor also has a loss angle of 0 °.

In contrast, an ideal electrical resistance has a loss angle of 90 °; it has no capacitive or inductive reactive components.

The loss angle can be calculated using the complex impedance Z or the phase shift between the current and voltage of the component: ${\displaystyle \delta }$ ${\displaystyle \varphi }$

${\displaystyle \delta =\arctan {\frac {\operatorname {Re} {\underline {Z}}}{\operatorname {Im} {\underline {Z}}}}}$

${\displaystyle \delta =90^{\circ }-\left|\varphi \right|}$

Loss factor of a coil:

${\displaystyle \tan \delta ={\frac {R}{\omega L}}}$

Loss factor of a capacitor:

${\displaystyle \tan \delta =R\omega C}$

with R the equivalent series resistance in the equivalent circuit diagram of the component

The equivalent series resistance (short ESR ., From the English Equivalent Series Resistance ) represents the equivalent circuit diagram all losses:

• the ohmic losses in the supply lines and winding wires
• In the case of coils, the eddy current , skin effect , proximity effect and magnetic reversal losses (hysteresis losses)
• for capacitors also the dielectric loss factor and the insulation resistance

Since in real components the real and imaginary parts of the impedance and thus the phase shift change to different degrees with the frequency, the loss angle usually also changes with the frequency; it usually increases with this.

The smaller the equivalent series resistance in the series equivalent circuit of a capacitor, the smaller its loss angle .
Correspondingly, the ESR in the series equivalent circuit is also smaller for a coil with a small loss angle. In addition to the capacitance value, the loss angle is one of its important parameters, especially with capacitors; it is determined at a certain frequency, which depends on the purpose of the capacitor and which is specified in the data sheet.

Note: All of the above statements apply to sinusoidal voltages and currents of the same frequency.

literature

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