Supply

This article explains a notation used in mathematics, physics and electrical engineering for complex quantities; the Thomist of the late Middle Ages is explained under Johannes Versor .

A sinusoidal alternating quantity can advantageously be written in a complex form. As a result, their mathematical treatment considerably simplified, and there is an explanatory view showing a rotating pointer or rotating vector in the complex plane .

Vector diagram of a voltage in the complex plane with the phase angle ${\displaystyle {\underline {u}}}$ ${\displaystyle \varphi =\omega t+\alpha }$

A supply is a rotary pointer in a notation that can be found in the electrotechnical literature in the field of complex alternating current calculations :

The complex number is on this form ${\displaystyle {\underline {c}}=a\cdot \mathrm {e} ^{\mathrm {j} \varphi }}$

• with the angular supply symbol represented by ${\displaystyle {\underline {c}}=a{\big /}\!\!\!{\underline {\;\,\varphi }}}$
• and then read as: is equal to Versor . ${\displaystyle c}$ ${\displaystyle a}$ ${\displaystyle \varphi }$

Here are the amount and the argument of the complex number as well as the imaginary unit . ${\displaystyle a}$ ${\displaystyle \varphi }$ ${\displaystyle {\underline {c}}}$ ${\displaystyle \mathrm {j} }$

This way of writing avoids the exponent and gives the argument the same writing line and the same character size as the amount. The notation can stand for a rotating (time-dependent) pointer and also for a stationary (time-independent) pointer.

A rotation pointer can be represented in the complex plane by a length pointer that rotates around the zero point at the angular velocity . ${\displaystyle {\underline {u}}={\hat {u}}\cdot \mathrm {e} ^{\mathrm {j} (\omega t+\alpha )}={\hat {u}}\,{\big /}\!\!\!{\underline {\,\;\omega t+\alpha _{\,}}}}$ ${\displaystyle {\hat {u}}}$ ${\displaystyle \omega }$

The factor it contains is a pointer at rest, which is also known as a complex amplitude or phasor . ${\displaystyle {\hat {u}}\cdot \mathrm {e} ^{\mathrm {j} \alpha }={\hat {u}}\,{\big /}\!\!\!{\underline {\;\,\alpha _{\,}}}}$

Individual evidence

1. ↑ ^{a b c} DIN 5483-3: 1994-09 Time- dependent quantities - complex representation of sinusoidal time-dependent quantities , No. 2.2
2. ^ Wolfgang Brauch, Hans-Joachim Dreyer, Wolfhart Haacke: Mathematics for engineers . Teubner, 11th edition 2006, page 525
3. ^ Ralf Kories and Heinz Schmidt-Walter: Taschenbuch der Elektrotechnik . 6th edition. Harri Deutsch, 2004, ISBN 3-8171-1734-5 , pp. 110-111 .